We introduce a formulation of regularized optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be approximated in terms of an (infinite-dimensional) Hilbert-Schmidt operator mapping a Hilbert space of functions to another. For numerous machine learning applications, data can be naturally viewed as samples drawn from spaces of functions, such as curves and surfaces, in high dimensions. Optimal transport for functional data analysis provides a useful framework of treatment for such domains. Since probability measures in infinite dimensional spaces generally lack absolute continuity (i.e., with respect to non-degenerate Gaussian measures), the Monge map in the standard optimal transport theory for finite dimensional spaces typically does not exist in the functional settings arising in such machine learning applications. This necessitates a suitable notion of approximation for the best pushforward measure to be obtained via a transport map. Indeed, our approach to the transportation problem in functional spaces is by a suitable regularization technique --- we restrict the class of transport maps to be a Hilbert-Schmidt space of operators.Within this regularization framework, we develop an efficient algorithm for finding the stochastic transport map between functional domains and provide theoretical guarantees on the existence, uniqueness, and consistency of our estimate for the Hilbert-Schmidt space of compact linear operators. We validate our method on synthetic datasets and examine the functional properties of the transport map. Experiments on real-world datasets of robot arm trajectories further demonstrate the effectiveness of our method on applications in domain adaptation.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

We propose to study and promote the robustness of a model as per its performance on a continuous geodesic interpolation of subpopulations, e.g., a class of samples in a classification problem. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the geodesic connecting subpopulation distributions. (2) we regularize the model for smoother performance on the continuous geodesic path connecting subpopulation distributions. (3) Additionally, we provide a theoretical guarantee of robustness improvement and investigate how the geodesic location and the sample size contribute, respectively. Experimental validations of the proposed strategy on four datasets including CIFAR-100 and ImageNet, establish the efficacy of our method, e.g., our method improves the baselines’ certifiable robustness on CIFAR10 upto 7.7%, with 16.8% on empirical robustness on CIFAR-100. Our work provides a new perspective of model robustness through the lens of Wasserstein geodesic-based interpolation with a practical off-the-shelf strategy that can be combined with existing robust training methods.

Learning and understanding heterogeneous patterns in complex spatio-temporal data is an important and challenging task across domains in science and engineering. In this work, we develop a model for learning heterogeneous and dynamic patterns of velocity field data, motivated by applications in the transportation domain. We draw from basic nonparametric Bayesian modeling elements such as the infinite hidden Markov model and Gaussian process and focus on making the learning of such a stochastic model scalable for voluminous and streaming data. This is achieved by employing sequential MAP estimates from the infinite HMM model, an efficient sequential sparse GP posterior computation, and refinement of the estimates using the Viterbi algorithm, which is shown to work effectively on a careful simulation study. We demonstrate the efficacy of our techniques to the NGSIM dataset of complex multi-vehicle interactions.

As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being deviated from the known estimate by a mixture distribution. To model this phenomenon, we consider the \emph{deviating mixture model} $(1-\lambda^{*})h_0 + \lambda^{*} (\sum_{i = 1}^{k} p_{i}^{*} f(x|\theta_{i}^{*}))$, where $h_0$ is a known density function, while the deviated proportion $\lambda^{*}$ and latent mixing measure $G_{*} = \sum_{i = 1}^{k} p_{i}^{*} \delta_{\theta_i^{*}}$ associated with the mixture distribution are unknown. Via a novel notion of distinguishability between the known density $h_{0}$ and the deviated mixture distribution, we establish rates of convergence for the maximum likelihood estimates of $\lambda^{*}$ and $G^{*}$ under Wasserstein metric. Simulation studies are carried out to illustrate the theory.

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose several variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experimental results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

Conventional machine learning algorithms cannot be applied until a data matrix is available to process. When the data matrix needs to be obtained from a relational database via a feature extraction query, the computation cost can be prohibitive, as the data matrix may be (much) larger than the total input relation size. This paper introduces Rk-means, or relational k-means algorithm, for clustering relational data tuples without having to access the full data matrix. As such, we avoid having to run the expensive feature extraction query and storing its output. Our algorithm leverages the underlying structures in relational data. It involves construction of a small grid coreset of the data matrix for subsequent cluster construction. This gives a constant approximation for the k-means objective, while having asymptotic runtime improvements over standard approaches of first running the database query and then clustering. Empirical results show orders-of-magnitude speedup, and Rk-means can run faster on the database than even just computing the data matrix.

