Causal discovery from observational data, i.e., learning the causal graph from a finite set of samples from the joint distribution of the variables, is often the first step toward the identification and estimation of causal effects, a key requirement in numerous scientific domains. Causal discovery is hampered by two main challenges: limited data results in errors in statistical testing and the computational complexity of the learning task is daunting. This paper builds upon and extends four of our prior publications (Mokhtarian et al., 2021; Akbari et al., 2021; Mokhtarian et al., 2022, 2023a). These works introduced the concept of removable variables, which are the only variables that can be removed recursively for the purpose of causal discovery. Presence and identification of removable variables allow recursive approaches for causal discovery, a promising solution that helps to address the aforementioned challenges by reducing the problem size successively. This reduction not only minimizes conditioning sets in each conditional independence (CI) test, leading to fewer errors but also significantly decreases the number of required CI tests. The worst-case performances of these methods nearly match the lower bound. In this paper, we present a unified framework for the proposed algorithms, refined with additional details and enhancements for a coherent presentation. A comprehensive literature review is also included, comparing the computational complexity of our methods with existing approaches, showcasing their state-of-the-art efficiency. Another contribution of this paper is the release of RCD, a Python package that efficiently implements these algorithms. This package is designed for practitioners and researchers interested in applying these methods in practical scenarios. The package is available at github.com/ban-epfl/rcd, with comprehensive documentation provided at rcdpackage.com.

Hierarchical reinforcement learning (HRL) improves the efficiency of long-horizon reinforcement-learning tasks with sparse rewards by decomposing the task into a hierarchy of subgoals. The main challenge of HRL is efficient discovery of the hierarchical structure among subgoals and utilizing this structure to achieve the final goal. We address this challenge by modeling the subgoal structure as a causal graph and propose a causal discovery algorithm to learn it. Additionally, rather than intervening on the subgoals at random during exploration, we harness the discovered causal model to prioritize subgoal interventions based on their importance in attaining the final goal. These targeted interventions result in a significantly more efficient policy in terms of the training cost. Unlike previous work on causal HRL, which lacked theoretical analysis, we provide a formal analysis of the problem. Specifically, for tree structures and, for a variant of Erdős-Rényi random graphs, our approach results in remarkable improvements. Our experimental results on HRL tasks also illustrate that our proposed framework outperforms existing work in terms of training cost.

This paper investigates causal effect identification in latent variable Linear Non-Gaussian Acyclic Models (lvLiNGAM) using higher-order cumulants, addressing two prominent setups that are challenging in the presence of latent confounding: (1) a single proxy variable that may causally influence the treatment and (2) underspecified instrumental variable cases where fewer instruments exist than treatments. We prove that causal effects are identifiable with a single proxy or instrument and provide corresponding estimation methods. Experimental results demonstrate the accuracy and robustness of our approaches compared to existing methods, advancing the theoretical and practical understanding of causal inference in linear systems with latent confounders.

We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up to a permutation-equivalence class. We obtain a combinatorial characterization of this class by showing that each equivalence class corresponds to a perfect matching in a bipartite graph. This bipartite representation allows us to analyze how interventions modify or constrain the matchings. Specifically, we show that each atomic intervention reveals one edge of the true matching and eliminates all incompatible causal graphs. Consequently, we formalize the optimal experiment design task as an adaptive stochastic optimization problem over the set of equivalence classes with a natural reward function that quantifies how many graphs are eliminated from the equivalence class by an intervention. We show that this reward function is adaptive submodular and provide a greedy policy with a provable near-optimal performance guarantee. A key technical challenge is to efficiently estimate the reward function without having to explicitly enumerate all the graphs in the equivalence class. We propose a sampling-based estimator using random matchings and analyze its bias and concentration behavior. Our simulation results show that performing a small number of interventions guided by our stochastic optimization framework recovers the true underlying causal structure.

Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. In recent years, several variance-reduced PG methods have been proposed with a theoretical guarantee of converging to an approximate first-order stationary point (FOSP) with the sample complexity of $O(\epsilon^{-3})$. However, FOSPs could be bad local optima or saddle points. Moreover, these algorithms often use importance sampling (IS) weights which could impair the statistical effectiveness of variance reduction. In this paper, we propose a variance-reduced second-order method that uses second-order information in the form of Hessian vector products (HVP) and converges to an approximate second-order stationary point (SOSP) with sample complexity of $\tilde{O}(\epsilon^{-3})$. This rate improves the best-known sample complexity for achieving approximate SOSPs by a factor of $O(\epsilon^{-0.5})$. Moreover, the proposed variance reduction technique bypasses IS weights by using HVP terms. Our experimental results show that the proposed algorithm outperforms the state of the art and is more robust to changes in random seeds.

We investigate the estimation of the causal effect of a treatment variable on an outcome in the presence of a latent confounder. We first show that the causal effect is identifiable under certain conditions when data is available from multiple environments, provided that the target causal effect remains invariant across these environments. Secondly, we propose a moment-based algorithm for estimating the causal effect as long as only a single parameter of the data-generating mechanism varies across environments – whether it be the exogenous noise distribution or the causal relationship between two variables. Conversely, we prove that identifiability is lost if both exogenous noise distributions of both the latent and treatment variables vary across environments. Finally, we propose a procedure to identify which parameter of the data-generating mechanism has varied across the environments and evaluate the performance of our proposed methods through experiments on synthetic data.

While significant progress has been made in designing algorithms that minimize regret in online decision-making, real-world scenarios often introduce additional complexities, with missing outcomes perhaps among the most challenging ones. Overlooking this aspect or simply assuming random missingness invariably leads to biased estimates of the rewards and may result in linear regret. Despite the practical relevance of this challenge, no rigorous methodology currently exists for systematically handling missingness, especially when the missingness mechanism is not random. In this paper, we address this gap in the context of multi-armed bandits (MAB) with missing outcomes by analyzing the impact of different missingness mechanisms on achievable regret bounds. We introduce algorithms that account for missingness under both missing at random (MAR) and missing not at random (MNAR) models. Through both analytical and simulation studies, we demonstrate the drastic improvements in decision-making by accounting for missingness in these settings.

Pearl’s do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing a collection of interventions with the minimum cost to identify the desired effect. First, we prove that this problem is NP-complete and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.

Causal discovery from observational data, i.e., learning the causal graph from a finite set of samples from the joint distribution of the variables, is often the first step toward the identification and estimation of causal effects, a key requirement in numerous scientific domains. Causal discovery is hampered by two main challenges: limited data results in errors in statistical testing and the computational complexity of the learning task is daunting. This paper builds upon and extends four of our prior publications (Mokhtarian et al., 2021; Akbari et al., 2021; Mokhtarian et al., 2022, 2023a). These works introduced the concept of removable variables, which are the only variables that can be removed recursively for the purpose of causal discovery. Presence and identification of removable variables allow recursive approaches for causal discovery, a promising solution that helps to address the aforementioned challenges by reducing the problem size successively. This reduction not only minimizes conditioning sets in each conditional independence (CI) test, leading to fewer errors but also significantly decreases the number of required CI tests. The worst-case performances of these methods nearly match the lower bound. In this paper, we present a unified framework for the proposed algorithms, refined with additional details and enhancements for a coherent presentation. A comprehensive literature review is also included, comparing the computational complexity of our methods with existing approaches, showcasing their state-of-the-art efficiency. Another contribution of this paper is the release of RCD, a Python package that efficiently implements these algorithms. This package is designed for practitioners and researchers interested in applying these methods in practical scenarios. The package is available at github.com/ban-epfl/rcd, with comprehensive documentation provided at rcdpackage.com.

Causal inference in a sub-population involves identifying the causal effect of an intervention on a specific subgroup, which is distinguished from the whole population through the influence of systematic biases in the sampling process. However, ignoring the subtleties introduced by sub-populations can either lead to erroneous inference or limit the applicability of existing methods. We introduce and advocate for a causal inference problem in sub-populations (henceforth called s-ID), in which we merely have access to observational data of the targeted sub-population (as opposed to the entire population). Existing inference problems in sub-populations operate on the premise that the given data distributions originate from the entire population, thus, cannot tackle the s-ID problem. To address this gap, we provide necessary and sufficient conditions that must hold in the causal graph for a causal effect in a sub-population to be identifiable from the observational distribution of that sub-population. Given these conditions, we present a sound and complete algorithm for the s-ID problem.

We study the problem of identifying the unknown intervention targets in structural causal models where we have access to heterogeneous data collected from multiple environments. The unknown intervention targets are the set of endogenous variables whose corresponding exogenous noises change across the environments. We propose a two-phase approach which in the first phase recovers the exogenous noises corresponding to unknown intervention targets whose distributions have changed across environments. In the second phase, the recovered noises are matched with the corresponding endogenous variables. For the recovery phase, we provide sufficient conditions for learning these exogenous noises up to some component-wise invertible transformation. For the matching phase, under the causal sufficiency assumption, we show that the proposed method uniquely identifies the intervention targets. In the presence of latent confounders, the intervention targets among the observed variables cannot be determined uniquely. We provide a candidate intervention target set which is a superset of the true intervention targets. Our approach improves upon the state of the art as the returned candidate set is always a subset of the target set returned by previous work. Moreover, we do not require restrictive assumptions such as linearity of the causal model or performing invariance tests to learn whether a distribution is changing across environments which could be highly sample inefficient. Our experimental results show the effectiveness of our proposed algorithm in practice.

The renowned difference-in-differences (DiD) estimator relies on the assumption of 'parallel trends,' which may not hold in many practical applications. To address this issue, economists are increasingly considering the triple difference estimator as a more credible alternative. Both DiD and triple difference are limited to assessing average effects exclusively. An alternative avenue is offered by the changes-in-changes (CiC) estimator, which provides an estimate of the entire counterfactual distribution by relying on assumptions imposed on the distribution of potential outcomes. In this work, we extend the triple difference estimator to accommodate the CiC framework, presenting the `triple changes estimator' and its identification assumptions, thereby expanding the scope of the CiC paradigm. Subsequently, we empirically evaluate the proposed framework and apply it to a study examining the impact of Medicaid expansion on children's preventive care.

