Relational reasoning is a central component of generally intelligent systems, enabling robust and data-efficient inductive generalization. Recent empirical evidence shows that many existing neural architectures, including Transformers, struggle with tasks requiring relational reasoning. In this work, we distinguish between two types of information: sensory information about the properties of individual objects, and relational information about the relationships between objects. While neural attention provides a powerful mechanism for controlling the flow of sensory information between objects, the Transformer lacks an explicit computational mechanism for routing and processing relational information. To address this limitation, we propose an architectural extension of the Transformer framework that we call the Dual Attention Transformer (DAT), featuring two distinct attention mechanisms: sensory attention for directing the flow of sensory information, and a novel relational attention mechanism for directing the flow of relational information. We empirically evaluate DAT on a diverse set of tasks ranging from synthetic relational benchmarks to complex real-world tasks such as language modeling and visual processing. Our results demonstrate that integrating explicit relational computational mechanisms into the Transformer architecture leads to significant performance gains in terms of data efficiency and parameter efficiency.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which augments training data with intermediate reasoning steps to provide a richer learning signal, has driven recent advances in large language model reasoning. This paper develops a statistical theory of learning under CoT supervision. Central to the theory is the *CoT information*, which measures the additional discriminative power offered by the chain-of-thought for distinguishing hypotheses with different end-to-end behaviors. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard end-to-end supervision, with both upper bounds and information-theoretic lower bounds characterized by the CoT information.

We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb R^d \times \mathbb R$ with $x \sim \mathcal N(0,I_d)$ and $y = x^\top \beta + z$, where $z$ is drawn from an unknown distribution that is independent of $x$. Moreover, $z$ satisfies $\mathbb P[z = 0] = \alpha>0$. The goal is to accurately recover the regressor $\beta$ to small $\ell_2$-error. Ignoring computational considerations, this problem is known to be solvable using $O(d/\alpha)$ samples. On the other hand, the best known polynomial-time algorithms require $\Omega(d/\alpha^2)$ samples. Here we provide formal evidence that the quadratic dependence in $1/\alpha$ is inherent for efficient algorithms. Specifically, we show that any efficient Statistical Query algorithm for this task requires VSTAT complexity at least $\tilde{\Omega}(d^{1/2}/\alpha^2)$.

An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the *Abstractor*. At the core of the Abstractor is a variant of attention called *relational cross-attention*. The approach is motivated by an architectural inductive bias for relational learning that disentangles relational information from object-level features. This enables explicit relational reasoning, supporting abstraction and generalization from limited data. The Abstractor is first evaluated on simple discriminative relational tasks and compared to existing relational architectures. Next, the Abstractor is evaluated on purely relational sequence-to-sequence tasks, where dramatic improvements are seen in sample efficiency compared to standard Transformers. Finally, Abstractors are evaluated on a collection of tasks based on mathematical problem solving, where consistent improvements in performance and sample efficiency are observed.

Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure---updating one neuron's synaptic weights requires knowledge of synaptic weights or receptive fields of downstream neurons. This limits the use of artificial neural networks as a tool for understanding the biological principles of information processing in the brain. Lillicrap et al. (2016) propose a more biologically plausible "feedback alignment" algorithm that uses random and fixed backpropagation weights, and show promising simulations. In this paper we study the mathematical properties of the feedback alignment procedure by analyzing convergence and alignment for two-layer networks under squared error loss. In the overparameterized setting, we prove that the error converges to zero exponentially fast, and also that regularization is necessary in order for the parameters to become aligned with the random backpropagation weights. Simulations are given that are consistent with this analysis and suggest further generalizations. These results contribute to our understanding of how biologically plausible algorithms might carry out weight learning in a manner different from Hebbian learning, with performance that is comparable with the full non-local backpropagation algorithm.

Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly generates mathematical equations and their surrounding text (TopicEq). Using an extension of the correlated topic model, the context is generated from a mixture of latent topics, and the equation is generated by an RNN that depends on the latent topic activations. To experiment with this model, we create a corpus of 400K equation-context pairs extracted from a range of scientific articles from arXiv, and fit the model using a variational autoencoder approach. Experimental results show that this joint model significantly outperforms existing topic models and equation models for scientific texts. Moreover, we qualitatively show that the model effectively captures the relationship between topics and mathematics, enabling novel applications such as topic-aware equation generation, equation topic inference, and topic-aware alignment of mathematical symbols and words.

