Probabilistic approaches to computer vision typically assume a centralized setting, with the algorithm granted access to all observed data points. However, many problems in wide-area surveillance can benefit from distributed modeling, either because of physical or computational constraints. Most distributed models to date use algebraic approaches (such as distributed SVD) and as a result cannot explicitly deal with missing data. In this work we present an approach to estimation and learning of generative probabilistic models in a distributed context where certain sensor data can be missing. In particular, we show how traditional centralized models, such as probabilistic PCA and missing-data PPCA, can be learned when the data is distributed across a network of sensors. We demonstrate the utility of this approach on the problem of distributed affine structure from motion. Our experiments suggest that the accuracy of the learned probabilistic structure and motion models rivals that of traditional centralized factorization methods while being able to handle challenging situations such as missing or noisy observations.

This paper proposes a novel image representation called a Graphical Gaussian Vector (GGV), which is a counterpart of the codebook and local feature matching approaches. We model the distribution of local features as a Gaussian Markov Random Field (GMRF) which can efficiently represent the spatial relationship among local features. Using concepts of information geometry, proper parameters and a metric from the GMRF can be obtained. Then we define a new image feature by embedding the proper metric into the parameters, which can be directly applied to scalable linear classifiers. We show that the GGV obtains better performance over the state-of-the-art methods in the standard object recognition datasets and comparable performance in the scene dataset.

Nonnegative Matrix Factorization (NMF) is a promising relaxation technique for clustering analysis. However, conventional NMF methods that directly approximate the pairwise similarities using the least square error often yield mediocre performance for data in curved manifolds because they can capture only the immediate similarities between data samples. Here we propose a new NMF clustering method which replaces the approximated matrix with its smoothed version using random walk. Our method can thus accommodate farther relationships between data samples. Furthermore, we introduce a novel regularization in the proposed objective function in order to improve over spectral clustering. The new learning objective is optimized by a multiplicative Majorization-Minimization algorithm with a scalable implementation for learning the factorizing matrix. Extensive experimental results on real-world datasets show that our method has strong performance in terms of cluster purity.

Characterizing the information carried by neural populations in the brain requires accurate statistical models of neural spike responses. The negative-binomial distribution provides a convenient model for over-dispersed spike counts, that is, responses with greater-than-Poisson variability. Here we describe a powerful data-augmentation framework for fully Bayesian inference in neural models with negative-binomial spiking. Our approach relies on a recently described latentvariable representation of the negative-binomial distribution, which equates it to a Polya-gamma mixture of normals. This framework provides a tractable, conditionally Gaussian representation of the posterior that can be used to design efficient EM and Gibbs sampling based algorithms for inference in regression and dynamic factor models. We apply the model to neural data from primate retina and show that it substantially outperforms Poisson regression on held-out data, and reveals latent structure underlying spike count correlations in simultaneously recorded spike trains.

In this paper, we consider the problem of clustering data points into lowdimensional subspaces in the presence of outliers. We pose the problem using a density estimation formulation with an associated generative model. Based on this probability model, we first develop an iterative expectation-maximization (EM) algorithm and then derive its global solution. In addition, we develop two Bayesian methods based on variational Bayesian (VB) approximation, which are capable of automatic dimensionality selection. While the first method is based on an alternating optimization scheme for all unknowns, the second method makes use of recent results in VB matrix factorization leading to fast and effective estimation. Both methods are extended to handle sparse outliers for robustness and can handle missing values. Experimental results suggest that proposed methods are very effective in subspace clustering and identifying outliers.

We propose a randomized, active sampling scheme for estimating such functions with uniform approximation guarantees. Our theoretical developments leverage recent techniques from low rank matrix recovery, which enables us to derive an estimator of the function f along with sample complexity bounds. We also characterize the noise robustness of the scheme, and provide empirical evidence that the highdimensional scaling of our sample complexity bounds are quite accurate.

We describe a new model for learning meaningful representations of text documents from an unlabeled collection of documents. This model is inspired by the recently proposed Replicated Softmax, an undirected graphical model of word counts that was shown to learn a better generative model and more meaningful document representations. Specifically, we take inspiration from the conditional mean-field recursive equations of the Replicated Softmax in order to define a neural network architecture that estimates the probability of observing a new word in a given document given the previously observed words. This paradigm also allows us to replace the expensive softmax distribution over words with a hierarchical distribution over paths in a binary tree of words. The end result is a model whose training complexity scales logarithmically with the vocabulary size instead of linearly as in the Replicated Softmax. Our experiments show that our model is competitive both as a generative model of documents and as a document representation learning algorithm.

We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for k-means in two separate directions. First, we provide new results for k-means reconstruction on manifolds and, secondly, we prove reconstruction bounds for higher-order approximation (k-flats), for which no known results were previously available. While the results for k-means are novel, some of the technical tools are well-established in the literature. In the case of k-flats, both the results and the mathematical tools are new.

We present a new model based on Gaussian processes (GPs) for learning pairwise preferences expressed by multiple users. Inference is simplified by using a preference kernel for GPs which allows us to combine supervised GP learning of user preferences with unsupervised dimensionality reduction for multi-user systems. The model not only exploits collaborative information from the shared structure in user behavior, but may also incorporate user features if they are available. Approximate inference is implemented using a combination of expectation propagation and variational Bayes. Finally, we present an efficient active learning strategy for querying preferences. The proposed technique performs favorably on real-world data against state-of-the-art multi-user preference learning algorithms.

We advocate the use of a new distribution family--the transelliptical--for robust inference of high dimensional graphical models. The transelliptical family is an extension of the nonparanormal family proposed by Liu et al. (2009). Just as the nonparanormal extends the normal by transforming the variables using univariate functions, the transelliptical extends the elliptical family in the same way. We propose a nonparametric rank-based regularization estimator which achieves the parametric rates of convergence for both graph recovery and parameter estimation. Such a result suggests that the extra robustness and flexibility obtained by the semiparametric transelliptical modeling incurs almost no efficiency loss. We also discuss the relationship between this work with the transelliptical component analysis proposed by Han and Liu (2012).