Motivated by conditional independence testing, an essential step in constraint-based causal discovery algorithms, we study the nonparametric Von Mises estimator for the entropy of multivariate distributions built on a kernel density estimator. We establish an exponential concentration inequality for this estimator. We design a test for conditional independence (CI) based on our estimator, called VM-CI, which achieves optimal parametric rates under smoothness assumptions. Leveraging the exponential concentration, we prove a tight upper bound for the overall error of VM-CI. This, in turn, allows us to characterize the sample complexity of any constraint-based causal discovery algorithm that uses VM-CI for CI tests. To the best of our knowledge, this is the first sample complexity guarantee for causal discovery for non-linear models and non-Gaussian continuous variables. Furthermore, we empirically show that VM-CI outperforms other popular CI tests in terms of either time, sample complexity, or both. This enhancement significantly improves the performance in structure learning as well.

We study the generic identifiability of causal effects in linear non-Gaussian acyclic models (LiNGAM) with latent variables. We consider the problem in two main settings: When the causal graph is known a priori, and when it is unknown. In both settings, we provide a complete graphical characterization of the identifiable direct or total causal effects among observed variables. Moreover, we propose efficient algorithms to certify the graphical conditions. Finally, we propose an adaptation of the reconstruction independent component analysis (RICA) algorithm that estimates the causal effects from the observational data given the causal graph. Experimental results show the effectiveness of the proposed method in estimating the causal effects.

The s-ID problem seeks to compute a causal effect in a specific sub-population from the observational data pertaining to the same sub population (Abouei et al., 2023). This problem has been addressed when all the variables in the system are observable. In this paper, we consider an extension of the s-ID problem that allows for the presence of latent variables. To tackle the challenges induced by the presence of latent variables in a sub-population, we first extend the classical relevant graphical definitions, such as c-components and Hedges, initially defined for the so-called ID problem (Pearl, 1995; Tian & Pearl, 2002), to their new counterparts. Subsequently, we propose a sound algorithm for the s-ID problem with latent variables.

Identifying causal effects is a key problem of interest across many disciplines. The two long-standing approaches to estimate causal effects are observational and experimental (randomized) studies. Observational studies can suffer from unmeasured confounding, which may render the causal effects unidentifiable. On the other hand, direct experiments on the target variable may be too costly or even infeasible to conduct. A middle ground between these two approaches is to estimate the causal effect of interest through proxy experiments, which are conducted on variables with a lower cost to intervene on compared to the main target. In an earlier work, we studied this setting and demonstrated that the problem of designing the optimal (minimum-cost) experiment for causal effect identification is NP-complete and provided a naive algorithm that may require solving exponentially many NP-hard problems as a sub-routine in the worst case. In this work, we provide a few reformulations of the problem that allow for designing significantly more efficient algorithms to solve it as witnessed by our extensive simulations. Additionally, we study the closely-related problem of designing experiments that enable us to identify a given effect through valid adjustments sets.

Causal discovery is essential for understanding relationships among variables of interest in many scientific domains. In this paper, we focus on permutation-based methods for learning causal graphs in Linear Gaussian Acyclic Models (LiGAMs), where the permutation encodes a causal ordering of the variables. Existing methods in this setting are not scalable due to their high computational complexity. These methods are comprised of two main components: (i) constructing a specific DAG, $\mathcal{G}^\pi$, for a given permutation $\pi$, which represents the best structure that can be learned from the available data while adhering to $\pi$, and (ii) searching over the space of permutations (i.e., causal orders) to minimize the number of edges in $\mathcal{G}^\pi$. We introduce QWO, a novel approach that significantly enhances the efficiency of computing $\mathcal{G}^\pi$ for a given permutation $\pi$. QWO has a speed-up of $O(n^2)$ ($n$ is the number of variables) compared to the state-of-the-art BIC-based method, making it highly scalable. We show that our method is theoretically sound and can be integrated into existing search strategies such as GRASP and hill-climbing-based methods to improve their performance.

We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature recover a graph through learning a causal order (c-order). We advocate for a novel order called removable order (r-order) as they are advantageous over c-orders for structure learning. This is because r-orders are the minimizers of an appropriately defined optimization problem that could be either solved exactly (using a reinforcement learning approach) or approximately (using a hill-climbing search). Moreover, the r-orders (unlike c-orders) are invariant among all the graphs in a MEC and include c-orders as a subset. Given that set of r-orders is often significantly larger than the set of c-orders, it is easier for the optimization problem to find an r-order instead of a c-order. We evaluate the performance and the scalability of our proposed approaches on both real-world and randomly generated networks.

Causal identification is at the core of the causal inference literature, where complete algorithms have been proposed to identify causal queries of interest. The validity of these algorithms hinges on the restrictive assumption of having access to a correctly specified causal structure. In this work, we study the setting where a probabilistic model of the causal structure is available. Specifically, the edges in a causal graph exist with uncertainties which may, for example, represent degree of belief from domain experts. Alternatively, the uncertainty about an edge may reflect the confidence of a particular statistical test. The question that naturally arises in this setting is: Given such a probabilistic graph and a specific causal effect of interest, what is the subgraph which has the highest plausibility and for which the causal effect is identifiable? We show that answering this question reduces to solving an NP-hard combinatorial optimization problem which we call the edge ID problem. We propose efficient algorithms to approximate this problem and evaluate them against both real-world networks and randomly generated graphs.

Drawbacks of ignoring the causal mechanisms when performing imitation learning have recently been acknowledged. Several approaches both to assess the feasibility of imitation and to circumvent causal confounding and causal misspecifications have been proposed in the literature. However, the potential benefits of the incorporation of additional information about the underlying causal structure are left unexplored. An example of such overlooked information is context-specific independence (CSI), i.e., independence that holds only in certain contexts. We consider the problem of causal imitation learning when CSI relations are known. We prove that the decision problem pertaining to the feasibility of imitation in this setting is NP-hard. Further, we provide a necessary graphical criterion for imitation learning under CSI and show that under a structural assumption, this criterion is also sufficient. Finally, we propose a sound algorithmic approach for causal imitation learning which takes both CSI relations and data into account.

We consider the problem of estimating the causal effect of a treatment on an outcome in linear structural causal models (SCM) with latent confounders when we have access to a single proxy variable. Several methods (such as difference-in-difference (DiD) estimator or negative outcome control) have been proposed in this setting in the literature. However, these approaches require either restrictive assumptions on the data generating model or having access to at least two proxy variables. We propose a method to estimate the causal effect using cross moments between the treatment, the outcome, and the proxy variable. In particular, we show that the causal effect can be identified with simple arithmetic operations on the cross moments if the latent confounder in linear SCM is non-Gaussian. In this setting, DiD estimator provides an unbiased estimate only in the special case where the latent confounder has exactly the same direct causal effects on the outcomes in the pre-treatment and post-treatment phases. This translates to the common trend assumption in DiD, which we effectively relax. Additionally, we provide an impossibility result that shows the causal effect cannot be identified if the observational distribution over the treatment, the outcome, and the proxy is jointly Gaussian. Our experiments on both synthetic and real-world datasets showcase the effectiveness of the proposed approach in estimating the causal effect.

We address the problem of identifiability of an arbitrary conditional causal effect given both the causal graph and a set of any observational and/or interventional distributions of the form $Q[S]:=P(S|do(V\setminus S))$, where $V$ denotes the set of all observed variables and $S\subseteq V$. We call this problem conditional generalized identifiability (c-gID in short) and prove the completeness of Pearl’s $do$-calculus for the c-gID problem by providing sound and complete algorithm for the c-gID problem. This work revisited the c-gID problem in Lee et al. [2020], Correa et al. [2021] by adding explicitly the positivity assumption which is crucial for identifiability. It extends the results of [Lee et al., 2019, Kivva et al., 2022] on general identifiability (gID) which studied the problem for unconditional causal effects and Shpitser and Pearl [2006b] on identifiability of conditional causal effects given merely the observational distribution $P(\mathbf{V})$ as our algorithm generalizes the algorithms proposed in [Kivva et al., 2022] and [Shpitser and Pearl, 2006b].

We study experiment design for unique identification of the causal graph of a simple SCM, where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skeleton of causal graphs with cycles may not be possible from merely the observational distribution. Furthermore, intervening on a variable in such graphs does not necessarily lead to orienting all the edges incident to it. In this paper, we propose an experiment design approach that can learn both cyclic and acyclic graphs and hence, unifies the task of experiment design for both types of graphs. We provide a lower bound on the number of experiments required to guarantee the unique identification of the causal graph in the worst case, showing that the proposed approach is order-optimal in terms of the number of experiments up to an additive logarithmic term. Moreover, we extend our result to the setting where the size of each experiment is bounded by a constant. For this case, we show that our approach is optimal in terms of the size of the largest experiment required for uniquely identifying the causal graph in the worst case.

We study the problem of learning a Bayesian network (BN) of a set of variables when structural side information about the system is available. It is well known that learning the structure of a general BN is both computationally and statistically challenging. However, often in many applications, side information about the underlying structure can potentially reduce the learning complexity. In this paper, we develop a recursive constraint-based algorithm that efficiently incorporates such knowledge (i.e., side information) into the learning process. In particular, we study two types of structural side information about the underlying BN: (I) an upper bound on its clique number is known, or (II) it is diamond-free. We provide theoretical guarantees for the learning algorithms, including the worst-case number of tests required in each scenario. As a consequence of our work, we show that bounded treewidth BNs can be learned with polynomial complexity. Furthermore, we evaluate the performance and the scalability of our algorithms in both synthetic and real-world structures and show that they outperform the state-of-the-art structure learning algorithms.

We study the problem of causal effect identification from observational distribution given the causal graph and some context-specific independence (CSI) relations. It was recently shown that this problem is NP-hard, and while a sound algorithm to learn the causal effects is proposed in Tikka et al. (2019), no complete algorithm for the task exists. In this work, we propose a sound and complete algorithm for the setting when the CSI relations are limited to observed nodes with no parents in the causal graph. One limitation of the state of the art in terms of its applicability is that the CSI relations among all variables, even unobserved ones, must be given (as opposed to learned). Instead, We introduce a set of graphical constraints under which the CSI relations can be learned from mere observational distribution. This expands the set of identifiable causal effects beyond the state of the art.