We investigate a sequential optimization procedure to minimize the empirical risk functional $f_{\hat\theta}(x) = \frac{1}{2}\|G_{\hat\theta}(x) - y\|^2$ for certain families of deep networks $G_{\theta}(x)$. The approach is to optimize a sequence of objective functions that use network parameters obtained during different stages of the training process. When initialized with random parameters $\theta_0$, we show that the objective $f_{\theta_0}(x)$ is ``nice'' and easy to optimize with gradient descent. As learning is carried out, we obtain a sequence of generative networks $x \mapsto G_{\theta_t}(x)$ and associated risk functions $f_{\theta_t}(x)$, where $t$ indicates a stage of stochastic gradient descent during training. Since the parameters of the network do not change by very much in each step, the surface evolves slowly and can be incrementally optimized. The algorithm is formalized and analyzed for a family of expansive networks. We call the procedure {\it surfing} since it rides along the peak of the evolving (negative) empirical risk function, starting from a smooth surface at the beginning of learning and ending with a wavy nonconvex surface after learning is complete. Experiments show how surfing can be used to find the global optimum and for compressed sensing even when direct gradient descent on the final learned network fails.

Many modern computing systems must provide reliable latency with minimal energy. Two central challenges arise when allocating system resources to meet these conflicting goals: (1) complexity modern hardware exposes diverse resources with complicated interactions and (2) dynamics latency must be maintained despite unpredictable changes in operating environment or input. Machine learning accurately models the latency of complex, interacting resources, but does not address system dynamics; control theory adjusts to dynamic changes, but struggles with complex resource interaction. We therefore propose CALOREE, a resource manager that learns key control parameters to meet latency requirements with minimal energy in complex, dynamic en- vironments. CALOREE breaks resource allocation into two sub-tasks: learning how interacting resources affect speedup, and controlling speedup to meet latency requirements with minimal energy. CALOREE deines a general control system whose parameters are customized by a learning framework while maintaining control-theoretic formal guarantees that the latency goal will be met. We test CALOREE's ability to deliver reliable latency on heterogeneous ARM big.LITTLE architectures in both single and multi-application scenarios. Compared to the best prior learning and control solutions, CALOREE reduces deadline misses by 60% and energy consumption by 13%.

Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied to any pre-trained prediction rule, while the second method deals specifically with random forests. In both cases, efficient algorithms are developed for computing the estimators, and experiments are performed to demonstrate their performance on four datasets. We find that reshaping methods enforce shape constraints without compromising predictive accuracy.

This paper studies the problem of nonparametric estimation of a smooth function with data distributed across multiple machines. We assume an independent sample from a white noise model is collected at each machine, and an estimator of the underlying true function needs to be constructed at a central machine. We place limits on the number of bits that each machine can use to transmit information to the central machine. Our results give both asymptotic lower bounds and matching upper bounds on the statistical risk under various settings. We identify three regimes, depending on the relationship among the number of machines, the size of data available at each machine, and the communication budget. When the communication budget is small, the statistical risk depends solely on this communication bottleneck, regardless of the sample size. In the regime where the communication budget is large, the classic minimax risk in the non-distributed estimation setting is recovered. In an intermediate regime, the statistical risk depends on both the sample size and the communication budget.

We study the estimation of flows on trees, a structured generalization of isotonic regression. A tree flow is defined recursively as a positive flow value into a node that is partitioned into an outgoing flow to the children nodes, with some amount of the flow possibly leaking outside. We study the behavior of the least squares estimator for flows, and the associated minimax lower bounds. We characterize the risk of the least squares estimator in two regimes. In the first regime, the diameter of the tree grows at most logarithmically with the number of nodes. In the second regime, the tree contains many long paths. The results are compared with known risk bounds for isotonic regression. In the many long paths regime, we find that the least squares estimator is not minimax rate optimal for flow estimation.

We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the function or its ``hardest local alternative'' to a given numerical precision. The bounds are expressed in terms of a localized and computational analogue of the modulus of continuity that is central to statistical minimax analysis. We show how the computational modulus of continuity can be explicitly calculated in concrete cases, and relates to the curvature of the function at the optimum. We also prove a superefficiency result that demonstrates it is a meaningful benchmark, acting as a computational analogue of the Fisher information in statistical estimation. The nature and practical implications of the results are demonstrated in simulations.

We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of the magnitude of the projection of the data onto a given subspace, and enables us to develop inference procedures for a broad class of group-sparse selection methods, including the group lasso, iterative hard thresholding, and forward stepwise regression. We give numerical results to illustrate these tools on simulated data and on health record data.

In many deployments, computer systems are underutilized -- meaning that applications have performance requirements that demand less than full system capacity. Ideally, we would take advantage of this under-utilization by allocating system resources so that the performance requirements are met and energy is minimized. This optimization problem is complicated by the fact that the performance and power consumption of various system configurations are often application -- or even input -- dependent. Thus, practically, minimizing energy for a performance constraint requires fast, accurate estimations of application-dependent performance and power tradeoffs. This paper investigates machine learning techniques that enable energy savings by learning Pareto-optimal power and performance tradeoffs. Specifically, we propose LEO, a probabilistic graphical model-based learning system that provides accurate online estimates of an application's power and performance as a function of system configuration. We compare LEO to (1) offline learning, (2) online learning, (3) a heuristic approach, and (4) the true optimal solution. We find that LEO produces the most accurate estimates and near optimal energy savings.

