We describe a novel method for learning templates for recognition and localization of objects drawn from categories. A generative model represents the configuration of multiple object parts with respect to an object coordinate system; these parts in turn generate image features. The complexity of the model in the number of features is low, meaning our model is much more efficient to train than comparative methods. Moreover, a variational approximation is introduced that allows learning to be orders of magnitude faster than previous approaches while incorporating many more features.

We extend radial basis function (RBF) networks to the scenario in which multiple correlated tasks are learned simultaneously, and present the corresponding learning algorithms. We develop the algorithms for learning the network structure, in either a supervised or unsupervised manner. Training data may also be actively selected to improve the network's generalization to test data. Experimental results based on real data demonstrate the advantage of the proposed algorithms and support our conclusions.

We argue that when objects are characterized by many attributes, clustering them on the basis of a relatively small random subset of these attributes can capture information on the unobserved attributes as well. Moreover, we show that under mild technical conditions, clustering the objects on the basis of such a random subset performs almost as well as clustering with the full attribute set. We prove a finite sample generalization theorems for this novel learning scheme that extends analogous results from the supervised learning setting. The scheme is demonstrated for collaborative filtering of users with movies rating as attributes.

Given a directed graphical model with binary-valued hidden nodes and real-valued noisy observations, consider deciding upon the maximum a-posteriori (MAP) or the maximum posterior-marginal (MPM) assignment under the restriction that each node broadcasts only to its children exactly one single-bit message. We present a variational formulation, viewing the processing rules local to all nodes as degrees-of-freedom, that minimizes the loss in expected (MAP or MPM) performance subject to such online communication constraints. The approach leads to a novel message-passing algorithm to be executed offline, or before observations are realized, which mitigates the performance loss by iteratively coupling all rules in a manner implicitly driven by global statistics. We also provide (i) illustrative examples, (ii) assumptions that guarantee convergence and efficiency and (iii) connections to active research areas.

Fisher linear discriminant analysis (LDA) can be sensitive to the problem data. Robust Fisher LDA can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a classification problem and optimizing for the worst-case scenario under this model. The main contribution of this paper is show that with general convex uncertainty models on the problem data, robust Fisher LDA can be carried out using convex optimization. For a certain type of product form uncertainty model, robust Fisher LDA can be carried out at a cost comparable to standard Fisher LDA. The method is demonstrated with some numerical examples. Finally, we show how to extend these results to robust kernel Fisher discriminant analysis, i.e., robust Fisher LDA in a high dimensional feature space.

Linear implementations of the efficient coding hypothesis, such as independent component analysis (ICA) and sparse coding models, have provided functional explanations for properties of simple cells in V1 [1, 2]. These models, however, ignore the nonlinear behavior of neurons and fail to match individual and population properties of neural receptive fields in subtle but important ways. Hierarchical models, including Gaussian Scale Mixtures [3, 4] and other generative statistical models [5, 6], can capture higher-order regularities in natural images and explain nonlinear aspects of neural processing such as normalization and context effects [6,7]. Previously, it had been assumed that the lower level representation is independent of the hierarchy, and had been fixed when training these models. Here we examine the optimal lower-level representations derived in the context of a hierarchical model and find that the resulting representations are strikingly different from those based on linear models. Unlike the the basis functions and filters learned by ICA or sparse coding, these functions individually more closely resemble simple cell receptive fields and collectively span a broad range of spatial scales. Our work unifies several related approaches and observations about natural image structure and suggests that hierarchical models might yield better representations of image structure throughout the hierarchy.

For this purpose, we propose a stochastic procedure, the mirror descent, which performs gradient descent in the dual space. The generated estimates are additionally averaged in a recursive fashion with specific weights. Mirror descent algorithms have been developed in different contexts and they are known to be particularly efficient in high dimensional problems. Moreover their implementation is adapted to the online setting. The main result of the paper is the upper bound on the convergence rate for the generalization error.

We introduce a new model of genetic diversity which summarizes a large input dataset into an epitome, a short sequence or a small set of short sequences of probability distributions capturing many overlapping subsequences from the dataset. The epitome as a representation has already been used in modeling real-valued signals, such as images and audio. The discrete sequence model we introduce in this paper targets applications in genetics, from multiple alignment to recombination and mutation inference. In our experiments, we concentrate on modeling the diversity of HIV where the epitome emerges as a natural model for producing relatively small vaccines covering a large number of immune system targets known as epitopes. Our experiments show that the epitome includes more epitopes than other vaccine designs of similar length, including cocktails of consensus strains, phylogenetic tree centers, and observed strains. We also discuss epitome designs that take into account uncertainty about T-cell cross reactivity and epitope presentation. In our experiments, we find that vaccine optimization is fairly robust to these uncertainties.

This paper presents a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose correlations between variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlations. We provide a walk-sum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. This perspective leads to a better understanding of Gaussian belief propagation and of its convergence in loopy graphs.

Spectral clustering enjoys its success in both data clustering and semisupervised learning. But, most spectral clustering algorithms cannot handle multi-class clustering problems directly. Additional strategies are needed to extend spectral clustering algorithms to multi-class clustering problems. Furthermore, most spectral clustering algorithms employ hard cluster membership, which is likely to be trapped by the local optimum. In this paper, we present a new spectral clustering algorithm, named "Soft Cut". It improves the normalized cut algorithm by introducing soft membership, and can be efficiently computed using a bound optimization algorithm. Our experiments with a variety of datasets have shown the promising performance of the proposed clustering algorithm.