Pearl’s do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this prob-em is NP-complete, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.

We study the complexity of finding the global solution to stochastic nonconvex optimization when the objective function satisfies global Kurdyka-{\L}ojasiewicz (KL) inequality and the queries from stochastic gradient oracles satisfy mild expected smoothness assumption. We first introduce a general framework to analyze Stochastic Gradient Descent (SGD) and its associated nonlinear dynamics under the setting. As a byproduct of our analysis, we obtain a sample complexity of $\mathcal{O}(\epsilon^{-(4-\alpha)/\alpha})$ for SGD when the objective satisfies the so called $\alpha$-P{\L} condition, where $\alpha$ is the degree of gradient domination. Furthermore, we show that a modified SGD with variance reduction and restarting (PAGER) achieves an improved sample complexity of $\mathcal{O}(\epsilon^{-2/\alpha})$ when the objective satisfies the average smoothness assumption. This leads to the first optimal algorithm for the important case of $\alpha=1$ which appears in applications such as policy optimization in reinforcement learning.

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with $1\le\alpha\le2$ which holds in a wide range of applications in machine learning and signal processing. This condition ensures that any first-order stationary point is a global optimum. We prove that the total sample complexity of SCRN in achieving $\epsilon$-global optimum is $\mathcal{O}(\epsilon^{-7/(2\alpha)+1})$ for $1\le\alpha< 3/2$ and $\mathcal{\tilde{O}}(\epsilon^{-2/(\alpha)})$ for $3/2\le\alpha\le 2$. SCRN improves the best-known sample complexity of stochastic gradient descent. Even under a weak version of gradient dominance property, which is applicable to policy-based reinforcement learning (RL), SCRN achieves the same improvement over stochastic policy gradient methods. Additionally, we show that the average sample complexity of SCRN can be reduced to ${\mathcal{O}}(\epsilon^{-2})$ for $\alpha=1$ using a variance reduction method with time-varying batch sizes. Experimental results in various RL settings showcase the remarkable performance of SCRN compared to first-order methods.

We focus on causal discovery in the presence of measurement error in linear systems where the mixing matrix, i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables, is identified up to permutation and scaling of the columns. We demonstrate a somewhat surprising connection between this problem and causal discovery in the presence of unobserved parentless causes, in the sense that there is a mapping, given by the mixing matrix, between the underlying models to be inferred in these problems. Consequently, any identifiability result based on the mixing matrix for one model translates to an identifiability result for the other model. We characterize to what extent the causal models can be identified under a two-part faithfulness assumption. Under only the first part of the assumption (corresponding to the conventional definition of faithfulness), the structure can be learned up to the causal ordering among an ordered grouping of the variables but not all the edges across the groups can be identified. We further show that if both parts of the faithfulness assumption are imposed, the structure can be learned up to a more refined ordered grouping. As a result of this refinement, for the latent variable model with unobserved parentless causes, the structure can be identified. Based on our theoretical results, we propose causal structure learning methods for both models, and evaluate their performance on synthetic data.

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show that without such an assumption the rules of do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are not sound. Moreover, adding the assumption will cause the completeness proof in [Lee et al., 2019] to fail. Under positivity assumption, we present a new algorithm that is provably both sound and complete. A nice property of this new algorithm is that it establishes a connection between general identifiability and classical identifiability by Pearl [1995] through decomposing the general identifiability problem into a series of classical identifiability sub-problems.

Temporal point-processes are often used for mathematical modeling of sequences of discrete events with asynchronous timestamps. We focus on a class of temporal point-process models called multivariate Wold processes (MWP). These processes are well suited to model real-world communication dynamics. Statistical inference on such processes often requires learning their corresponding parameters using a set of observed timestamps. In this work, we relax some of the restrictive modeling assumptions made in the state-of-the-art and introduce a Bayesian approach for inferring the parameters of MWP. We develop a computationally efficient variational inference algorithm that allows scaling up the approach to high-dimensional processes and long sequences of observations. Our experimental results on both synthetic and real-world datasets show that our proposed algorithm outperforms existing methods.

Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts.

We study the impact of pre and postprocessing for reducing discrimination in data-driven decision makers. We first analyze the fundamental trade-off between fairness and accuracy in a preprocessing approach, and propose a design for a preprocessing module based on a convex optimization program, which can be added before the original classifier. This leads to a fundamental lower bound on attainable discrimination, given any acceptable distortion in the outcome. Furthermore, we reformulate an existing postprocessing method in terms of our accuracy and fairness measures, which allows comparing postprocessing and preprocessing approaches. We show that under some mild conditions, preprocessing outperforms postprocessing. Finally, we show that by the appropriate choice of the discrimination measure, the optimization problem for both pre and postprocessing approaches will reduce to a linear program and hence can be solved efficiently.

As a basic and effective tool for explanation, prediction and decision making, causal relationships have been utilized in almost all disciplines. Traditionally, causal relationships are identified by making use of interventions or randomized controlled experiments. However, conducting such experiments is often expensive or even impossible due to cost or ethical concerns. Therefore, there has been an increasing interest in discovering causal relationships based on observational data, and in the past few decades, significant contributions have been made to this field by computer scientists.

We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the existing methods are either computationally impractical when dealing with large graphs or lacking completeness guarantees. We propose a novel computationally efficient recursive constraint-based method that is sound and complete. The key idea of our approach is that at each iteration a specific type of variable is identified and removed. This allows us to learn the structure efficiently and recursively, as this technique reduces both the number of required conditional independence (CI) tests and the size of the conditioning sets. The former substantially reduces the computational complexity, while the latter results in more reliable CI tests. We provide an upper bound on the number of required CI tests in the worst case. To the best of our knowledge, this is the tightest bound in the literature. We further provide a lower bound on the number of CI tests required by any constraint-based method. The upper bound of our proposed approach and the lower bound at most differ by a factor equal to the number of variables in the worst case. We provide experimental results to compare the proposed approach with the state of the art on both synthetic and real-world structures.

This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity bounds for the two settings, respectively. Our result reveals substantial gaps between these limits and best-known upper bounds in the literature. To close these gaps, we introduce a generic acceleration scheme that deploys existing gradient-based methods to solve a sequence of crafted strongly-convex-strongly-concave subproblems. In the general setting, the complexity of our proposed algorithm nearly matches the lower bound; in particular, it removes an additional poly-logarithmic dependence on accuracy present in previous works. In the averaged smooth finite-sum setting, our proposed algorithm improves over previous algorithms by providing a nearly-tight dependence on the condition number.

We consider a learning system based on the conventional multiplicative weight (MW) rule that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the system. The system's loss is naturally defined to be the aggregate absolute difference between the sequence of predicted outcomes and the true outcomes. We consider this problem under both offline and online settings. In the offline setting where the malicious expert must choose its entire sequence of decisions a priori, we show somewhat surprisingly that a simple greedy policy of always reporting false prediction is asymptotically optimal with an approximation ratio of 1+O√(ln N)/N, where N is the total number of prediction stages. In particular, we describe a policy that closely resembles the structure of the optimal offline policy. For the online setting where the malicious expert can adaptively make its decisions, we show that the optimal online policy can be efficiently computed by solving a dynamic program in O(N3). We also discuss a generalization of our model to multi-expert settings. Our results provide a new direction for vulnerability assessment of commonly-used learning algorithms to internal adversarial attacks.

The causal relationships among a set of random variables are commonly represented by a Directed Acyclic Graph (DAG), where there is a directed edge from variable $X$ to variable $Y$ if $X$ is a direct cause of $Y$. From the purely observational data, the true causal graph can be identified up to a Markov Equivalence Class (MEC), which is a set of DAGs with the same conditional independencies between the variables. The size of an MEC is a measure of complexity for recovering the true causal graph by performing interventions. We propose a method for efficient iteration over possible MECs given intervention results. We utilize the proposed method for computing MEC sizes and experiment design in active and passive learning settings. Compared to previous work for computing the size of MEC, our proposed algorithm reduces the time complexity by a factor of $O(n)$ for sparse graphs where $n$ is the number of variables in the system. Additionally, integrating our approach with dynamic programming, we design an optimal algorithm for passive experiment design. Experimental results show that our proposed algorithms for both computing the size of MEC and experiment design outperform the state of the art.

The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence. However, it is known that when cycles are allowed in the causal structure, conditional independence may not be a suitable notion for equivalence of two structures, as it does not reflect all the information in the distribution that is useful for identification of the underlying structure. In this paper, we present a general, unified notion of equivalence for linear Gaussian causal directed graphical models, whether they are cyclic or acyclic. In our proposed definition of equivalence, two structures are equivalent if they can generate the same set of data distributions. We also propose a weaker notion of equivalence called quasi-equivalence, which we show is the extent of identifiability from observational data. We propose analytic as well as graphical methods for characterizing the equivalence of two structures. Additionally, we propose a score-based method for learning the structure from observational data, which successfully deals with both acyclic and cyclic structures.

We study the conditions that allow for the alignment of correlated databases with multivariate Gaussian features. We present some analysis tools that allow us to go beyond the achievability result for exact alignment and derive the condition for nearly-exact alignment. Our main theorem gives an expression for the order of magnitude of the error in alignment as a function of mutual information between features.

Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice for solving these nonconvex games and receive lots of empirical success. Yet, it is known that these vanilla GDA algorithms with constant stepsize can potentially diverge even in the convex setting. In this work, we show that for a subclass of nonconvex-nonconcave objectives satisfying a so-called two-sided Polyak-{\L}ojasiewicz inequality, the alternating gradient descent ascent (AGDA) algorithm converges globally at a linear rate and the stochastic AGDA achieves a sublinear rate. We further develop a variance reduced algorithm that attains a provably faster rate than AGDA when the problem has the finite-sum structure.

Macroscopic data aggregated from microscopic events are pervasive in machine learning, such as country-level COVID-19 infection statistics based on city-level data. Yet, many existing approaches for predicting macroscopic behavior only use aggregated data, leaving a large amount of fine-grained microscopic information unused. In this paper, we propose a principled optimization framework for macroscopic prediction by fitting microscopic models based on conditional stochastic optimization. The framework leverages both macroscopic and microscopic information, and adapts to individual microscopic models involved in the aggregation. In addition, we propose efficient learning algorithms with convergence guarantees. In our experiments, we show that the proposed learning framework clearly outperforms other plug-in supervised learning approaches in real-world applications, including the prediction of daily infections of COVID-19 and medicare claims.