We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random measurements of a positive semidefinite $n\times n$ matrix of rank $r$ and condition number $\kappa$, our method is guaranteed to converge linearly to the global optimum.

The i.i.d. assumption in machine learning is endemic, but often flawed. Complex data sets exhibit partial correlations between both instances and features. A model specifying both types of correlation can have a number of parameters that scales quadratically with the number of features and data points. We introduce the bigraphical lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs. A prominent product in spectral graph theory, this structure has appealing properties for regression, enhanced sparsity and interpretability. To deal with the parameter explosion we introduce L1 penalties and fit the model through a flip-flop algorithm that results in a linear number of lasso regressions.

We present a family of linear regression estimators that provides a fine-grained tradeoff between statistical accuracy and computational efficiency. The estimators are based on hard thresholding of the sample covariance matrix entries together with l2-regularizion(ridge regression). We analyze the predictive risk of this family of estimators as a function of the threshold and regularization parameter. With appropriate parameter choices, the estimate is the solution to a sparse, diagonally dominant linear system, solvable in near-linear time. Our analysis shows how the risk varies with the sparsity and regularization level, thus establishing a statistical estimation setting for which there is an explicit, smooth tradeoff between risk and computation. Simulations are provided to support the theoretical analyses.

We derive a novel relation between mismatched estimation and relative entropy (KL divergence) in vector Gaussian channels under the mean squared estimation criterion. This relation includes as special cases several previous results connecting estimation theory and information theory. A direct proof is provided, together with a verification using Gaussian inputs. An interesting relationship between the KL divergence and Fisher divergence is derived as a direct consequence of our work. The relations established here are potentially useful for inference in graphical models and the design of information systems.

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional predictor variable. To control the complexity of the model, we employ a functional form of the Ky-Fan or nuclear norm, resulting in a set of function estimates that have low rank. Backfitting algorithms are derived and justified using a nonparametric form of the nuclear norm subdifferential. Oracle inequalities on excess risk are derived that exhibit the scaling behavior of the procedure in the high dimensional setting. The methods are illustrated on gene expression data.

We prove a new exponential concentration inequality for a plug-in estimator of the Shannon mutual information. Previous results on mutual information estimation only bounded expected error. The advantage of having the exponential inequality is that, combined with the union bound, we can guarantee accurate estimators of the mutual information for many pairs of random variables simultaneously. As an application, we show how to use such a result to optimally estimate the density function and graph of a distribution which is Markov to a forest graph.

We present a method for learning image representations using a two-layer sparse coding scheme at the pixel level. The first layer encodes local patches of an image. After pooling within local regions, the first layer codes are then passed to the second layer, which jointly encodes signals from the region. Unlike traditional sparse coding methods that encode local patches independently, this approach accounts for high-order dependency among patterns in a local image neighborhood. We develop algorithms for data encoding and codebook learning, and show in experiments that the method leads to more invariant and discriminative image representations. The algorithm gives excellent results for hand-written digit recognition on MNIST and object recognition on the Caltech101 benchmark. This marks the first time that such accuracies have been achieved using automatically learned features from the pixel level, rather than using hand-designed descriptors.

Undirected graphical models encode in a graph $G$ the dependency structure of a random vector $Y$. In many applications, it is of interest to model $Y$ given another random vector $X$ as input. We refer to the problem of estimating the graph $G(x)$ of $Y$ conditioned on $X=x$ as ``graph-valued regression''. In this paper, we propose a semiparametric method for estimating $G(x)$ that builds a tree on the $X$ space just as in CART (classification and regression trees), but at each leaf of the tree estimates a graph. We call the method ``Graph-optimized CART'', or Go-CART. We study the theoretical properties of Go-CART using dyadic partitioning trees, establishing oracle inequalities on risk minimization and tree partition consistency. We also demonstrate the application of Go-CART to a meteorological dataset, showing how graph-valued regression can provide a useful tool for analyzing complex data.

A nonparametric model is introduced that allows multiple related regression tasks to take inputs from a common data space. Traditional transfer learning models can be inappropriate if the dependence among the outputs cannot be fully resolved by known input-specific and task-specific predictors. The proposed model treats such output responses as conditionally independent, given known predictors and appropriate unobserved random effects. The model is nonparametric in the sense that the dimensionality of random effects is not specified a priori but is instead determined from data. An approach to estimating the model is presented uses an EM algorithm that is efficient on a very large scale collaborative prediction problem. The obtained prediction accuracy is competitive with state-of-the-art results.

