We introduce a novel adaptive nonparametric anomaly detection approach, called GEM, that is based on the minimal covering properties of K-point entropic graphs when constructed on N training samples from a nominal probability distribution. Such graphs have the property that as N their span recovers the entropy minimizing set that supports at least ρ K/N(100)% of the mass of the Lebesgue part of the distribution. When a test sample falls outside of the entropy minimizing set an anomaly can be declared at a statistical level of significance α 1 ρ. A method for implementing this nonparametric anomaly detector is proposed that approximates this minimum entropy set by the influence region of a K-point entropic graph built on the training data. By implementing an incremental leave-one-out k-nearest neighbor graph on resampled subsets of the training data GEM can efficiently detect outliers at a given level of significance and compute their empirical p-values. We illustrate GEM for several simulated and real data sets in high dimensional feature spaces.

Pyramid intersection is an efficient method for computing an approximate partial matching between two sets of feature vectors. We introduce a novel pyramid embedding based on a hierarchy of non-uniformly shaped bins that takes advantage of the underlying structure of the feature space and remains accurate even for sets with high-dimensional feature vectors. The matching similarity is computed in linear time and forms a Mercer kernel. Whereas previous matching approximation algorithms suffer from distortion factors that increase linearly with the feature dimension, we demonstrate that our approach can maintain constant accuracy even as the feature dimension increases. When used as a kernel in a discriminative classifier, our approach achieves improved object recognition results over a state-of-the-art set kernel.

A number of exact and approximate methods are available for inference calculations in graphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models. The resulting algorithm also allows for the estimation of marginals. We compare our planar decomposition to the tree decomposition method of Wainwright et.

By adopting Gaussian process priors a fully Bayesian solution to the problem of integrating possibly heterogeneous data sets within a classification setting is presented. Approximate inference schemes employing Variational & Expectation Propagation based methods are developed and rigorously assessed. We demonstrate our approach to integrating multiple data sets on a large scale protein fold prediction problem where we infer the optimal combinations of covariance functions and achieve state-of-the-art performance without resorting to any ad hoc parameter tuning and classifier combination.

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate this gradient. Since Monte Carlo methods tend to have high variance, a large number of samples is required, resulting in slow convergence. In this paper, we propose a Bayesian framework that models the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient as well as a measure of the uncertainty in the gradient estimates are provided at little extra cost.

We present a generalization of dynamic Bayesian networks to concisely describe complex probability distributions such as in problems with multiple interacting variable-length streams of random variables. Our framework incorporates recent graphical model constructs to account for existence uncertainty, value-specific independence, aggregation relationships, and local and global constraints, while still retaining a Bayesian network interpretation and efficient inference and learning techniques. We introduce one such general technique, which is an extension of Value Elimination, a backtracking search inference algorithm. Multi-dynamic Bayesian networks are motivated by our work on Statistical Machine Translation (MT). We present results on MT word alignment in support of our claim that MDBNs are a promising framework for the rapid prototyping of new MT systems.

In this paper we introduce and experiment with a framework for learning local perceptual distance functions for visual recognition. We learn a distance function for each training image as a combination of elementary distances between patch-based visual features. We apply these combined local distance functions to the tasks of image retrieval and classification of novel images. On the Caltech 101 object recognition benchmark, we achieve 60.3% mean recognition across classes using 15 training images per class, which is better than the best published performance by Zhang, et al.

Many computer aided diagnosis (CAD) problems can be best modelled as a multiple-instance learning (MIL) problem with unbalanced data: i.e., the training data typically consists of a few positive bags, and a very large number of negative instances. Existing MIL algorithms are much too computationally expensive for these datasets. We describe CH, a framework for learning a Convex Hull representation of multiple instances that is significantly faster than existing MIL algorithms. Our CH framework applies to any standard hyperplane-based learning algorithm, and for some algorithms, is guaranteed to find the global optimal solution. Experimental studies on two different CAD applications further demonstrate that the proposed algorithm significantly improves diagnostic accuracy when compared to both MIL and traditional classifiers. Although not designed for standard MIL problems (which have both positive and negative bags and relatively balanced datasets), comparisons against other MIL methods on benchmark problems also indicate that the proposed method is competitive with the state-of-the-art.

We consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the target distribution is completely known to the learner and the learner's goal is to construct a classifier capable of guaranteeing a given tolerance for the false-positive error while minimizing the false negative error. We identify both "hard" and "soft" optimal classification strategies for different types of games and demonstrate that soft classification can provide a significant advantage. Our optimal strategies and bounds provide worst-case lower bounds for standard, finite-sample SCC and also motivate new approaches to solving SCC.

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation with various interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.