We introduce a generic \emph{two-loop} scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated \emph{dual problem} and takes full advantage of existing gradient-based algorithms to solve a sequence of well-balanced strongly-convex-strongly-concave minimax problems. Despite its simplicity, this leads to a family of near-optimal algorithms with improved complexity over all existing methods designed for strongly-convex-concave minimax problems. Additionally, we obtain the first variance-reduced algorithms for this class of minimax problems with finite-sum structure and establish even faster convergence rate. Furthermore, when extended to the nonconvex-concave minimax optimization, our algorithm again achieves the state-of-the-art complexity for finding a stationary point. We carry out several numerical experiments showcasing the superiority of the Catalyst framework in practice.

Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the curse of dimensionality or computational complexity. We propose a novel two-step approach which facilitates Markov blanket feature selection in high dimensions. First, neural networks are used to map features to low-dimensional representations. In the second step, CI testing is performed by applying the $k$-NN conditional mutual information estimator to the learned feature maps. The mappings are designed to ensure that mapped samples both preserve information and share similar information about the target variable if and only if they are close in Euclidean distance. We show that these properties boost the performance of the $k$-NN estimator in the second step. The performance of the proposed method is evaluated on both synthetic and real data.

We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, the inferred causal relationships among the observed variables are often wrong. Under faithfulness assumption, we propose a method to check whether there exists a causal path between any two observed variables. From this information, we can obtain the causal order among the observed variables. The next question is whether the causal effects can be uniquely identified as well. We show that causal effects among observed variables cannot be identified uniquely under mere assumptions of faithfulness and non-Gaussianity of exogenous noises. However, we are able to propose an efficient method that identifies the set of all possible causal effects that are compatible with the observational data. We present additional structural conditions on the causal graph under which causal effects among observed variables can be determined uniquely. Furthermore, we provide necessary and sufficient graphical conditions for unique identification of the number of variables in the system. Experiments on synthetic data and real-world data show the effectiveness of our proposed algorithm for learning causal models.

A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equivalence, based on conditional independence relations among the variables. Therefore, the number of DAGs equivalent to the ground truth DAG is an indicator of the causal complexity of the underlying structure–roughly speaking, it shows how many interventions or how much additional information is further needed to recover the underlying DAG. In this paper, we propose a new technique for counting the number of DAGs in a Markov equivalence class. Our approach is based on the clique tree representation of chordal graphs. We show that in the case of bounded degree graphs, the proposed algorithm is polynomial time. We further demonstrate that this technique can be utilized for uniform sampling from a Markov equivalence class, which provides a stochastic way to enumerate DAGs in the equivalence class and may be needed for finding the best DAG or for causal inference given the equivalence class as input. We also extend our counting and sampling method to the case where prior knowledge about the underlying DAG is available, and present applications of this extension in causal experiment design and estimating the causal effect of joint interventions.

We consider the problem of aligning a pair of databases with jointly Gaussian features. We consider two algorithms, complete database alignment via MAP estimation among all possible database alignments, and partial alignment via a thresholding approach of log likelihood ratios. We derive conditions on mutual information between feature pairs, identifying the regimes where the algorithms are guaranteed to perform reliably and those where they cannot be expected to succeed.

Multivariate Hawkes processes (MHP) are widely used in a variety of fields to model the occurrence of discrete events. Prior work on learning MHPs has only focused on inference in the presence of perfect traces without noise. We address the problem of learning the causal structure of MHPs when observations are subject to an unknown delay. In particular, we introduce the so-called synchronization noise, where the stream of events generated by each dimension is subject to a random and unknown time shift. We characterize the robustness of the classic maximum likelihood estimator to synchronization noise, and we introduce a new approach for learning the causal structure in the presence of noise. Our experimental results show that our approach accurately recovers the causal structure of MHPs for a wide range of noise levels, and significantly outperforms classic estimation methods.

The nonparametric learning of positive-valued functions appears widely in machine learning, especially in the context of estimating intensity functions of point processes. Yet, existing approaches either require computing expensive projections or semidefinite relaxations, or lack convexity and theoretical guarantees after introducing nonlinear link functions. In this paper, we propose a novel algorithm, pseudo mirror descent, that performs efficient estimation of positive functions within a Hilbert space without expensive projections. The algorithm guarantees positivity by performing mirror descent with an appropriately selected Bregman divergence, and a pseudo-gradient is adopted to speed up the gradient evaluation procedure in practice. We analyze both asymptotic and nonasymptotic convergence of the algorithm. Through simulations, we show that pseudo mirror descent outperforms the state-of-the-art benchmarks for learning intensities of Poisson and multivariate Hawkes processes, in terms of both computational efficiency and accuracy.

We demonstrate the presence of a novel scheduler side-channel in preemptive, fixed-priority real-time systems (RTS); examples of such systems can be found in automotive systems, avionic systems, power plants and industrial control systems among others. This side-channel can leak important timing information such as the future arrival times of real-time tasks. This information can then be used to launch devastating attacks, two of which are demonstrated here (on real hardware platforms). Note that it is not easy to capture this timing information due to runtime variations in the schedules, the presence of multiple other tasks in the system and the typical constraints (e.g., deadlines) in the design of RTS. Our ScheduLeak algorithms demonstrate how to effectively exploit this side-channel. A complete implementation is presented on real operating systems (in Real-time Linux and FreeRTOS). Timing information leaked by ScheduLeak can significantly aid other, more advanced, attacks in better accomplishing their goals.

We study the problem of causal structure learning when the experimenter is limited to perform at most $k$ non-adaptive experiments of size $1$. We formulate the problem of finding the best intervention target set as an optimization problem, which aims to maximize the average number of edges whose directions are resolved. We prove that the corresponding objective function is submodular and a greedy algorithm suffices to achieve $(1-\frac{1}{e})$-approximation of the optimal value. We further present an accelerated variant of the greedy algorithm, which can lead to orders of magnitude performance speedup. We validate our proposed approach on synthetic and real graphs. The results show that compared to the purely observational setting, our algorithm orients the majority of the edges through a considerably small number of interventions.

We consider the problem of aligning a pair of databases with correlated entries. We introduce a new measure of correlation in a joint distribution that we call cycle mutual information. This measure has operational significance: it determines whether exact recovery of the correspondence between database entries is possible for any algorithm. Additionally, there is an efficient algorithm for database alignment that achieves this information theoretic threshold.

Automated decision making systems are increasingly being used in real-world applications. In these systems for the most part, the decision rules are derived by minimizing the training error on the available historical data. Therefore, if there is a bias related to a sensitive attribute such as gender, race, religion, etc. in the data, say, due to cultural/historical discriminatory practices against a certain demographic, the system could continue discrimination in decisions by including the said bias in its decision rule. We present an information theoretic framework for designing fair predictors from data, which aim to prevent discrimination against a specified sensitive attribute in a supervised learning setting. We use equalized odds as the criterion for discrimination, which demands that the prediction should be independent of the protected attribute conditioned on the actual label. To ensure fairness and generalization simultaneously, we compress the data to an auxiliary variable, which is used for the prediction task. This auxiliary variable is chosen such that it is decontaminated from the discriminatory attribute in the sense of equalized odds. The final predictor is obtained by applying a Bayesian decision rule to the auxiliary variable.

We study the problem of causal structure learning in linear systems from observational data given in multiple domains, across which the causal coefficients and/or the distribution of the exogenous noises may vary. The main tool used in our approach is the principle that in a causally sufficient system, the causal modules, as well as their included parameters, change independently across domains. We first introduce our approach for finding causal direction in a system comprising two variables and propose efficient methods for identifying causal direction. Then we generalize our methods to causal structure learning in networks of variables. Most of previous work in structure learning from multi-domain data assume that certain types of invariance are held in causal modules across domains. Our approach unifies the idea in those works and generalizes to the case that there is no such invariance across the domains. Our proposed methods are generally capable of identifying causal direction from fewer than ten domains. When the invariance property holds, two domains are generally sufficient.

Approximate Bayesian computation (ABC) is an important methodology for Bayesian inference when the likelihood function is intractable. Sampling-based ABC algorithms such as rejection- and K2-ABC are inefficient when the parameters have high dimensions, while the regression-based algorithms such as K- and DR-ABC are hard to scale. In this paper, we introduce an optimization-based ABC framework that addresses these deficiencies. Leveraging a generative model for posterior and joint distribution matching, we show that ABC can be framed as saddle point problems, whose objectives can be accessed directly with samples. We present the predictive ABC algorithm (P-ABC), and provide a probabilistically approximately correct (PAC) bound that guarantees its learning consistency. Numerical experiment shows that P-ABC outperforms both K2- and DR-ABC significantly.

We study covert queueing channels (CQCs), which are a kind of covert timing channel that may be exploited in shared queues across supposedly isolated users. In our system model, a user sends messages to another user via his pattern of access to the shared resource, which serves the users according to a first come first served (FCFS) policy. One example of such a channel is the cross-virtual network covert channel in data center networks, resulting from the queueing effects of the shared resource. First, we study a system comprising a transmitter and a receiver that share a deterministic and work-conserving FCFS scheduler, and we compute the capacity of this channel. We also consider the effect of the presence of other users on the information transmission rate of this channel. The achievable information transmission rates obtained in this paper demonstrate the possibility of significant information leakage and great privacy threats brought by CQCs in FCFS schedulers.

Motivated by many real-world examples, such as recommendation systems or sensor fusion, and aiming to capture the influence of malicious experts who intentionally degrade the performance of learning systems, we analyze optimal adversarial strategies against the weighted average prediction algorithm in the learning with expert advice framework. All but one expert is honest and the malicious expert's goal is to sabotage the performance of the algorithm by strategically providing dishonest recommendations. We formulate the problem as a Markov decision process and analyze it under various settings. For the logarithmic loss, somewhat surprisingly, we prove that the optimal strategy for the adversary is the greedy policy, i.e., lying at every step. For the absolute loss, in the 2-experts, discounted cost setting, we prove that the optimal strategy is a threshold policy, where the malicious expert tells the truth until he earns enough weight and then lies afterwards. We extend the results to the infinite horizon problem and find the exact thresholds for the stationary optimal policy. Finally, we use a mean field approach in the N-experts setting to find the optimal strategy when the predictions of the honest experts are independent and identically distributed. We justify our results using simulations throughout this paper.