With the sheer growth of online user data, it becomes challenging to develop preference learning algorithms that are sufficiently flexible in modeling but also affordable in computation. In this paper we develop nonparametric matrix factorization methods by allowing the latent factors of two low-rank matrix factorization methods, the singular value decomposition (SVD) and probabilistic principal component analysis (pPCA), to be data-driven, with the dimensionality increasing with data size. We show that the formulations of the two nonparametric models are very similar, and their optimizations share similar procedures. Compared to traditional parametric low-rank methods, nonparametric models are appealing for their flexibility in modeling complex data dependencies. However, this modeling advantage comes at a computational price--it is highly challenging to scale them to large-scale problems, hampering their application to applications such as collaborative filtering. In this paper we introduce novel optimization algorithms, which are simple to implement, which allow learning both nonparametric matrix factorization models to be highly efficient on large-scale problems. Our experiments on EachMovie and Netflix, the two largest public benchmarks to date, demonstrate that the nonparametric models make more accurate predictions of user ratings, and are computationally comparable or sometimes even faster in training, in comparison with previous state-of-the-art parametric matrix factorization models.

Recent research has studied the role of sparsity in high-dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models. This line of work shows that$\ell _{1}$-regularized least squares regression can accurately estimate a sparse linear model from noisy examples in high dimensions. We study a variant of this problem where the original$n$input variables are compressed by a random linear transformation to$m \ll n$examples in$p$dimensions, and establish conditions under which a sparse linear model can be successfully recovered from the compressed data. A primary motivation for this compression procedure is to anonymize the data and preserve privacy by revealing little information about the original data. We characterize the number of projections that are required for$\ell _{1}$-regularized compressed regression to identify the nonzero coefficients in the true model with probability approaching one, a property called “sparsistence.” We also show that$\ell _{1}$-regularized compressed regression asymptotically predicts as well as an oracle linear model, a property called “persistence.” Finally, we characterize the privacy properties of the compression procedure, establishing upper bounds on the mutual information between the compressed and uncompressed data that decay to zero.

We propose new families of models and algorithms for high-dimensional nonparametric learning with joint sparsity constraints. Our approach is based on a regularization method that enforces common sparsity patterns across different function components in a nonparametric additive model. The algorithms employ a coordinate descent approach that is based on a functional soft-thresholding operator. The framework yields several new models, including multi-task sparse additive models, multi-response sparse additive models, and sparse additive multi-category logistic regression. The methods are illustrated with experiments on synthetic data and gene microarray data.

Admixture models are "mixtures of mixtures" that decompose an object into multiple latent components, with the component proportions varying stochastically across objects. Recent work in machine learning has successfully developed admixture models for text, and work in population genetics has developed such models to analyze complex groups of individuals having mixed ancestry. We introduce a family of graphical admixture models for decomposing a signal into multiple components based on a wavelet representation of the signal. Two models are developed, one using a fixed segmentation of the signal, another using recursive dyadic partitioning. Variational algorithms are derived for inferring mixture proportions and estimating parameters.

Temporal classification, such as activity recognition, is a key component for creating intelligent robot systems. In the case of robots, classification algorithms must robustly incorporate complex, non-independent features extracted from streams of sensor data. Conditional random fields are discriminatively trained temporal models that can easily incorporate such features. However, robots have few computational resources to spare for computing a large number of features from high bandwidth sensor data, which creates opportunities for feature selection. Creating models that contain only the most relevant features reduces the computational burden of temporal classification. In this paper, we show that lscr1regularization is an effective technique for feature selection in conditional random fields. We present results from a multi-robot tag domain with data from both real and simulated robots that compare the classification accuracy of models trained with lscr1regularization, which simultaneously smoothes the model and selects features; lscr2regularization, which smoothes to avoid over-fitting, but performs no feature selection; and models trained with no smoothing.

Modeling the evolution of topics with time is of great value in automatic summarization and analysis of large document collections. In this work, we propose a new probabilistic graphical model to address this issue. The new model, which we call the Multiscale Topic Tomography Model (MTTM), employs non-homogeneous Poisson processes to model generation of word-counts. The evolution of topics is modeled through a multi-scale analysis using Haar wavelets. One of the new features of the model is its modeling the evolution of topics at various time-scales of resolution, allowing the user to zoom in and out of the time-scales. Our experiments on Science data using the new model uncovers some interesting patterns in topics. The new model is also comparable to LDA in predicting unseen data as demonstrated by our perplexity experiments.

Semi-supervised methods use unlabeled data in addition to labeled data to con- struct predictors. While existing semi-supervised methods have shown some promising empirical performance, their development has been based largely based on heuristics. In this paper we study semi-supervised learning from the viewpoint of minimax theory. Our first result shows that some common methods based on regularization using graph Laplacians do not lead to faster minimax rates of con- vergence. Thus, the estimators that use the unlabeled data do not have smaller risk than the estimators that use only labeled data. We then develop several new approaches that provably lead to improved performance. The statistical tools of minimax analysis are thus used to offer some new perspective on the problem of semi-supervised learning.

We present a new class of models for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We de- rive a method for fitting the models that is effective even when the number of covariates is larger than the sample size. A statistical analysis of the properties of SpAM is given together with empirical results on synthetic and real data, show- ing that SpAM can be effective in fitting sparse nonparametric models in high dimensional data.

Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. In this paper we study a variant of this problem where the original $n$ input variables are compressed by a random linear transformation to $m \ll n$ examples in $p$ dimensions, and establish conditions under which a sparse linear model can be successfully recovered from the compressed data. A primary motivation for this compression procedure is to anonymize the data and preserve privacy by revealing little information about the original data. We characterize the number of random projections that are required for $\ell_1$-regularized compressed regression to identify the nonzero coefficients in the true model with probability approaching one, a property called ``sparsistence.'' In addition, we show that $\ell_1$-regularized compressed regression asymptotically predicts as well as an oracle linear model, a property called ``persistence.'' Finally, we characterize the privacy properties of the compression procedure in information-theoretic terms, establishing upper bounds on the rate of information communicated between the compressed and uncompressed data that decay to zero.

A family of probabilistic time series models is developed to analyze the time evolution of topics in large document collections. The approach is to use state space models on the natural parameters of the multinomial distributions that represent the topics. Variational approximations based on Kalman filters and nonparametric wavelet regression are developed to carry out approximate posterior inference over the latent topics. In addition to giving quantitative, predictive models of a sequential corpus, dynamic topic models provide a qualitative window into the contents of a large document collection. The models are demonstrated by analyzing the OCR'ed archives of the journal Science from 1880 through 2000.

Quadratic program relaxations are proposed as an alternative to linear program relaxations and tree reweighted belief propagation for the metric labeling or MAP estimation problem. An additional convex relaxation of the quadratic approximation is shown to have additive approximation guarantees that apply even when the graph weights have mixed sign or do not come from a metric. The approximations are extended in a manner that allows tight variational relaxations of the MAP problem, although they generally involve non-convex optimization. Experiments carried out on synthetic data show that the quadratic approximations can be more accurate and computationally efficient than the linear programming and propagation based alternatives.

Graph-based methods for semi-supervised learning have recently been shown to be promising for combining labeled and unlabeled data in classification problems. However, inference for graph-based methods often does not scale well to very large data sets, since it requires inversion of a large matrix or solution of a large linear program. Moreover, such approaches are inherently transductive, giving predictions for only those points in the unlabeled set, and not for an arbitrary test point. In this paper a new approach is presented that preserves the strengths of graph-based semi-supervised learning while overcoming the limitations of scalability and non-inductive inference, through a combination of generative mixture models and discriminative regularization using the graph Laplacian. Experimental results show that this approach preserves the accuracy of purely graph-based transductive methods when the data has "manifold structure," and at the same time achieves inductive learning with significantly reduced computational cost.

Topic models, such as latent Dirichlet allocation (LDA), can be useful tools for the statistical analysis of document collections and other discrete data. The LDA model assumes that the words of each document arise from a mixture of topics, each of which is a distribution over the vocabulary. A limitation of LDA is the inability to model topic correlation even though, for example, a document about genetics is more likely to also be about disease than x-ray astronomy. This limitation stems from the use of the Dirichlet distribution to model the variability among the topic proportions. In this paper we develop the correlated topic model (CTM), where the topic proportions exhibit correlation via the logistic normal distribution [1]. We derive a mean-field variational inference algorithm for approximate posterior inference in this model, which is complicated by the fact that the logistic normal is not conjugate to the multinomial. The CTM gives a better fit than LDA on a collection of OCRed articles from the journal Science. Furthermore, the CTM provides a natural way of visualizing and exploring this and other unstructured data sets.

We present a method for nonparametric regression that performs bandwidth selection and variable selection simultaneously. The approach is based on the technique of incrementally decreasing the bandwidth in directions where the gradient of the estimator with respect to bandwidth is large. When the unknown function satisfies a sparsity condition, our approach avoids the curse of dimensionality, achieving the optimal minimax rate of convergence, up to logarithmic factors, as if the relevant variables were known in advance. The method--called rodeo (regularization of derivative expectation operator)--conducts a sequence of hypothesis tests, and is easy to implement. A modified version that replaces hard with soft thresholding effectively solves a sequence of lasso problems.

We present a family of approximation techniques for probabilistic graphical models, based on the use of graphical preconditioners developed in the scientific computing literature. Our framework yields rigorous upper and lower bounds on event probabilities and the log partition function of undirected graphical models, using non-iterative procedures that have low time complexity. As in mean field approaches, the approximations are built upon tractable subgraphs; however, we recast the problem of optimizing the tractable distribution parameters and approximate inference in terms of the well-studied linear systems problem of obtaining a good matrix preconditioner. Experiments are presented that compare the new approximation schemes to variational methods.

A family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. The kernels are based on the heat equation on the Riemannian manifold defined by the Fisher information metric associated with a statistical family, and generalize the Gaussian kernel of Euclidean space. As an important special case, kernels based on the geometry of multinomial families are derived, leading to kernel-based learning algorithms that apply naturally to discrete data. Bounds on covering numbers and Rademacher averages for the kernels are proved using bounds on the eigenvalues of the Laplacian on Riemannian manifolds. Experimental results are presented for document classification, for which the use of multinomial geometry is natural and well motivated, and improvements are obtained over the standard use of Gaussian or linear kernels, which have been the standard for text classification.

