Links between probabilistic and non-probabilistic learning algorithms can arise by performing small-variance asymptotics, i.e., letting the variance of particular distributions in a graphical model go to zero. For instance, in the context of clustering, such an approach yields precise connections between the k-means and EM algorithms. In this paper, we explore small-variance asymptotics for exponential family Dirichlet process (DP) and hierarchical Dirichlet process (HDP) mixture models. Utilizing connections between exponential family distributions and Bregman divergences, we derive novel clustering algorithms from the asymptotic limit of the DP and HDP mixtures that feature the scalability of existing hard clustering methods as well as the flexibility of Bayesian nonparametric models. We focus on special cases of our analysis for discrete-data problems, including topic modeling, and we demonstrate the utility of our results by applying variants of our algorithms to problems arising in vision and document analysis.

Hashing-based methods provide a very promising approach to large-scale similarity search. To obtain compact hash codes, a recent trend seeks to learn the hash functions from data automatically. In this paper, we study hash function learning in the context of multimodal data. We propose a novel multimodal hash function learning method, called Co-Regularized Hashing (CRH), based on a boosted co-regularization framework. The hash functions for each bit of the hash codes are learned by solving DC (difference of convex functions) programs, while the learning for multiple bits proceeds via a boosting procedure so that the bias introduced by the hash functions can be sequentially minimized. We empirically compare CRH with two state-of-the-art multimodal hash function learning methods on two publicly available data sets.

This paper is concerned with the statistical consistency of ranking methods. Recently, it was proven that many commonly used pairwise ranking methods are inconsistent with the weighted pairwise disagreement loss (WPDL), which can be viewed as the true loss of ranking, even in a low-noise setting. This result is interesting but also surprising, given that the pairwise ranking methods have been shown very effective in practice. In this paper, we argue that the aforementioned result might not be conclusive, depending on what kind of assumptions are used. We give a new assumption that the labels of objects to rank lie in a rank-differentiable probability space (RDPS), and prove that the pairwise ranking methods become consistent with WPDL under this assumption. What is especially inspiring is that RDPS is actually not stronger than but similar to the low-noise setting. Our studies provide theoretical justifications of some empirical findings on pairwise ranking methods that are unexplained before, which bridge the gap between theory and applications.

Topic modeling is a widely used approach to analyzing large text collections. A small number of multilingual topic models have recently been explored to discover latent topics among parallel or comparable documents, such as in Wikipedia. Other topic models that were originally proposed for structured data are also applicable to multilingual documents. Correspondence Latent Dirichlet Allocation (CorrLDA) is one such model; however, it requires a pivot language to be specified in advance. We propose a new topic model, Symmetric Correspondence LDA (SymCorrLDA), that incorporates a hidden variable to control a pivot language, in an extension of CorrLDA. We experimented with two multilingual comparable datasets extracted from Wikipedia and demonstrate that SymCorrLDA is more effective than some other existing multilingual topic models.

The variational Bayesian (VB) approach is one of the best tractable approximations to the Bayesian estimation, and it was demonstrated to perform well in many applications. However, its good performance was not fully understood theoretically. For example, VB sometimes produces a sparse solution, which is regarded as a practical advantage of VB, but such sparsity is hardly observed in the rigorous Bayesian estimation. In this paper, we focus on probabilistic PCA and give more theoretical insight into the empirical success of VB. More specifically, for the situation where the noise variance is unknown, we derive a sufficient condition for perfect recovery of the true PCA dimensionality in the large-scale limit when the size of an observed matrix goes to infinity. In our analysis, we obtain bounds for a noise variance estimator and simple closed-form solutions for other parameters, which themselves are actually very useful for better implementation of VB-PCA.

Hierarchical Hidden Markov Models (HHMMs) are sophisticated stochastic models that enable us to capture a hierarchical context characterization of sequence data. However, existing HHMM parameter estimation methods require large computations of time complexity O(TN^{2D}) at least for model inference, where D is the depth of the hierarchy, N is the number of states in each level, and T is the sequence length. In this paper, we propose a new inference method of HHMMs for which the time complexity is O(TN^{D+1}). A key idea of our algorithm is application of the forward-backward algorithm to ''state activation probabilities''. The notion of a state activation, which offers a simple formalization of the hierarchical transition behavior of HHMMs, enables us to conduct model inference efficiently. We present some experiments to demonstrate that our proposed method works more efficiently to estimate HHMM parameters than do some existing methods such as the flattening method and Gibbs sampling method.

We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.

We propose a novel kernel approach to dimension reduction for supervised learning: feature extraction and variable selection; the former constructs a small number of features from predictors, and the latter finds a subset of predictors. First, a method of linear feature extraction is proposed using the gradient of regression function, based on the recent development of the kernel method. In comparison with other existing methods, the proposed one has wide applicability without strong assumptions on the regressor or type of variables, and uses computationally simple eigendecomposition, thus applicable to large data sets. Second, in combination of a sparse penalty, the method is extended to variable selection, following the approach by Chen et al. (2010). Experimental results show that the proposed methods successfully find effective features and variables without parametric models.

Label space dimension reduction (LSDR) is an efficient and effective paradigm for multi-label classification with many classes. Existing approaches to LSDR, such as compressive sensing and principal label space transformation, exploit only the label part of the dataset, but not the feature part. In this paper, we propose a novel approach to LSDR that considers both the label and the feature parts. The approach, called conditional principal label space transformation, is based on minimizing an upper bound of the popular Hamming loss. The minimization step of the approach can be carried out efficiently by a simple use of singular value decomposition. In addition, the approach can be extended to a kernelized version that allows the use of sophisticated feature combinations to assist LSDR. The experimental results verify that the proposed approach is more effective than existing ones to LSDR across many real-world datasets.

This paper proposes a novel image representation called a Graphical Gaussian Vector, which is a counterpart of the codebook and local feature matching approaches. In our method, we model the distribution of local features as a Gaussian Markov Random Field (GMRF) which can efficiently represent the spatial relationship among local features. We consider the parameter of GMRF as a feature vector of the image. Using concepts of information geometry, proper parameters and a metric from the GMRF can be obtained. Finally we define a new image feature by embedding the metric into the parameters, which can be directly applied to scalable linear classifiers. Our method obtains superior performance over the state-of-the-art methods in the standard object recognition datasets and comparable performance in the scene dataset. As the proposed method simply calculates the local auto-correlations of local features, it is able to achieve both high classification accuracy and high efficiency.