We consider a generalized model of learning from expert advice in which experts could abstain from participating at some rounds. Our proposed online algorithm falls into the class of weighted average predictors and uses a time-varying multiplicative weight update rule. This update rule changes the weight of an expert based on his or her relative performance compared to the average performance of available experts at the current round. This makes the algorithm suitable for recommendation systems in the presence of an adversary with many potential applications in the new emerging area of the Internet of Things. We prove the convergence of our algorithm to the best expert, defined in terms of both availability and accuracy, in the stochastic setting. In particular, we show the applicability of our definition of best expert through convergence analysis of another well-known algorithm in this setting. Finally, through simulation results on synthetic and real datasets, we justify the out-performance of our proposed algorithms compared to the existing ones in the literature.

Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount of information shared among a set of variables, beyond the information shared in any proper subset of those variables. Unlike (conditional) mutual information, which is always non-negative, interaction information can be negative. We utilize this property to find the direction of causal influences among variables in a triangle topology under some mild assumptions.

We propose an approach for learning the causal structure in stochastic dynamical systems with a 1-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations.

We study causal discovery in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We introduce the idea of using the invariance of the functional relations of the variables to their causes across a set of environments for structure learning. We define a notion of completeness for a causal inference algorithm in this setting and prove the existence of such algorithm by proposing the baseline algorithm. Additionally, we present an alternate algorithm that has significantly improved computational and sample complexity compared to the baseline algorithm. Experiment results show that the proposed algorithm outperforms the other existing algorithms.

We develop a nonparametric and online learning algorithm that estimates the triggering functions of a multivariate Hawkes process (MHP). The approach we take approximates the triggering function $f_{i,j}(t)$ by functions in a reproducing kernel Hilbert space (RKHS), and maximizes a time-discretized version of the log-likelihood, with Tikhonov regularization. Theoretically, our algorithm achieves an $\calO(\log T)$ regret bound. Numerical results show that our algorithm offers a competing performance to that of the nonparametric batch learning algorithm, with a run time comparable to the parametric online learning algorithm.

Abstract The majority of people across the globe rely on telephony networks as their primary means of communication. As such, many of the most sensitive personal, corporate and government related communications pass through these systems every day. Unsurprisingly, such connections are subject to a wide range of attacks. Of increasing concern is the use of metadata contained in Call Detail Records (CDRs), which contain source, destination, start time and duration of a call. This information is potentially dangerous as the very act of two parties communicating can reveal significant details about their relationship and put them in the focus of targeted observation or surveillance, which is highly critical especially for journalists and activists. To address this problem, we develop the Phonion architecture to frustrate such attacks by separating call setup functions from call delivery. Specifically, Phonion allows users to preemptively establish call circuits across multiple providers and technologies before dialing into the circuit and does not require constant Internet connectivity. Since no single carrier can determine the ultimate destination of the call, it provides unlinkability for its users and helps them to avoid passive surveillance. We define and discuss a range of adversary classes and analyze why current obfuscation technologies fail to protect users against such metadata attacks. In our extensive evaluation we further analyze advanced anonymity technologies (e.g., VoIP over Tor), which do not preserve our functional requirements for high voice quality in the absence of constant broadband Internet connectivity and compatibility with landline and feature phones. Phonion is the first practical system to provide guarantees of unlinkable communication against a range of practical adversaries in telephony systems.

With the advent of big data, modern businesses face an increasing need to store and process large volumes of sensitive customer information on the cloud. In these environments, resources are shared across a multitude of mutually untrusting tenants increasing propensity for data leakage. This problem stands to grow further in severity with increasing use of clouds in all aspects of our daily lives and the recent spate of high-profile data exfiltration attacks are evidence. To highlight this serious issue, we present a novel and highspeed network-based covert channel that is robust and circumvents a broad set of security mechanisms currently deployed by cloud vendors. We successfully test our channel on numerous network environments, including commercial clouds such as EC2 and Azure. Using an information theoretic model of the channel, we derive an upper bound on the maximum information rate and propose an optimal coding scheme. Our adaptive decoding algorithm caters to the cross traffic in the channel and maintains high bit rates and extremely low error rates. Finally, we discuss several effective avenues for mitigation of the aforementioned channel and provide insights into how data exfiltration can be prevented in such shared environments.

In this paper, we introduce a new type of graphical model, interventional dependency graphs, to encode interactions among processes. These type of graphical models are defined using a measure that captures the influence relationships based on the principle of intervention. Principle of intervention discovers an influence relationship by making assignment to certain variables while fixing other variables to see how these changes influence statistics of variables of interest. Furthermore, we derive some properties of the dynamics that can be inferred from these graphs and establish the relationship between this new graphical model and the directed information graphs used for causal inference.

In a symmetric-key cryptography system, it is often required to transmit a nonuniform message from a very large set. In this case, a computationally unbounded adversary can take advantage of the non-uniformity of the posterior to recover the message. Recently an encryption scheme called Honey Encryption has been proposed to increase the information-theoretic security of the system, i.e., guaranteed level of security regardless of the computational power of the adversary. In this paper, we present a technique called message partitioning which can be used to accomplish the same goal. We analyze the overall security of the combination of this technique with Honey Encryption, which uses a Distribution Transforming Encoder (DTE) block. We propose a new DTE which has an acceptable performance under limited amount of available auxiliary randomness. Achievable bounds are presented for both cases, which under certain conditions, are close to the lower bounds on the level of the success of the adversary.

We consider the problem of perfectly recovering the vertex correspondence between two correlated Erdos-Renyi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. In some cases, the structural information in the graphs allow this correspondence to be recovered. We investigate the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources. Pedarsani and Grossglauser provided an achievability result of this type. Their result establishes the scaling dependence of the threshold on the number of vertices. We improve on their achievability bound. We also provide a converse bound, establishing conditions under which exact recovery is impossible. Together, these establish the scaling dependence of the threshold on the level of correlation between the two graphs. The converse and achievability bounds differ by a factor of two for sparse, significantly correlated graphs.

We propose an approach for learning latent directed polytrees as long as there exists an appropriately defined discrepancy measure between the observed nodes. Specifically, we use our approach for learning directed information polytrees where samples are available from only a subset of processes. Directed information trees are a new type of probabilistic graphical models that represent the causal dynamics among a set of random processes in a stochastic system. We prove that the approach is consistent for learning minimal latent directed trees. We analyze the sample complexity of the learning task when the empirical estimator of mutual information is used as the discrepancy measure.

Many of the classic problems of the coding theory are highly symmetric, which makes it easy to derive the sphere-packing upper bounds on the size of codes. We discuss the generalizations of the sphere-packing bounds to the arbitrary error models. These generalizations become especially important when the sizes of the error spheres are nonuniform. The best possible sphere-packing bounds are the solutions to the linear programs. We derive a series of bounds from the approximations to the packing and covering problems and study the relationships and the trade-offs between them. We show the method to obtain the upper bounds by optimizing across a family of channels that admit the same codes. We present a generalization of the local degree bound of Kulkarni and Kiyavash, and use it to improve the best-known upper bounds on the sizes of the single deletion correcting codes and the single grain error correcting codes.

We investigate deletion correcting codes and restricted composition codes in particular. Restricted composition codes generalize codes on permutations and multipermutations. We use graph theoretic methods to characterize codes, establish bounds on code size, and describe constructions. The substring partial order has a well-known property. For any string, the number of superstrings of a particular length depends only on the length of the original string. We generalize this property to take compositions into account. For any string, the number of superstrings of a particular composition depends only on the composition of the original string. We present a bijective proof of this fact. We apply this result to obtain a lower bound on the size of restricted composition codes. We obtain an upper bound by analyzing deletion errors when the composition of deleted symbols is restricted to a particular worst case composition. We construct binary restricted composition single-deletion correcting codes and show that they are asymptotically optimal and form an optimal coloring. There is a natural distance on compositions that provides a lower bound on deletion distance. Unrestricted deletion correcting codes can be constructed from the union of restricted composition codes as long as the set of compositions used themselves form a code. The nonbinary single-deletion correcting codes constructed by Tenengolts are a special case of our method.

When multiple job processes are served by a single scheduler, the queueing delays of one process are often affected by the others, resulting in a timing side channel that leaks the arrival pattern of one process to the others. In this work, we study such a timing side channel between a regular user and a malicious attacker. Utilizing Shannon’s mutual information as a measure of information leakage between the user and attacker, we analyze privacy-preserving behaviors of common work-conserving schedulers. We find that the attacker can always learn perfectly the user’s arrival process in a longest-queue-first (LQF) scheduler. When the user’s job arrival rate is very low (near zero), first-come–first-serve (FCFS) and round-robin schedulers both completely reveal the user’s arrival pattern. The near-complete information leakage in the low-rate traffic region is proven to be reduced by half in a work-conserving version of TDMA (WC-TDMA) scheduler, which turns out to be privacy-optimal in the class of deterministic working-conserving (det-WC) schedulers, according to a universal lower bound on information leakage we derive for all det-WC schedulers.

In this work, we study information leakage in timing side channels that arise in the context of shared event schedulers. Consider two processes, one of them an innocuous process (referred to as Alice) and the other a malicious one (referred to as Bob), using a common scheduler to process their jobs. There are other innocuous users in addition to Alice and Bob using the scheduler to process their jobs. Based on when his jobs get processed, Bob wishes to learn about the pattern (size and timing) of Alice's jobs. Depending on the context, knowledge of this pattern could have serious implications on Alice's privacy and security. For instance, shared routers can reveal traffic patterns, shared memory access can reveal cloud usage patterns, and suchlike. We present a formal framework to study the information leakage in shared resource schedulers using the pattern estimation error as a performance metric. The first-come-first-serve (FCFS) scheduling policy and time-division-multiple-access (TDMA) are identified as two extreme policies on the privacy metric, FCFS has the least, and TDMA has the highest. However, on performance-based metrics, such as throughput and delay, it is well known that FCFS significantly outperforms TDMA. We then derive two parameterized policies, accumulate and serve, and proportional TDMA, which take two different approaches to offer a tunable trade-off between privacy and performance.