Motivated by fundamental applications in databases and relational machine learning, we formulate and study the problem of answering functional aggregate queries (FAQ) in which some of the input factors are defined by a collection of additive inequalities between variables. We refer to these queries as FAQ-AI for short. To answer FAQ-AI in the Boolean semiring, we define relaxed tree decompositions and relaxed submodular and fractional hypertree width parameters. We show that an extension of the InsideOut algorithm using Chazelle’s geometric data structure for solving the semigroup range search problem can answer Boolean FAQ-AI in time given by these new width parameters. This new algorithm achieves lower complexity than known solutions for FAQ-AI. It also recovers some known results in database query answering. Our second contribution is a relaxation of the set of polymatroids that gives rise to the counting version of the submodular width, denoted by #subw. This new width is sandwiched between the submodular and the fractional hypertree widths. Any FAQ and FAQ-AI over one semiring can be answered in time proportional to #subw and respectively to the relaxed version of #subw. We present three applications of our FAQ-AI framework to relational machine learning: k -means clustering, training linear support vector machines, and training models using non-polynomial loss. These optimization problems can be solved over a database asymptotically faster than computing the join of the database relations.

Integrated solutions for analytics over relational databases are of great practical importance as they avoid the costly repeated loop data scientists have to deal with on a daily basis: select features from data residing in relational databases using feature extraction queries involving joins, projections, and aggregations; export the training dataset defined by such queries; convert this dataset into the format of an external learning tool; and train the desired model using this tool. These integrated solutions are also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models. This article introduces a unified framework for training and evaluating a class of statistical learning models over relational databases. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from database theory such as schema information, query structure, functional dependencies, recent advances in query evaluation algorithms, and from linear algebra such as tensor and matrix operations, one can formulate relational analytics problems and design efficient (query and data) structure-aware algorithms to solve them. This theoretical development informed the design and implementation of the AC/DC system for structure-aware learning. We benchmark the performance of AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting and advertisement planning applications, AC/DC can learn polynomial regression models and factorization machines with at least the same accuracy as its competitors and up to three orders of magnitude faster than its competitors whenever they do not run out of memory, exceed 24-hour timeout, or encounter internal design limitations.

We propose Dirichlet Simplex Nest, a class of probabilistic models suitable for a variety of data types, and develop fast and provably accurate inference algorithms by accounting for the model’s convex geometry and low dimensional simplicial structure. By exploiting the connection to Voronoi tessellation and properties of Dirichlet distribution, the proposed inference algorithm is shown to achieve consistency and strong error bound guarantees on a range of model settings and data distributions. The effectiveness of our model and the learning algorithm is demonstrated by simulations and by analyses of text and financial data.

We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes.

Motivated by fundamental applications in databases and relational machine learning, we formulate and study the problem of answering functional aggregate queries (FAQ) in which some of the input factors are defined by a collection of additive inequalities between variables. We refer to these queries as FAQ-AI for short. To answer FAQ-AI in the Boolean semiring, we define relaxed tree decompositions and relaxed submodular and fractional hypertree width parameters. We show that an extension of the InsideOut algorithm using Chazelle's geometric data structure for solving the semigroup range search problem can answer Boolean FAQ-AI in time given by these new width parameters. This new algorithm achieves lower complexity than known solutions for FAQ-AI. It also recovers some known results in database query answering. Our second contribution is a relaxation of the set of polymatroids that gives rise to the counting version of the submodular width, denoted by #subw. This new width is sandwiched between the submodular and the fractional hypertree widths. Any FAQ and FAQ-AI over one semiring can be answered in time proportional to #subw and respectively to the relaxed version of #subw. We present three applications of our FAQ-AI framework to relational machine learning: k-means clustering, training linear support vector machines, and training models using non-polynomial loss. These optimization problems can be solved over a database asymptotically faster than computing the join of the database relations.

This paper introduces LMFAO (Layered Multiple Functional Aggregate Optimization), an in-memory optimization and execution engine for batches of aggregates over the input database. The primary motivation for this work stems from the observation that for a variety of analytics over databases, their data-intensive tasks can be decomposed into group-by aggregates over the join of the input database relations. We exemplify the versatility and competitiveness of LMFAO for a handful of widely used analytics: learning ridge linear regression, classification trees, regression trees, and the structure of Bayesian networks using Chow-Liu trees; and data cubes used for exploration in data warehousing. LMFAO consists of several layers of logical and code optimizations that systematically exploit sharing of computation, parallelism, and code specialization. We conducted two types of performance benchmarks. In experiments with four datasets, LMFAO outperforms by several orders of magnitude on one hand, a commercial database system and MonetDB for computing batches of aggregates, and on the other hand, TensorFlow, Scikit, R, and AC/DC for learning a variety of models over databases.