In many application domains there is a large amount of unlabeled data but only a very limited amount of labeled training data. One general approach that has been explored for utilizing this unlabeled data is to construct a graph on all the data points based on distance relationships among examples, and then to use the known labels to perform some type of graph partitioning. One natural partitioning to use is the minimum cut that agrees with the labeled data (Blum & Chawla, 2001), which can be thought of as giving the most probable label assignment if one views labels as generated according to a Markov Random Field on the graph. Zhu et al. (2003) propose a cut based on a relaxation of this field, and Joachims (2003) gives an algorithm based on finding an approximate min-ratio cut.In this paper, we extend the mincut approach by adding randomness to the graph structure. The resulting algorithm addresses several short-comings of the basic mincut approach, and can be given theoretical justification from both a Markov random field perspective and from sample complexity considerations. In cases where the graph does not have small cuts for a given classification problem, randomization may not help. However, our experiments on several datasets show that when the structure of the graph supports small cuts, this can result in highly accurate classifiers with good accuracy/coverage tradeoffs. In addition, we are able to achieve good performance with a very simple graph-construction procedure.

Kernel conditional random fields (KCRFs) are introduced as a framework for discriminative modeling of graph-structured data. A representer theorem for conditional graphical models is given which shows how kernel conditional random fields arise from risk minimization procedures defined using Mercer kernels on labeled graphs. A procedure for greedily selecting cliques in the dual representation is then proposed, which allows sparse representations. By incorporating kernels and implicit feature spaces into conditional graphical models, the framework enables semi-supervised learning algorithms for structured data through the use of graph kernels. The framework and clique selection methods are demonstrated in synthetic data experiments, and are also applied to the problem of protein secondary structure prediction.

The assumptions behind linear classifiers for categorical data are examined and reformulated in the context of the multinomial manifold, the simplex of multinomial models furnished with the Riemannian structure induced by the Fisher information. This leads to a new view of hyperplane classifiers which, together with a generalized margin concept, shows how to adapt existing margin-based hyperplane models to multinomial geometry. Experiments show the new classification framework to be effective for text classification, where the categorical structure of the data is modeled naturally within the multinomial family.

We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine la- beled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonpara- metric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is compu- tationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.

Language modeling approaches to information retrieval are attractive and promising because they connect the problem of retrieval with that of language model estimation, which has been studied extensively in other application areas such as speech recognition. The basic idea of these approaches is to estimate a language model for each document, and to then rank documents by the likelihood of the query according to the estimated language model. A central issue in language model estimation is smoothing , the problem of adjusting the maximum likelihood estimator to compensate for data sparseness. In this article, we study the problem of language model smoothing and its influence on retrieval performance. We examine the sensitivity of retrieval performance to the smoothing parameters and compare several popular smoothing methods on different test collections. Experimental results show that not only is the retrieval performance generally sensitive to the smoothing parameters, but also the sensitivity pattern is affected by the query type, with performance being more sensitive to smoothing for verbose queries than for keyword queries. Verbose queries also generally require more aggressive smoothing to achieve optimal performance. This suggests that smoothing plays two different role---to make the estimated document language model more accurate and to "explain" the noninformative words in the query. In order to decouple these two distinct roles of smoothing, we propose a two-stage smoothing strategy, which yields better sensitivity patterns and facilitates the setting of smoothing parameters automatically. We further propose methods for estimating the smoothing parameters automatically. Evaluation on five different databases and four types of queries indicates that the two-stage smoothing method with the proposed parameter estimation methods consistently gives retrieval performance that is close to---or better than---the best results achieved using a single smoothing method and exhaustive parameter search on the test data.

A new family of kernels for statistical learning is introduced that ex- ploits the geometric structure of statistical models. Based on the heat equation on the Riemannian manifold defined by the Fisher informa- tion metric, information diffusion kernels generalize the Gaussian kernel of Euclidean space, and provide a natural way of combining generative statistical modeling with non-parametric discriminative learning. As a special case, the kernels give a new approach to applying kernel-based learning algorithms to discrete data. Bounds on covering numbers for the new kernels are proved using spectral theory in differential geometry, and experimental results are presented for text classification.

A distance-based conditional model on the ranking poset is presented for use in classification and ranking. The model is an extension of the Mallows model, and generalizes the classifier combination methods used by several ensemble learning algorithms, including error correcting output codes, discrete AdaBoost, logistic regression and cranking. The algebraic structure of the ranking poset leads to a simple Bayesian inter- pretation of the conditional model and its special cases. In addition to a unifying view, the framework suggests a probabilistic interpretation for error correcting output codes and an extension beyond the binary coding scheme.