The capacity of a queueing timing channel in which a user modulates messages to another user via his pattern of access to a shared resource scheduled in an FCFS manner is calculated. One example of such a channel is the cross-Virtual Network (VN) covert channel in data center networks. In data center networks, software-defined-networks generate logically isolated virtual networks, across which direct data exchange is impossible. However, since packet flows belonging to different VNs inevitably share underlying network infrastructure, it is possible to transfer data across VNs through timing channels resulting from the queueing effects of the shared resource.

A combinatorial channel specifies a set of possible channel outputs for each channel input. A ranked partially ordered set, or ranked poset, gives us a notion of up errors and down errors. This allows us to define a variety of combinatorial channels. There is a family of channels that have the rank-n elements of the poset as the input, and introduce s total errors, each performing a different mixture of up errors and down errors. If a ranked poset has the “parallelogram property,” the family of channels all have the same confusion graph and thus the same codes. Furthermore, there is a natural metric on each rank of the poset. In the common confusion graph of the channel, vertices are adjacent if and only if their distance in this metric is at most 2s. Although all of the channels in the family have the same set of codes, each channel corresponds to a different integer linear program that characterizes the set of codes. Because each integer linear program has a different fractional relaxation, each leads to a different sphere-packing upper bound for the codes. We take advantage of this phenomenon by optimizing across the family of channels to obtain the best bound. This formulation includes many of classical error models, including erasures and substitutions in q-ary vectors, Hamming errors in constant weight binary codes, insertions and deletions in q-ary strings, the error model of subspace codes, the natural error model for compositions, and various errors models for permutations.

Traditionally, scheduling policies have been optimized to perform well on metrics, such as throughput, delay, and fairness. In the context of shared event schedulers, where a common processor is shared among multiple users, one also has to consider the privacy offered by the scheduling policy. The privacy offered by a scheduling policy measures how much information about the usage pattern of one user of the system can be learned by another as a consequence of sharing the scheduler. We introduced an estimation error-based metric to quantify this privacy. We showed that the most commonly deployed scheduling policy, the first-come-first-served offers very little privacy to its users. We also proposed a parametric nonwork conserving policy, which traded off delay for improved privacy. In this paper, we ask the question, is a tradeoff between delay and privacy fundamental to the design to scheduling policies? In particular, is there a work conserving, possibly randomized, and scheduling policy that scores high on the privacy metric? Answering the first question, we show that there does exist a fundamental limit on the privacy performance of a work-conserving scheduling policy. We quantify this limit. Furthermore, answering the second question, we demonstrate that the round-robin scheduling policy (deterministic policy) is privacy optimal within the class of work-conserving policies.

We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper bounds are not valid, the resulting graph is nonetheless an optimal approximation in terms of Kullback-Leibler (KL) divergence. Another algorithm uses near-minimal dimension statistics when no bounds are known, but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Last, we demonstrate the effectiveness of the proposed algorithms through the analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times.

A code for a combinatorial channel is a feasible point in an integer linear program derived from that channel. Sphere-packing upper bounds are closely related to the fractional relaxation of this program. When bounding highly symmetric channels, this formulation can often be avoided, but it is essential in less symmetric cases. We present a few low-complexity upper bounds on the value of the relaxed linear program. We also discuss a more general bound derived from the codeword constraint graph for the channel. This bound is not necessarily computationally tractable. When there is a family of channels with the same constraint graph, tractable bounds can be applied to each channel and the best bound will apply to the whole family.

To be considered for an IEEE Jack Keil Wolf ISIT Student Paper Award. This paper proposes a novel, non-linear collusion attack on digital fingerprints from a finite alphabet. We analyze the error probability of this attack for some classes of proposed random and deterministic schemes. We then obtain a threshold on the number of colluders necessary to correctly estimate the host signal. Our simulation results show that our attack is more powerful in practice than predicted by the theoretical threshold.

Modern neuroscientific recording technologies are increasingly generating rich, multimodal data that provide unique opportunities to investigate the intricacies of brain function. However, our ability to exploit the dynamic, interactive interplay among neural processes is limited by the lack of appropriate analysis methods. In this paper, some challenging issues in neuroscience data analysis are described, and some general-purpose approaches to address such challenges are proposed. Specifically, we discuss statistical methodologies with a theme of loss functions, and hierarchical Bayesian inference methodologies from the perspective of constructing optimal mappings. These approaches are demonstrated on both simulated and experimentally acquired neural data sets to assess causal influences and track time-varying interactions among neural processes on a fine time scale.

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code size, we apply a packing argument to channels that perform different mixtures of insertions and deletions. Even though the set of codes is identical for all of these channels, the bounds that we obtain vary. Prior to this paper, only the bounds corresponding to the all-insertion case and the all-deletion case were known. We recover these as special cases. The bound from the all-deletion case, due to Levenshtein, has been the best known for more than 45 years. Our generalized bound is better than Levenshtein's bound whenever the number of deletions to be corrected is larger than the alphabet size.

Linking network flows is an important problem in intrusion detection as well as anonymity. Passive traffic analysis can link flows, but requires long periods of observation to reduce errors. Active traffic analysis, also known as flow watermarking, allows for better precision and is more scalable. Previous flow watermarks introduce significant delays to the traffic flow as a side effect of using a blind detection scheme; this enables attacks that detect and remove the watermark, while at the same time slowing down legitimate traffic. We propose the first non-blind approach for flow watermarking, called RAINBOW, that improves watermark invisibility by inserting delays hundreds of times smaller than previous blind watermarks, hence reduces the watermark interference on network flows. We derive and analyze the optimum detectors for RAINBOW as well as the passive traffic analysis under different traffic models by using hypothesis testing. Comparing the detection performance of RAINBOW and the passive approach, we observe that both RAINBOW and passive traffic analysis perform similarly good in the case of uncorrelated traffic, however the RAINBOW detector drastically outperforms the optimum passive detector in the case of correlated network flows. This justifies the use of non-blind watermarks over passive traffic analysis even though both approaches have similar scalability constraints. We confirm our analysis by simulating the detectors and testing them against large traces of real network flows.

Traffic analysis often requires direct observations of network connections at local vantage points. In this work, we show that traffic analysis can be performed remotely by taking advantage of a timing side channel. The timing side channel results from a shared resource, namely, the scheduler between two users. Utilizing Shannon equivocation as a privacy metric, we prove that one user can learn the complete traffic pattern of the other user if the scheduler employs a first come first serve (FCFS) policy. Moreover, we show the feasibility of a real system attack exploiting the timing side channel inside a home digital subscriber line (DSL) router. This demonstrates the magnitude of the threat timing side channels pose for traffic analysis.

Traditionally, scheduling policies have been optimized to perform well on metrics such as throughput, delay and fairness. In the context of shared event schedulers, where a common processor is shared among multiple users, one also has to consider the privacy offered by the scheduling policy. The privacy offered by a scheduling policy measures how much information about the usage pattern of one user of the system can be learnt by another as a consequence of sharing the scheduler. In [1], we introduced an estimation error based metric to quantify this privacy. We showed that the most commonly deployed scheduling policy, the first-come-first-served (FCFS) offers very little privacy to its users. We also proposed a parametric non-work-conserving policy which traded off delay for improved privacy. In this work, we ask the question, is a trade-off between delay and privacy fundamental to the design to scheduling policies? In particular, is there a work-conserving, possibly randomized, scheduling policy that scores high on the privacy metric? Answering the first question, we show that there does exist a fundamental limit on the privacy performance of a work-conserving scheduling policy. We quantify this limit. Furthermore, answering the second question, we demonstrate that the round-robin scheduling policy (a deterministic policy) is privacy optimal within the class of work-conserving policies.

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code size, we apply a packing argument to channels that perform different mixtures of insertions and deletions. Even though the set of codes is identical for all of these channels, the bounds that we obtain vary. Prior to this work, only the bounds corresponding to the all insertion case and the all deletion case were known. We recover these as special cases. The bound from the all deletion case, due to Levenshtein, has been the best known for more than forty five years. Our generalized bound is better than Levenshtein's bound whenever the number of deletions to be corrected is larger than the alphabet size.

We develop low-complexity algorithms to robustly identify the best directed tree approximation for a network of stochastic processes in the finite-sample regime. Directed information is used to quantify influence between stochastic processes and identify the best directed tree approximation in terms of Kullback-Leibler (KL) divergence. We provide finite-sample complexity bounds for confidence intervals of directed information estimates. We use these confidence intervals to develop a minimax framework to identify the best directed tree that is robust to point estimation errors. We provide algorithms for this minimax calculation and describe the relationships between exactness and complexity.

We propose two algorithms to identify approximations for joint distributions of networks of stochastic processes. The approximations correspond to low-complexity network structures - connected, directed graphs with bounded indegree. The first algorithm identifies an optimal approximation in terms of KL divergence. The second efficiently finds a near-optimal approximation. Sufficient conditions are introduced to guarantee near-optimality.

Flow watermarks efficiently link packet flows in a network in order to thwart various attacks such as stepping stones. We study the problem of designing good flow watermarks. Earlier flow watermarking schemes mostly considered substitution errors, neglecting the effects of packet insertions and deletions that commonly happen within a network. More recent schemes considered packet deletions but often at the expense of the watermark visibility. We present an invisible flow watermarking scheme capable of enduring a large number of packet losses and insertions. To maintain invisibility, our scheme uses quantization-index-modulation (QIM) to embed the watermark into interpacket delays, as opposed to time intervals including many packets. As the watermark is injected within individual packets, packet losses and insertions may lead to watermark desynchronization and substitution errors. To address this issue, we add a layer of error-correction coding to our scheme. Experimental results on both synthetic and real network traces demonstrate that our scheme is robust to network jitter, packet drops, and splits, while remaining invisible to an attacker.