In-database analytics is of great practical importance as it avoids the costly repeated loop data scientists have to deal with on a daily basis: select features, export the data, convert data format, train models using an external tool, reimport the parameters. It is also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models. This paper introduces a unified framework for training and evaluating a class of statistical learning models inside a relational database. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from relational database theory such as schema information, query structure, recent advances in query evaluation algorithms, and from linear algebra such as various tensor and matrix operations, one can formulate in-database learning problems and design efficient algorithms to solve them. The algorithms and models proposed in the paper have already been implemented and deployed in retail-planning and forecasting applications, with significant performance benefits over out-of-database solutions that require the costly data-export loop.

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex hull of vertices representing the latent topics. Our algorithms are shown in practice to have accuracy comparable to a Gibbs sampler in terms of topic estimation, which requires the number of topics be given. Moreover, they are one of the fastest among several state of the art parametric techniques. Statistical consistency of our estimator is established under some conditions.

We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is guided by a prior distribution on random hypergraphs, a construction which generalizes the Finite Feature Model. We present a posterior inference algorithm based on Gibbs sampling, and establish posterior consistency of our regression model. Our method is evaluated with extensive experiments on simulated data and demonstrated to be able to identify meaningful interactions in applications in genetics and retail demand forecasting.

We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Our method involves a fast optimization based weighted clustering procedure augmented with geometric corrections, which overcomes the computational and statistical inefficiencies encountered by other techniques based on Gibbs sampling and variational inference, while achieving the accuracy comparable to that of a Gibbs sampler. The topic estimates produced by our method are shown to be statistically consistent under some conditions. The algorithm is evaluated with extensive experiments on simulated and real data.

Homogeneous charge compression ignition (HCCI) is a futuristic automotive engine technology that can significantly improve fuel economy and reduce emissions. HCCI engine operation is constrained by combustion instabilities, such as knock, ringing, misfires, high-variability combustion, and so on, and it becomes important to identify the operating envelope defined by these constraints for use in engine diagnostics and controller design. HCCI combustion is dominated by complex nonlinear dynamics, and a first-principle-based dynamic modeling of the operating envelope becomes intractable. In this paper, a machine learning approach is presented to identify the stable operating envelope of HCCI combustion, by learning directly from the experimental data. Stability is defined using thresholds on combustion features obtained from engine in-cylinder pressure measurements. This paper considers instabilities arising from engine misfire and high-variability combustion. A gasoline HCCI engine is used for generating stable and unstable data observations. Owing to an imbalance in class proportions in the data set, the models are developed both based on resampling the data set (by undersampling and oversampling) and based on a cost-sensitive learning method (by overweighting the minority class relative to the majority class observations). Support vector machines (SVMs) and recently developed extreme learning machines (ELM) are utilized for developing dynamic classifiers. The results compared against linear classification methods show that cost-sensitive nonlinear ELM and SVM classification algorithms are well suited for the problem. However, the SVM envelope model requires about 80% more parameters for an accuracy improvement of 3% compared with the ELM envelope model indicating that ELM models may be computationally suitable for the engine application. The proposed modeling approach shows that HCCI engine misfires and high-variability combustion can be predicted ahead of time, given the present values of available sensor measurements, making the models suitable for engine diagnostics and control applications.

We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-measure with a nested structure to accommodate content and context observations at multiple levels. The proposed model possesses properties that link the nested Dirichlet processes (nDP) and the Dirichlet process mixture models (DPM) in an interesting way: integrating out all contents results in the DPM over contexts, whereas integrating out group-specific contexts results in the nDP mixture over content variables. We provide a Polya-urn view of the model and an efficient collapsed Gibbs inference procedure. Extensive experiments on real-world datasets demonstrate the advantage of utilizing context information via our model in both text and image domains.

