Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep neural network methods. These approaches seek maximally correlated projections among families of functions, which the user specifies (by choosing a kernel or neural network structure), and are computationally demanding. Interestingly, the theory of nonlinear CCA, without functional restrictions, had been studied in the population setting by Lancaster already in the 1950s, but these results have not inspired practical algorithms. We revisit Lancaster's theory to devise a practical algorithm for nonparametric CCA (NCCA). Specifically, we show that the solution can be expressed in terms of the singular value decomposition of a certain operator associated with the joint density of the views. Thus, by estimating the population density from data, NCCA reduces to solving an eigenvalue system, superficially like kernel CCA but, importantly, without requiring the inversion of any kernel matrix. We also derive a partially linear CCA (PLCCA) variant in which one of the views undergoes a linear projection while the other is nonparametric. Using a kernel density estimate based on a small number of nearest neighbors, our NCCA and PLCCA algorithms are memory-efficient, often run much faster, and perform better than kernel CCA and comparable to deep CCA.

It is becoming increasingly important for machine learning methods to make predictions that are interpretable as well as accurate. In many practical applications, it is of interest which features and feature interactions are relevant to the prediction task. We present a novel method, Selective Bayesian Forest Classifier, that strikes a balance between predictive power and interpretability by simultaneously performing classification, feature selection, feature interaction detection and visualization. It builds parsimonious yet flexible models using tree-structured Bayesian networks, and samples an ensemble of such models using Markov chain Monte Carlo. We build in feature selection by dividing the trees into two groups according to their relevance to the outcome of interest. Our method performs competitively on classification and feature selection benchmarks in low and high dimensions, and includes a visualization tool that provides insight into relevant features and interactions.

The stochastic block model (SBM) is a generative model revealing macroscopic structures in graphs. Bayesian methods are used for (i) cluster assignment inference and (ii) model selection for the number of clusters. In this paper, we study the behavior of Bayesian inference in the SBM in the large sample limit. Combining variational approximation and Laplace's method, a consistent criterion of the fully marginalized log-likelihood is established. Based on that, we derive a tractable algorithm that solves tasks (i) and (ii) concurrently, obviating the need for an outer loop to check all model candidates. Our empirical and theoretical results demonstrate that our method is scalable in computation, accurate in approximation, and concise in model selection.

Multinomial probit (MNP) model for discrete choice modeling is often used in economics, market research, political sciences and transportation. It models the choices made by agents given their demographic characteristics and/or the features of the K 2 available choice alternatives. Examples include the study of consumer's purchasing behavior (e.g., McCulloch et al. (2000); Imai and van Dyk (2005)); voting behavior in multi-party elections (e.g., Quinn et al. (1999)); and choice of different modes of transportation (e.g., Bolduc (1999)). Details of the MNP model in which choices depend on predictors in a linear fashion is studied in McFadden et al.(1973); McFadden(1989); Keane(1992); McCulloch and Rossi (1994); Nobile (1998); McCulloch et al. (2000); Imai and van Dyk (2005); Train (2009); Burgette and Nordheim (2012) among others. Among widely used multinomial choice modeling procedures are the multinomial logit model (e.g., McFadden et al. (1973); Train (2009)) and multinomial probit model (e.g., McFadden (1989); McCulloch and Rossi (1994); Imai and van Dyk (2005)). The former relies on an assumption that a choice outcome is independent of removal (or introduction) of an irrelevant choice alternative while the latter including MPBART does not make this restrictive assumption.

We show how deep learning methods can be applied in the context of crowdsourcing and unsupervised ensemble learning. First, we prove that the popular model of Dawid and Skene, which assumes that all classifiers are conditionally independent, is {\em equivalent} to a Restricted Boltzmann Machine (RBM) with a single hidden node. Hence, under this model, the posterior probabilities of the true labels can be instead estimated via a trained RBM. Next, to address the more general case, where classifiers may strongly violate the conditional independence assumption, we propose to apply RBM-based Deep Neural Net (DNN). Experimental results on various simulated and real-world datasets demonstrate that our proposed DNN approach outperforms other state-of-the-art methods, in particular when the data violates the conditional independence assumption.

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to {\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the problem of finding an assignment to the variables in {\Phi} that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.

Word representations induced from models with discrete latent variables (e.g.\ HMMs) have been shown to be beneficial in many NLP applications. In this work, we exploit labeled syntactic dependency trees and formalize the induction problem as unsupervised learning of tree-structured hidden Markov models. Syntactic functions are used as additional observed variables in the model, influencing both transition and emission components. Such syntactic information can potentially lead to capturing more fine-grain and functional distinctions between words, which, in turn, may be desirable in many NLP applications. We evaluate the word representations on two tasks -- named entity recognition and semantic frame identification. We observe improvements from exploiting syntactic function information in both cases, and the results rivaling those of state-of-the-art representation learning methods. Additionally, we revisit the relationship between sequential and unlabeled-tree models and find that the advantage of the latter is not self-evident.

When data analysts train a classifier and check if its accuracy is significantly different from random guessing, they are implicitly and indirectly performing a hypothesis test (two sample testing) and it is of importance to ask whether this indirect method for testing is statistically optimal or not. Given that hypothesis tests attempt to maximize statistical power subject to a bound on the allowable false positive rate, while prediction attempts to minimize statistical risk on future predictions on unseen data, we wish to study whether a predictive approach for an ultimate aim of testing is prudent. We formalize this problem by considering the two-sample mean-testing setting where one must determine if the means of two Gaussians (with known and equal covariance) are the same or not, but the analyst indirectly does so by checking whether the accuracy achieved by Fisher's LDA classifier is significantly different from chance or not. Unexpectedly, we find that the asymptotic power of LDA's sample-splitting classification accuracy is actually minimax rate-optimal in terms of problem-dependent parameters. Since prediction is commonly thought to be harder than testing, it might come as a surprise to some that solving a harder problem does not create a information-theoretic bottleneck for the easier one. On the flip side, even though the power is rate-optimal, our derivation suggests that it may be worse by a small constant factor; hence practitioners must be wary of using (admittedly flexible) prediction methods on disguised testing problems.

We propose a general framework for sequential and dynamic acquisition of useful information in order to solve a particular task. While our goal could in principle be tackled by general reinforcement learning, our particular setting is constrained enough to allow more efficient algorithms. In this paper, we work under the Learning to Search framework and show how to formulate the goal of finding a dynamic information acquisition policy in that framework. We apply our formulation on two tasks, sentiment analysis and image recognition, and show that the learned policies exhibit good statistical performance. As an emergent byproduct, the learned policies show a tendency to focus on the most prominent parts of each instance and give harder instances more attention without explicitly being trained to do so.

Contrary to the situation with stochastic gradient descent, we argue that when using stochastic methods with variance reduction, such as SDCA, SAG or SVRG, as well as their variants, it could be beneficial to reuse previously used samples instead of fresh samples, even when fresh samples are available. We demonstrate this empirically for SDCA, SAG and SVRG, studying the optimal sample size one should use, and also uncover be-havior that suggests running SDCA for an integer number of epochs could be wasteful.