This paper presents the design and implementation of spyware communication circuits built into the widely used carrier sense multiple access with collision avoidance (CSMA/CA) protocol. The spyware components are embedded within the sequential and combinational communication circuit structure during synthesis, rendering the distinction or dissociation of the spyware from the original circuit impossible. We take advantage of the timing channel resulting from transmission of packets to implement a new practical coding scheme that covertly transfers the spied data. Our codes are robust against the CSMA/CA's random retransmission time for collision avoidance and in fact take advantage of it to disguise the covert communication. The data snooping may be sporadically triggered, either externally or internally. The occasional trigger and the real-time traffic's variability make the spyware timing covert channel detection a challenge. The spyware is implemented and tested on a widely used open-source wireless CSMA/CA radio platform. We identify the following performance metrics and evaluate them on our architecture: 1) efficiency of implementation of the encoder; 2) robustness of the communication scheme to heterogeneous CSMA/CA effects; and 3) difficulty of covert channel detection. We evaluate criterion 1) completely theoretically. Criterion 2) is evaluated by simulating a wireless CSMA/CA architecture and testing the robustness of the decoder in different heterogeneous wireless conditions. Criterion 3) is confirmed experimentally using the state-of-the-art covert timing channel detection methods.

Explicit nonasymptotic upper bounds on the sizes of multiple-deletion correcting codes are presented. In particular, the largest single-deletion correcting code for q-ary alphabet and string length is shown to be of size at most (qn-q)/{(q-1)(n-1)}. An improved bound on the asymptotic rate function is obtained as a corollary. Upper bounds are also derived on sizes of codes for a constrained source that does not necessarily comprise of all strings of a particular length, and this idea is demonstrated by application to sets of run-length limited strings. The problem of finding the largest deletion correcting code is modeled as a matching problem on a hypergraph. This problem is formulated as an integer linear program. The upper bound is obtained by the construction of a feasible point for the dual of the linear programming relaxation of this integer linear program. The nonasymptotic bounds derived imply the known asymptotic bounds of Levenshtein and Tenengolts and improve on known nonasymptotic bounds. Numerical results support the conjecture that in the binary case, the Varshamov-Tenengolts codes are the largest single-deletion correcting codes.

Digital fingerprinting is a framework for marking media files, such as images, music, or movies, with user-specific signatures to deter illegal distribution. Multiple users can collude to produce a forgery that can potentially overcome a fingerprinting system. This paper proposes an equiangular tight frame fingerprint design which is robust to such collusion attacks. We motivate this design by considering digital fingerprinting in terms of compressed sensing. The attack is modeled as linear averaging of multiple marked copies before adding a Gaussian noise vector. The content owner can then determine guilt by exploiting correlation between each user's fingerprint and the forged copy. The worst case error probability of this detection scheme is analyzed and bounded. Simulation results demonstrate that the average-case performance is similar to the performance of orthogonal and simplex fingerprint designs, while accommodating several times as many users.

Flow watermarking1is an efficient technique for linking packet flows that helps thwart various attacks in networks such as over the Internet. Current state-of-the-art water-marking schemes withstand packet losses at the expense of compromising invisibility. We present an invisible flow watermarking scheme that can endure large numbers of packet losses. To maintain invisibility, our scheme embeds quantization-index modulation watermarks into inter-packet delays (as opposed to intervals). As the watermark is injected within individual packets, packet losses may lead to water-mark desynchronization and substitution errors. To deal with this issue we propose a maximum likelihood decoding (ML) scheme based on a hidden-Markov model (HMM) of the channel. Experimental results demonstrate that our scheme is robust to both network jitters and packet deletions while remaining invisible to an attacker.

In this work, we study information leakage in timing side channels that arise in the context of shared event schedulers. Consider two processes, one of them an innocuous process (referred to as Alice) and the other a malicious one (referred to as Bob), using a common scheduler to process their jobs. Based on when his jobs get processed, Bob wishes to learn about the pattern (size and timing) of jobs of Alice. Depending on the context, knowledge of this pattern could have serious implications on Alice's privacy and security. For instance, shared routers can reveal traffic patterns, shared memory access can reveal cloud usage patterns, and suchlike. We present a formal framework to study the information leakage in shared resource schedulers using the pattern estimation error as a performance metric. In this framework, a uniform upper bound is derived to benchmark different scheduling policies. The first-come-first-serve scheduling policy is analyzed, and shown to leak significant information when the scheduler is loaded heavily. To mitigate the timing information leakage, we propose an “Accumulate-and-Serve” policy which trades in privacy for a higher delay. The policy is analyzed under the proposed framework and is shown to leak minimum information to the attacker, and is shown to have comparatively lower delay than a fixed scheduler that preemptively assigns service times irrespective of traffic patterns.

We take a graph theoretic view of deletion correcting codes. The problem of finding an n-bit s-deletion correcting code is equivalent to finding an independent set in a particular graph. We discuss the relationship between codes and colorings and demonstrate that the VT codes are optimal in a coloring sense. We describe a method of partitioning the set of bit strings by Hamming weight and finding codes within each partition. In the single deletion case, we find an optimal coloring of the constant Hamming weight induced subgraphs. We show that the resulting code is asymptotically optimal. We also prove a lower bound on size of codes constructed using these partitions for any number of deletions.

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD - We propose a framework for learning the structure of a minimal latent tree with an associated discrepancy measure. Specifically, we apply this algorithm to recover the minimal latent directed information tree on a mixture of set of observed and unobserved random processes. Directed information trees are a new type of probabilistic graphical model based on directed information that represent the casual dynamics among random processes in a stochastic systems. To the best of our knowledge, this is the first approach that recovers these type of latent graphical models where samples are available only from a subset of processes.

In multi-tasking systems where a finite resource is to be shared, a scheduler dictates how the resource is divided among competing processes. Examples of systems which have schedulers include, a computer where the CPU needs to be shared between the different threads running, a cloud computing infrastructure with shared computing resources, a network router serving packets from different streams etc. In such situations, when a processor is shared by multiple users, the delays experienced by jobs from one user are a function of the arrival pattern of jobs from other users, and the scheduling policy of the server. Consequently, a scheduling system creates a timing side channel in which information about arrival pattern from one user is inadvertently leaked to another. In this work, this information leakage is studied for a two user scheduling system. We first introduce a measure of privacy and then demonstrate that no scheduler can provide maximum privacy without idling/taking vacations, and consequently no policy can simultaneously be delay and privacy optimal.

The Naval Research Laboratory (NRL) Network Pump, or Pump, is a standard for mitigating covert channels that arise in a multilevel secure (MLS) system when a high user (HU) sends acknowledgements to a low user (LU). The issue here is that HU can encode information in the "timings" of the acknowledgements. The Pump aims at mitigating the covert timing channel by introducing buffering between HU and LU, as well as adding noise to the acknowledgment timings. We model the working of the Pump in certain situations, as a communication system with feedback and use then this perspective to derive an upper bound on the capacity of the covert channel between HU and LU in the Pump. This upper bound is presented in terms of a directed information flow over the dynamics of the system. We also present an achievable scheme that can transmit information over this channel. When the support of the noise added by Pump to acknowledgment timings is finite, the achievable rate is nonzero, i.e., infinite number of bits can be reliably communicated. If the support of the noise is infinite, the achievable rate is zero and hence a finite number of bits can be communicated.

We show that equiangular tight frames (ETFs) are particularly well suited as additive fingerprint designs against Gaussian averaging collusion attacks when the number of users is less than the square of the signal dimension. The detector performs a binary hypothesis test in order to decide whether a user of interest is among the colluders. Given a maximum coalition size, we show that the geometric figure of merit of distance between the corresponding "guilty" and "not guilty" linear forgeries for each user is bounded away from zero. Moreover, we show that for a normalized correlation detector, reliable detection is guaranteed provided that the number of users is less than the square of the signal dimension. Moreover, we show that the coalition has the best chance of evading detection when it uses equal weights.

The information leakage of a queuing side channel in two-user-shared scheduling system is studied from an information theoretic perspective. In the queueing side channel, a malicious attacker can learn the pattern of jobs from a legitimate user using the queuing delays experienced at the shared buffer. An analytical framework is proposed to quantify information leakage using Shannon's equivocation, and the information leakage of the standard First-come-First-serve scheduler is studied in a slotted system with geometric arrivals. The analysis of the FCFS scheduler demonstrates that the policy provides “good privacy” when arrival rates are very low; the leaked information increases with the rate of the attacker's jobs and approaches the maximum retrievable information as the sum-rate of arrivals approaches the boundary of the stability region of the queue.

We propose a new type of probabilistic graphical model, based on directed information, to represent the causal dynamics between processes in a stochastic system. We show the practical significance of such graphs by proving their equivalence to generative model graphs which succinctly summarize interdependencies for causal dynamical systems under mild assumptions. This equivalence means that directed information graphs may be used for causal inference and learning tasks in the same manner Bayesian networks are used for correlative statistical inference and learning.

A general construction for deletion/insertion - correcting codes is proposed by concatenating codes derived from a heuristic maximal independent set algorithm on an appropriately defined graph. Our heuristic algorithm is polynomial with respect to the number of nodes in the graph. This methodology may be used for construction of any length n, s-deletion code. Our experimental results show that cardinalities of our codebooks exceed sizes of all previously known constructions. In fact, they are comparable to Levenshteins lower bound.

Recent work has shown that traffic analysis of data carried on encrypted tunnels can be used to recover important semantic information. As one example, attackers can find out which website, or which page on a website, a user is accessing simply by monitoring the traffic patterns. We show that traffic analysis is a much greater threat to privacy than previously thought, as such attacks can be carried out remotely. In particular, we show that, to perform traffic analysis, adversaries do not need to directly observe the traffic patterns. Instead, they can send probes from a far-off vantage point that exploit a queuing side channel in routers.

We examine a queuing side channel which results from a shared resource between two users in the context of packet networks. We consider the scenario where one of them is a legitimate user and the other is an attacker who is trying to learn about the former's activities. We show that the waiting time of an adversary sending a small but frequent probe stream to the shared resource (e.g., a router) is highly correlated with traffic pattern of the user.