Topic models such as the latent Dirichlet allocation (LDA) have become a standard staple in the modeling toolbox of machine learning. They have been applied to a vast variety of data sets, contexts, and tasks to varying degrees of success. However, to date there is almost no formal theory explicating the LDA’s behavior, and despite its familiarity there is very little systematic analysis of and guidance on the properties of the data that affect the inferential performance of the model. This paper seeks to address this gap, by providing a systematic analysis of factors which characterize the LDA’s performance. We present theorems elucidating the posterior contraction rates of the topics as the amount of data increases, and a thorough supporting empirical study using synthetic and real data sets, including news and web-based articles and tweet messages. Based on these results we provide practical guidance on how to identify suitable data sets for topic models, and how to specify particular model parameters.

We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors of exact and approximate message-passing algorithms that arise in a sequential change point detection problem formulated via a latent variable directed graphical model. The sequential inference algorithm and its supporting theory are illustrated by simulated examples.

We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for certain functionals of change points (minimum among a subset), and prove their asymptotic optimality in terms of expected detection delay. Drawing from graphical model formalism, the sequential detection rules can be implemented by a computationally efficient message-passing protocol which may scale up linearly in network size and in waiting time. The effectiveness of our inference algorithm is demonstrated by simulations.

We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for functionals of change points, and prove their asymptotic optimality properties in terms of expected detection delay time. Drawing from graphical model formalism, the sequential detection rules can be implemented by a computationally efficient message-passing protocol which may scale up linearly in network size and in waiting time. The effectiveness of our exact and approximate inference algorithms are demonstrated by simulations.

We develop and analyzeM-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a nonasymptotic variational characterization off-divergences, which allows the problem of estimating divergences to be tackled via convex empirical risk optimization. The resulting estimators are simple to implement, requiring only the solution of standard convex programs. We present an analysis of consistency and convergence for these estimators. Given conditions only on the ratios of densities, we show that our estimators can achieve optimal minimax rates for the likelihood ratio and the divergence functionals in certain regimes. We derive an efficient optimization algorithm for computing our estimates, and illustrate their convergence behavior and practical viability by simulations.

Monitoring its health by detecting its failed sensors is essential to the reliable functioning of any sensor network. This paper presents a distributed, online, sequential algorithm for detecting multiple faults in a sensor network. The algorithm works by detecting change points in the correlation statistics of neighboring sensors, requiring only neighbors to exchange information. The algorithm provides guarantees on detection delay and false alarm probability. This appears to be the first work to offer such guarantees for a multiple sensor network. Based on the performance guarantees, we compute a tradeoff between sensor node density, detection delay and energy consumption. We also address synchronization, finite storage and data quantization. We validate our approach with some example applications.

We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two competing hypotheses), and a set of quantization rules (the local decisions on the basis of which the global decision is made). This correspondence addresses an open problem of whether in the Bayesian formulation of sequential decentralized detection, optimal local decision functions can be found within the class of stationary rules. We develop an asymptotic approximation to the optimal cost of stationary quantization rules and exploit this approximation to show that stationary quantizers are not optimal in a broad class of settings. We also consider the class of blockwise-stationary quantizers, and show that asymptotically optimal quantizers are likelihood-based threshold rules.

There has been growing interest in building large-scale distributed monitoring systems for sensor, enterprise, and ISP networks. Recent work has proposed using principal component analysis (PCA) over global traffic matrix statistics to effectively isolate network-wide anomalies. To allow such a PCA-based anomaly detection scheme to scale, we propose a novel approximation scheme that dramatically reduces the burden on the production network. Our scheme avoids the expensive step of centralizing all the data by performing intelligent filtering at the distributed monitors. This filtering reduces monitoring bandwidth overheads, but can result in the anomaly detector making incorrect decisions based on a perturbed view of the global data set. We employ stochastic matrix perturbation theory to bound such errors. Our algorithm selects the filtering parameters at local monitors such that the errors made by the detector are guaranteed to lie below a user-specified upper bound. Our algorithm thus allows network operators to explicitly balance the tradeoff between detection accuracy and the amount of data communicated over the network. In addition, our approach enables real-time detection because we exploit continuous monitoring at the distributed monitors. Experiments with traffic data from Abilene backbone network demonstrate that our methods yield significant communication benefits while simultaneously achieving high detection accuracy.

We develop and analyze a nonparametric method for estimating the class of f-divergence functionals, and the density ratio of two probability distributions. Our method is based on a non-asymptotic variational characterization of the f-divergence, which allows us to cast the problem of estimating divergences in terms of risk minimization. We thus obtain an M-estimator for divergences, based on a convex and differentiable optimization problem that can be solved efficiently. We analyze the consistency and convergence rates for this M-estimator given conditions only on the ratio of densities.