The optimal settings of retrieval parameters often depend on both the document collection and the query, and are usually found through empirical tuning. In this paper, we propose a family of two-stage language models for information retrieval that explicitly captures the different influences of the query and document collection on the optimal settings of retrieval parameters. As a special case, we present a two-stage smoothing method that allows us to estimate the smoothing parameters completely automatically. In the first stage, the document language model is smoothed using a Dirichlet prior with the collection language model as the reference model. In the second stage, the smoothed document language model is further interpolated with a query background language model. We propose a leave-one-out method for estimating the Dirichlet parameter of the first stage, and the use of document mixture models for estimating the interpolation parameter of the second stage. Evaluation on five different databases and four types of queries indicates that the two-stage smoothing method with the proposed parameter estimation methods consistently gives retrieval performance that is close to---or better than---the best results achieved using a single smoothing method and exhaustive parameter search on the test data.

The language modeling approach to retrieval has been shown to perform well empirically. One advantage of this new approach is its statistical foundations. However, feedback, as one important component in a retrieval system, has only been dealt with heuristically in this new retrieval approach: the original query is usually literally expanded by adding additional terms to it. Such expansion-based feedback creates an inconsistent interpretation of the original and the expanded query. In this paper, we present a more principled approach to feedback in the language modeling approach. Specifically, we treat feedback as updating the query language model based on the extra evidence carried by the feedback documents. Such a model-based feedback strategy easily fits into an extension of the language modeling approach. We propose and evaluate two different approaches to updating a query language model based on feedback documents, one based on a generative probabilistic model of feedback documents and one based on minimization of the KL-divergence over feedback documents. Experiment results show that both approaches are effective and outperform the Rocchio feedback approach.

We derive an equivalence between AdaBoost and the dual of a convex optimization problem, showing that the only difference between mini- mizing the exponential loss used by AdaBoost and maximum likelihood for exponential models is that the latter requires the model to be normal- ized to form a conditional probability distribution over labels. In addi- tion to establishing a simple and easily understood connection between the two methods, this framework enables us to derive new regularization procedures for boosting that directly correspond to penalized maximum likelihood. Experiments on UCI datasets support our theoretical analy- sis and give additional insight into the relationship between boosting and logistic regression.

We present a framework for information retrieval that combines document models and query models using a probabilistic ranking function based on Bayesian decision theory. The framework suggests an operational retrieval model that extends recent developments in the language modeling approach to information retrieval. A language model for each document is estimated, as well as a language model for each query, and the retrieval problem is cast in terms of risk minimization. The query language model can be exploited to model user preferences, the context of a query, synonomy and word senses. While recent work has incorporated word translation models for this purpose, we introduce a new method using Markov chains defined on a set of documents to estimate the query models. The Markov chain method has connections to algorithms from link analysis and social networks. The new approach is evaluated on TREC collections and compared to the basic language modeling approach and vector space models together with query expansion using Rocchio. Significant improvements are obtained over standard query expansion methods for strong baseline TF-IDF systems, with the greatest improvements attained for short queries on Web data.

We present a framework for designing incremental learning algorithms derived from generalized entropy functionals.Our approach is based on the use of Bregman divergences together with the associated class of additive models constructed using the Legendre transform.A particular one-parameter family of Bregman divergences is shown to yield a family of loss functions that includes the log-likelihood criterion of logistic regression as a special case, and that closely approximates the exponential loss criterion used in the AdaBoost algorithms of Schapire et a/., as the natural parameter of the family varies.We also show how the quadratic approximation of the gain in Bregman divergence results in a weighted least-squares criterion.This leads to a family of incremental learning algorithms that builds upon and extends the recent interpretation of boosting in terms of additive models proposed by Friedman, Hastie, and Tibshirani.

Article Free Access Share on Information retrieval as statistical translation Authors: Adam Berger School of Computer Science, Carnegie Mellon University, Pittsburgh, PA School of Computer Science, Carnegie Mellon University, Pittsburgh, PAView Profile , John Lafferty School of Computer Science, Carnegie Mellon University, Pittsburgh, PA School of Computer Science, Carnegie Mellon University, Pittsburgh, PAView Profile Authors Info & Claims SIGIR '99: Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrievalAugust 1999 Pages 222–229https://doi.org/10.1145/312624.312681Published:01 August 1999Publication History 393citation2,207DownloadsMetricsTotal Citations393Total Downloads2,207Last 12 Months125Last 6 weeks18 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Ordered binary decision diagrams (OBDDs) are graph-based data structures for representing Boolean functions. They have found widespread use in computer-aided design and in formal verification of digital circuits. Minimal trellises are graphical representations of error-correcting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphical models, as follows. Let /spl Cscr/ be a binary code of length n, and let f/sub c/(x/sub 1/, ..., x/sub n/) be the Boolean function that takes the value 0 at x/sub 1/, ..., x/sub n/ if and only if (x/sub 1/, ..., x/sub n/)/spl isin//spl Cscr/. Given this natural one-to-one correspondence between Boolean functions and binary codes, we prove that the minimal proper trellis for a code /spl Cscr/ with minimum distance d>1 is isomorphic to the single-terminal OBDD for its Boolean indicator function f/sub c/(x/sub 1/, ..., x/sub n/). Prior to this result, the extensive research during the past decade on binary decision diagrams (in computer engineering) and on minimal trellises (in coding theory) has been carried out independently. As outlined in this work, the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines.