This paper presents a dangerous low-cost traffic analysis attack in packet-based networks, such as the Internet. The attack is mountable in any scenario where a shared routing resource exists among users. A real-world attack successfully compromised the privacy of a user without requiring significant resources in terms of access, memory, or computational power. The effectiveness of our attack is demonstrated in a scenario where the user's DSL router uses FCFS scheduling policy. Specifically, we show that by using a low-rate sequence of probes, a remote attacker can obtain significant traffic-timing and volume information about a particular user, just by observing the round trip time of the probes. We also observe that even when the scheduling policy is changed to round-robin, while the correlation reduces significantly, the attacker can still reliably deduce user's traffic pattern. Most of the router scheduling policies designed to date are evaluated mostly on the metrics of throughput, delay and fairness. Our work is aimed to demonstrate a need for considering an additional metric that quantifies the information leak between the individual traffic flows through the router.

The NRL Network Pump®, or Pump, is a standard for mitigating covert channels that arise in a multi-level secure (MLS) system when a high user (HU) sends acknowledgements to a low user (LU). The issue here is that HU can encode information in the “timings” of the acknowledgements. The Pump aims at mitigating the covert timing channel by introducing buffering between HU and LU, as well as adding noise to the acknowledgment timings. Here, for the first time, we model the workings of the Pump in certain situations, as a communication system with feedback and use then this novel perspective to derive a upper bound on the rate of the covert channel between HU and LU in the Pump, in specific situations. This upper bound is presented in terms of a directed information flow over the dynamics of the system.

Chow and Liu considered the problem of approximating discrete joint distributions with dependence tree distributions where the goodness of the approximations were measured in terms of KL distance. They (i) demonstrated that the minimum divergence approximation was the tree with maximum sum of mutual informations, and (ii) specified a low-complexity minimum-weight spanning tree algorithm to find the optimal tree. In this paper, we consider an analogous problem of approximating the joint distribution on discrete random processes with causal, directed, dependence trees, where the approximation is again measured in terms of KL distance. We (i) demonstrate that the minimum divergence approximation is the directed tree with maximum sum of directed informations, and (ii) specify a low-complexity minimum weight directed spanning tree, or arborescence, algorithm to find the optimal tree. We also present an example to demonstrate the algorithm.

In this work we present a multi-flow attack resistant interval centroid based watermarking (MAR-ICBW) scheme for network flows. Our proposed scheme can withstand the newly introduced multi-flow watermarking attack that defeats the state-of-the-art interval-based network flow watermarking schemes. Multi-flow attack uses the dependent correlations among the flows marked with the same watermark to recover the secret parameters, and remove the watermark from a flow. The attack can be effective even if different flows are marked with different values of a watermark. MAR-ICBW survives the attack by virtue of randomizing the location of the embedded watermark across multiple flows and therefore, effectively removing the correlations between the flows. While we represent our counter measure to multi-flow attack in terms of an improved version of ICBW, the same methodology can be used to strengthen other interval-based flow watermarking schemes.

This paper presents the first practical perfectly-secure steganography codes for covert communication via packet timings across interactive traffic relayed over network queuing systems. It has recently been shown that sparse-graph linear codes followed by shaping techniques, combined with message-passing decoding, can enable practical timing channel codes with low symbol error rates near the information capacity of the famous ldquobits through queuesrdquo channel. Inspired by this new class of codes, we use an alternative shaping technique that employs random dithers and construct provably secure steganographic codes for communication using packet timings in interactive traffic. To validate the perfect secrecy of our steganographic codes, we model interactive traffic as a two-state Markov modulated Poisson process (MMPP) and show its goodness-of-fit.

This paper discusses practical codes for communication via packet timings across network queuing systems - an instantiation of the "Bits Through Queues" result for timing channels. It has recently been shown that sparse-graph linear codes followed by shaping techniques, combined with message-passing decoding, can enable practical timing channel codes with low symbol error rates near the capacity. The previous work had two main drawbacks. First, the shaping technique was only effective for very large finite field sizes. Secondly, the complexity of the message-passing decoder was quadratic in the block length. In this work, 1) we develop an alternative shaping technique using random dithers with provably good statistical guarantees; 2) we exploit Little's Law from queuing theory along with a large deviations argument to reduce the message-passing decoder's complexity from quadratic to linear in block length. We illustrate the effectiveness of this approach on simulated queuing systems with low symbol error rates near the capacity.

We study the effect of the noise distribution on the error probability of the detection test when a class of randomly rotated spherical fingerprints is used. The detection test is performed by a focused correlation detector, and the spherical codes studied here form a randomized orthogonal constellation. The colluders create a noise-free forgery by uniform averaging of their individual copies, and then add a noise sequence to form the actual forgery. We derive the noise distribution that maximizes the error probability of the detector under average and almost-sure distortion constraints. Moreover, we characterize the noise distribution that minimizes the decoder's error exponent under a large-deviations distortion constraint.

This paper addresses the design of additive fingerprints that are maximally resilient against linear collusion attacks on a focused correlation detector, as defined below. LetNbe the length of the host vector andMlesN+ 1 the number of users. The focused detector performs a correlation test in order to decide whether a user of interest is among the colluders. Both the fingerprint embedder and the colluders are subject to squared-error distortion constraints. We show that simplex fingerprints maximize a geometric figure of merit for this detector. In that sense they outperform orthogonal fingerprints but the advantage vanishes asMrarr infin. They are also optimal in terms of minimizing the probability of error of the focused detector when the attack is a uniform averaging of the marked copies followed by the addition of white Gaussian noise. Reliable detection is guaranteed provided that the number of colludersKLt radic(N). Moreover, we study the probability of error performance of simplex fingerprints for the focused correlation detector when the colluders use nonuniform averaging plus white Gaussian noise attacks.

This paper presents a proof of the rate distortion function of a Poisson process with a queuing distortion measure that is in complete analogy with the proofs associated with the rate distortion functions of a Bernoulli source with Hamming distortion measure and a Gaussian source with squared-error distortion measure. Analogous to those problems, the distortion measure that we consider is related to the logarithm of the conditional distribution relating the input to the output of a well-known channel coding problem, specifically the Anantharam and Verdu "Bits through Queues" [1] coding problem. Our proof of the converse utilizes McFadden's point process entropy formulation [2] and involves a number of mutual information inequalities, one of which exploits the maximum-entropy achieving property of the Poisson process. Our test channel uses Burke's theorem [3], [4] to prove achievability.

This paper examines more closely the probabilistic dynamics of queueing timing channels and discusses a new practical coding scheme which is tailored to them and approaches capacity. We consider using sparse graph coset codes over nonbinary finite fields. We use a shaping technique to map algebraic symbols to non-uniform codewords using the inverse cumulative distribution of a target random variable. We exploit the graphical structure of the conditional distribution of the departure process given the arrival process to arrive at a Forney factor graph of the joint likelihood that has graphical structure reminiscent of coding on inter-symbol interference channels with LDPC codes. We show through simulation that this technique, when using low-complexity iterative decoding, is capacity-approaching.

This paper analyzes the performance of arbitrary nonlinear collusion attacks on random fingerprinting codes. We derive the error exponent of the fingerprinting system, which determines the exponential decay of the error probability. A Gaussian ensemble and an expurgated Gaussian ensemble of codes are considered. The collusion attacks include order-statistics attacks as special cases. In our model, a correlation detector is used. The colluders create a noise-free forgery by applying an arbitrary nonlinear mapping to their individual copies, and next they add a Gaussian noise sequence to form the final forgery. The colluders are subject to a mean-squared distortion constraint between host and forgery. We prove that the uniform linear averaging attack outperforms all others.

This paper analyzes the performance of collusion attacks on random fingerprinting codes, when the colluders are subject to an almost sure squared distortion constraint and a list decoder is used. We derive an exact characterization of the type-I and type-II error exponents of the fingerprinting system. A Gaussian ensemble and an expurgated Gaussian ensemble of codes are considered, and the corresponding random-coding exponents are derived. Explicit optimal strategies for the colluders are derived as well.

Sensor networks are highly susceptible to errors and malicious attacks. A host of nefarious attacks are targeted at preventing nodes from discovering their correct positions. In this work, we present a novel framework for position estimation in presence of malicious attacks on distance measurements of sensor networks. Additionally, we propose a practical randomized algorithm in the framework, which efficiently detects and rejects the corrupted measurements. The algorithm searches for an agreeable solution starting from randomly sampled minimal subsets of data; it subsequently enhances its estimate by augmenting consistent data points to the best random sample. The performance of the proposed algorithm is evaluated and compared to state-of-the-art robust positioning algorithms, both for independent and colluding attackers. While our method performs the same or better compared with the other algorithms on independent attacks, it is significantly more robust against collusion attacks, in terms of both the position estimation error and attack diagnosis and isolation. Moreover, the algorithm has a shorter runtime due to its randomized nature.

We study the theoretical performance of linear and nonlinear collusion attacks under the assumptions that orthogonal or regular-simplex fingerprints are used, and that the detector performs a linear correlation test in order to decide whether a user of interest is among the colluders. The colluders create a noise-free forgery by applying a mapping / to their individual copies, and then add a noise sequence e to form the actual forgery. They seek the mapping / and the distribution of e that maximize the probability of error of the detector. The performance of mappings such as linear-averaging and interleaving can be compared in this framework. It is also shown that impulsive noise attacks are far more effective than Gaussian attacks

We will illustrate the connection between the Ising problem in statistical mechanics and the problem of computing the constrained capacity of an array of the same dimension. Using this connection, we show that for a given amount of violation, a soft constrained capacity can be computed. The classical Shannon capacity of a constrained channel is merely an end point of the soft capacity curve, where no violations are allowed. Moreover we reduce the problem of computing the constrained capacity to that of computing the eigenvalues of a special matrix. We claim that an analytical solution to calculating the eigenvalues of interest corresponds to solving the special case of the two-dimensional constrained channel with the constraint (1,infin)

In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal pseudo-codewords. This paper studies the minimal codewords and minimal pseudo-codewords of some families of codes derived from projective and Euclidean planes. Although our numerical results are only for codes of very modest length, they suggest that these code families exhibit an interesting property. Namely, all minimal pseudo-codewords that are not multiples of a minimal codeword have an AWGNC pseudo-weight that is strictly larger than the minimum Hamming weight of the code. This observation has positive consequences not only for LP decoding but also for iterative decoding

The paper presents the vector decomposition problem (VDP) for m-torsion points on an elliptic curve. We prove that any elliptic curve for which the sufficient conditions hold is bound to be supersingular.