We develop and analyze an algorithm for nonparametric estimation of divergence functionals and the density ratio of two probability distributions. Our method is based on a variational characterization of f-divergences, which turns the estima- tion into a penalized convex risk minimization problem. We present a derivation of our kernel-based estimation algorithm and an analysis of convergence rates for the estimator. Our simulation results demonstrate the convergence behavior of the method, which compares favorably with existing methods in the literature.

We consider the problem of sequential decentralized detection, a problem that entails the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two competing hypotheses), and a set of quantization rules (the local decisions on the basis of which the global decision is made). The main result of this paper is to resolve an open problem posed by Veeravalli et al. (1993) concerning whether optimal local decision functions for the Bayesian formulation of sequential decentralized detection can be found within the class of stationary rules. We provide a negative answer to this question by exploiting an asymptotic approximation to the optimal cost of stationary quantization rules, and the asymmetry of the Kullback-Leibler divergences. In addition, we show that asymptotically optimal quantizers, when restricted to the space of blockwise stationary quantizers, are likelihood-based threshold rules

We consider the problem of network anomaly detection in large distributed systems. In this setting, Principal Component Analysis (PCA) has been proposed as a method for discover- ing anomalies by continuously tracking the projection of the data onto a residual subspace. This method was shown to work well empirically in highly aggregated networks, that is, those with a limited number of large nodes and at coarse time scales. This approach, how- ever, has scalability limitations. To overcome these limitations, we develop a PCA-based anomaly detector in which adaptive local data (cid:2)lters send to a coordinator just enough data to enable accurate global detection. Our method is based on a stochastic matrix perturba- tion analysis that characterizes the tradeoff between the accuracy of anomaly detection and the amount of data communicated over the network.

In this paper, we provide a general theorem that establishes a correspon- dence between surrogate loss functions in classification and the family of f-divergences. Moreover, we provide constructive procedures for determining the f-divergence induced by a given surrogate loss, and conversely for finding all surrogate loss functions that realize a given f-divergence. Next we introduce the notion of universal equivalence among loss functions and corresponding f-divergences, and provide nec- essary and sufficient conditions for universal equivalence to hold. These ideas have applications to classification problems that also involve a com- ponent of experiment design; in particular, we leverage our results to prove consistency of a procedure for learning a classifier under decen- tralization requirements.

We show that the coarse-grained and fine-grained localization problems for ad hoc sensor networks can be posed and solved as a pattern recognition problem using kernel methods from statistical learning theory. This stems from an observation that the kernel function, which is a similarity measure critical to the effectiveness of a kernel-based learning algorithm, can be naturally defined in terms of the matrix of signal strengths received by the sensors. Thus we work in the natural coordinate system provided by the physical devices. This not only allows us to sidestep the difficult ranging procedure required by many existing localization algorithms in the literature, but also enables us to derive a simple and effective localization algorithm. The algorithm is particularly suitable for networks with densely distributed sensors, most of whose locations are unknown. The computations are initially performed at the base sensors, and the computation cost depends only on the number of base sensors. The localization step for each sensor of unknown location is then performed locally in linear time. We present an analysis of the localization error bounds, and provide an evaluation of our algorithm on both simulated and real sensor networks.

We consider the problem of decentralized detection under constraints on the number of bits that can be transmitted by each sensor. In contrast to most previous work, in which the joint We consider the problem of decentralized detection under constraints on the number of bits that can be transmitted by each sensor. In contrast to most previous work, in which the joint distribution of sensor observations is assumed to be known, we address the problem when only a set of empirical samples is available. We propose a novel algorithm using the framework of empirical risk minimization and marginalized kernels, and analyze its computational and statistical properties both theoretically and empirically. We provide an efficient implementation of the algorithm, and demonstrate its performance on both simulated and real data sets.

We present an analysis of concentration-of-expectation phenomena in layered Bayesian networks that use generalized linear models as the local conditional probabilities. This framework encompasses a wide variety of probability distributions, including both discrete and continuous random variables. We utilize ideas from large deviation analysis and the delta method to devise and evaluate a class of approximate inference algo- rithms for layered Bayesian networks that have superior asymptotic error bounds and very fast computation time.