This paper describes a lightweight method for the automatic insertion of intra-sentence punctuation into text. Despite the intuition that pauses in an acoustic stream are a positive indicator for some types of punctuation, this work will demonstrate the feasibility of a system which relies solely on lexical information. Besides its potential role in a speech recognition system, such a system could serve equally well in non-speech applications such as automatic grammar correction in a word processor and parsing of spoken text. After describing the design of a punctuation-restoration system, which relies on a trigram language model and a straightforward application of the Viterbi algorithm, we summarize results, both quantitative and subjective, of the performance and behavior of a prototype system.

This paper introduces new methods based on exponential families for modeling the correlations between words in text and speech. While previous work assumed the effects of word co-occurrence statistics to be constant over a window of several hundred words, we show that their influence is nonstationary on a much smaller time scale. Empirical data drawn from English and Japanese text, as well as conversational speech, reveals that the "attraction" between words decays exponentially, while stylistic and syntactic contraints create a "repulsion" between words that discourages close co-occurrence. We show that these characteristics are well described by simple mixture models based on two-stage exponential distributions which can be trained using the EM algorithm. The resulting distance distributions can then be incorporated as penalizing features in an exponential language model.

This paper introduces methods based on generalized Fourier analysis for working with a class of errorcorrecting codes constructed in terms of Cayley graphs. Our work is motivated by the recent results of Sipser and Spielman [15] showing graph expansion to be essential for efficient decoding of certain low-density parity-check codes. They leave open the problem of sub-quadratic encoding for this class of codes, and it is this problem that we address. We show that when the codes are constructed in terms of Cayley graphs, the symmetry of the graphs can be exploited by using the representation theory of the underlying group to devise a sub-quadratic encoding algorithm that, in the case where the group is PSL 2 (Z=qZ), requires O(n 4=3 ) operations, where n = O(q 3 ) is the block length. Our results indicate that this new class of codes may combine many of the strengths of two of the most powerful and successful, but previously disparate areas of coding theory: the class of cyclic codes...

We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing the Kullback-Leibler divergence between the model and the empirical distribution of the training data. A greedy algorithm determines how features are incrementally added to the field and an iterative scaling algorithm is used to estimate the optimal values of the weights. The random field models and techniques introduced in this paper differ from those common to much of the computer vision literature in that the underlying random fields are non-Markovian and have a large number of parameters that must be estimated. Relations to other learning approaches, including decision trees, are given. As a demonstration of the method, we describe its application to the problem of automatic word classification in natural language processing.

Most speech recognition systems try to reconstruct a word sequence given an acoustic input, using prior information about the language being spoken.In some cases, there is more information available to the decoder than simply the acoustics.When decoding a television news broadcast, for example, the closed-caption information that is often recorded for hearing impaired viewers may also be available.While these captions are generally not completely accurate transcriptions, they can be considered to be a strong hint as to what was actually spoken.In this paper, we present a formalization of this problem in terms of the source channel paradigm.We propose a simple translation model for mapping caption sequences to word sequences which updates the language model with the prior information inherent in the captions.We also describe an efficient implementation of the search in a Viterbi decoder, and present results using this system in the broadcast news domain.

In this paper we i n troduce a word clustering algorithm which uses a bilingual, parallel corpus to group together words in the source and target language.Our method generalizes previous mutual information clustering algorithms for monolingual data by incorporating a statistical translation model.Preliminary experiments have shown that the algorithm can e ectively employ the constraints implicit in bilingual data to extract classes which are well-suited to machine translation tasks.

We describe a generative probabilistic model of natural language, which we call HBG, that takes advantage of detailed linguistic information to resolve ambiguity. HBG incorporates lexical, syntactic, semantic, and structural information from the parse tree into the disambiguation process in a novel way. We use a corpus of bracketed sentences, called a Treebank, in combination with decision tree building to tease out the relevant aspects of a parse tree that will determine the correct parse of a sentence. This stands in contrast to the usual approach of further grammar tailoring via the usual linguistic introspection in the hope of generating the correct parse. In head-to-head tests against one of the best existing robust probabilistic parsing models, which we call P-CFG, the HBG model significantly outperforms P-CFG, increasing the parsing accuracy rate from 60% to 75%, a 37% reduction in error.

Americanae nace como un proyecto conjunto que surge dentro de la Red Europea de Información y Documentación sobre América Latina (REDIAL), y que ha afrontado la Biblioteca de la Agencia Española de Cooperación Internacional para el Desarrollo (AECID). Esta nueva biblioteca virtual hace más accesibles los libros digitales de tema americanista a los investigadores y usuarios interesados de cualquier parte del mundo.