Semantic matching is of central importance to many natural language tasks \cite{bordes2014semantic,RetrievalQA}. A successful matching algorithm needs to adequately model the internal structures of language objects and the interaction between them. As a step toward this goal, we propose convolutional neural network models for matching two sentences, by adapting the convolutional strategy in vision and speech. The proposed models not only nicely represent the hierarchical structures of sentences with their layer-by-layer composition and pooling, but also capture the rich matching patterns at different levels. Our models are rather generic, requiring no prior knowledge on language, and can hence be applied to matching tasks of different nature and in different languages. The empirical study on a variety of matching tasks demonstrates the efficacy of the proposed model on a variety of matching tasks and its superiority to competitor models.

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on either variational approximation or Monte Carlo sampling. This paper presents a novel spectral decomposition algorithm to recover the parameters of supervised latent Dirichlet allocation (sLDA) models. The Spectral-sLDA algorithm is provably correct and computationally efficient. We prove a sample complexity bound and subsequently derive a sufficient condition for the identifiability of sLDA. Thorough experiments on a diverse range of synthetic and real-world datasets verify the theory and demonstrate the practical effectiveness of the algorithm.

The global Markov property for Gaussian graphical models ensures graph separation implies conditional independence. Specifically if a node set $S$ graph separates nodes $u$ and $v$ then $X_u$ is conditionally independent of $X_v$ given $X_S$. The opposite direction need not be true, that is, $X_u \perp X_v \mid X_S$ need not imply $S$ is a node separator of $u$ and $v$. When it does, the relation $X_u \perp X_v \mid X_S$ is called faithful. In this paper we provide a characterization of faithful relations and then provide an algorithm to test faithfulness based only on knowledge of other conditional relations of the form $X_i \perp X_j \mid X_S$.

Scene recognition is one of the hallmark tasks of computer vision, allowing definition of a context for object recognition. Whereas the tremendous recent progress in object recognition tasks is due to the availability of large datasets like ImageNet and the rise of Convolutional Neural Networks (CNNs) for learning high-level features, performance at scene recognition has not attained the same level of success. This may be because current deep features trained from ImageNet are not competitive enough for such tasks. Here, we introduce a new scene-centric database called Places with over 7 million labeled pictures of scenes. We propose new methods to compare the density and diversity of image datasets and show that Places is as dense as other scene datasets and has more diversity. Using CNN, we learn deep features for scene recognition tasks, and establish new state-of-the-art results on several scene-centric datasets. A visualization of the CNN layers' responses allows us to show differences in the internal representations of object-centric and scene-centric networks.

We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response $y$, conditional on the model being selected (``condition on selection framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix $X$. Furthermore, the computational cost of marginal regression, constructing confidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit and marginal screening+Lasso."

Various factors, such as identities, views (poses), and illuminations, are coupled in face images. Disentangling the identity and view representations is a major challenge in face recognition. Existing face recognition systems either use handcrafted features or learn features discriminatively to improve recognition accuracy. This is different from the behavior of human brain. Intriguingly, even without accessing 3D data, human not only can recognize face identity, but can also imagine face images of a person under different viewpoints given a single 2D image, making face perception in the brain robust to view changes. In this sense, human brain has learned and encoded 3D face models from 2D images. To take into account this instinct, this paper proposes a novel deep neural net, named multi-view perceptron (MVP), which can untangle the identity and view features, and infer a full spectrum of multi-view images in the meanwhile, given a single 2D face image. The identity features of MVP achieve superior performance on the MultiPIE dataset. MVP is also capable to interpolate and predict images under viewpoints that are unobserved in the training data.

Developments in neural recording technology are rapidly enabling the recording of populations of neurons in multiple brain areas simultaneously, as well as the identification of the types of neurons being recorded (e.g., excitatory vs. inhibitory). There is a growing need for statistical methods to study the interaction among multiple, labeled populations of neurons. Rather than attempting to identify direct interactions between neurons (where the number of interactions grows with the number of neurons squared), we propose to extract a smaller number of latent variables from each population and study how the latent variables interact. Specifically, we propose extensions to probabilistic canonical correlation analysis (pCCA) to capture the temporal structure of the latent variables, as well as to distinguish within-population dynamics from across-population interactions (termed Group Latent Auto-Regressive Analysis, gLARA). We then applied these methods to populations of neurons recorded simultaneously in visual areas V1 and V2, and found that gLARA provides a better description of the recordings than pCCA. This work provides a foundation for studying how multiple populations of neurons interact and how this interaction supports brain function.

We develop a fast algorithm for the Admixture of Poisson MRFs (APM) topic model and propose a novel metric to directly evaluate this model. The APM topic model recently introduced by Inouye et al. (2014) is the first topic model that allows for word dependencies within each topic unlike in previous topic models like LDA that assume independence between words within a topic. Research in both the semantic coherence of a topic models (Mimno et al. 2011, Newman et al. 2010) and measures of model fitness (Mimno & Blei 2011) provide strong support that explicitly modeling word dependencies---as in APM---could be both semantically meaningful and essential for appropriately modeling real text data. Though APM shows significant promise for providing a better topic model, APM has a high computational complexity because $O(p^2)$ parameters must be estimated where $p$ is the number of words (Inouye et al. could only provide results for datasets with $p = 200$). In light of this, we develop a parallel alternating Newton-like algorithm for training the APM model that can handle $p = 10^4$ as an important step towards scaling to large datasets. In addition, Inouye et al. only provided tentative and inconclusive results on the utility of APM. Thus, motivated by simple intuitions and previous evaluations of topic models, we propose a novel evaluation metric based on human evocation scores between word pairs (i.e. how much one word brings to mind" another word (Boyd-Graber et al. 2006)). We provide compelling quantitative and qualitative results on the BNC corpus that demonstrate the superiority of APM over previous topic models for identifying semantically meaningful word dependencies. (MATLAB code available at: http://bigdata.ices.utexas.edu/software/apm/)"

Lifted inference algorithms for probabilistic first-order logic frameworks such as Markov logic networks (MLNs) have received significant attention in recent years. These algorithms use so called lifting rules to identify symmetries in the first-order representation and reduce the inference problem over a large probabilistic model to an inference problem over a much smaller model. In this paper, we present two new lifting rules, which enable fast MAP inference in a large class of MLNs. Our first rule uses the concept of single occurrence equivalence class of logical variables, which we define in the paper. The rule states that the MAP assignment over an MLN can be recovered from a much smaller MLN, in which each logical variable in each single occurrence equivalence class is replaced by a constant (i.e., an object in the domain of the variable). Our second rule states that we can safely remove a subset of formulas from the MLN if all equivalence classes of variables in the remaining MLN are single occurrence and all formulas in the subset are tautology (i.e., evaluate to true) at extremes (i.e., assignments with identical truth value for groundings of a predicate). We prove that our two new rules are sound and demonstrate via a detailed experimental evaluation that our approach is superior in terms of scalability and MAP solution quality to the state of the art approaches.

The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit the structure of problems. BADMM provides a unified framework for ADMM and its variants, including generalized ADMM, inexact ADMM and Bethe ADMM. We establish the global convergence and the $O(1/T)$ iteration complexity for BADMM. In some cases, BADMM can be faster than ADMM by a factor of $O(n/\ln n)$ where $n$ is the dimensionality. In solving the linear program of mass transportation problem, BADMM leads to massive parallelism and can easily run on GPU. BADMM is several times faster than highly optimized commercial software Gurobi.