We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. At the same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments.

We extend position and phase-shift tuning, concepts already well established in the disparity energy neuron literature, to motion energy neurons. We show that Reichardt-like detectors can be considered examples of position tuning, and that motion energy filters whose complex valued spatiotemporal receptive fields are space-time separable can be considered examples of phase tuning. By combining these two types of detectors, we obtain an architecture for constructing motion energy neurons whose center frequencies can be adjusted by both phase and position shifts. Similar to recently described neurons in the primary visual cortex, these new motion energy neurons exhibit tuning that is between purely spacetime separable and purely speed tuned. We propose a functional role for this intermediate level of tuning by demonstrating that comparisons between pairs of these motion energy neurons can reliably discriminate between inputs whose velocities lie above or below a given reference velocity.

Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a significant challenge in clustering large data sets into many clusters. In this paper, we present a different approach to approximate mixture fitting for clustering. We introduce an exemplar-based likelihood function that approximates the exact likelihood. This formulation leads to a convex minimization problem and an efficient algorithm with guaranteed convergence to the globally optimal solution. The resulting clustering can be thought of as a probabilistic mapping of the data points to the set of exemplars that minimizes the average distance and the information-theoretic cost of mapping.

Statistical models on full and partial rankings of n items are often of limited practical use for large n due to computational consideration. We explore the use of nonparametric models for partially ranked data and derive efficient procedures for their use for large n. The derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings. In particular, we demonstrate for the first time a nonparametric coherent and consistent model capable of efficiently aggregating partially ranked data of different types.

The classical hypothesis, that bottom-up saliency is a center-surround process, is combined with a more recent hypothesis that all saliency decisions are optimal in a decision-theoretic sense. The combined hypothesis is denoted as discriminant center-surround saliency, and the corresponding optimal saliency architecture is derived. This architecture equates the saliency of each image location to the discriminant power of a set of features with respect to the classification problem that opposes stimuli at center and surround, at that location. It is shown that the resulting saliency detector makes accurate quantitative predictions for various aspects of the psychophysics of human saliency, including non-linear properties beyond the reach of previous saliency models. Furthermore, it is shown that discriminant center-surround saliency can be easily generalized to various stimulus modalities (such as color, orientation and motion), and provides optimal solutions for many other saliency problems of interest for computer vision. Optimal solutions, under this hypothesis, are derived for a number of the former (including static natural images, dense motion fields, and even dynamic textures), and applied to a number of the latter (the prediction of human eye fixations, motion-based saliency in the presence of ego-motion, and motion-based saliency in the presence of highly dynamic backgrounds). In result, discriminant saliency is shown to predict eye fixations better than previous models, and produce background subtraction algorithms that outperform the state-of-the-art in computer vision.

Fair discriminative pedestrian finders are now available. In fact, these pedestrian finders make most errors on pedestrians in configurations that are uncommon in the training data, for example, mounting a bicycle. This is undesirable. However, the human configuration can itself be estimated discriminatively using structure learning. We demonstrate a pedestrian finder which first finds the most likely human pose in the window using a discriminative procedure trained with structure learning on a small dataset. We then present features (local histogram of oriented gradient and local PCA of gradient) based on that configuration to an SVM classifier. We show, using the INRIA Person dataset, that estimates of configuration significantly improve the accuracy of a discriminative pedestrian finder.

This contribution develops a theoretical framework that takes into account the effect of approximate optimization on learning algorithms. The analysis shows distinct tradeoffs for the case of small-scale and large-scale learning problems. Small-scale learning problems are subject to the usual approximation--estimation tradeoff. Large-scale learning problems are subject to a qualitatively different tradeoff involving the computational complexity of the underlying optimization algorithms in non-trivial ways.

Clustering is often formulated as a discrete optimization problem. The objective is to find, among all partitions of the data set, the best one according to some quality measure. However, in the statistical setting where we assume that the finite data set has been sampled from some underlying space, the goal is not to find the best partition of the given sample, but to approximate the true partition of the underlying space.We argue that the discrete optimization approach usually does not achieve this goal. As an alternative, we suggest the paradigm of "nearest neighbor clustering". Instead of selecting the best out of all partitions of the sample, it only considers partitions in some restricted function class. Using tools from statistical learning theory we prove that nearest neighbor clustering is statistically consistent. Moreover,its worst case complexity is polynomial by construction, and it can be implemented with small average case complexity using branch and bound.

In this paper, we consider collaborative filtering as a ranking problem. We present a method which uses Maximum Margin Matrix Factorization and optimizes ranking insteadof rating. We employ structured output prediction to optimize directly for ranking scores. Experimental results show that our method gives very good ranking scores and scales well on collaborative filtering tasks.

We provide a provably efficient algorithm for learning Markov Decision Processes (MDPs) with continuous state and action spaces in the online setting. Specifically, we take a model-based approach and show that a special type of online linear regression allows us to learn MDPs with (possibly kernalized) linearly parameterized dynamics. This result builds on Kearns and Singh's work that provides a provably efficient algorithm for finite state MDPs. Our approach is not restricted to the linear setting, and is applicable to other classes of continuous MDPs.