We show that the relevant information about a classification problem in feature space is contained up to negligible error in a finite number of leading kernel PCA components if the kernel matches the underlying learning problem. Thus, kernels not only transform data sets such that good generalization can be achieved even by linear discriminant functions, but this transformation is also performed in a manner which makes economic use of feature space dimensions. In the best case, kernels provide efficient implicit representations of the data to perform classification. Practically, we propose an algorithm which enables us to recover the subspace and dimensionality relevant for good classification. Our algorithm can therefore be applied (1) to analyze the interplay of data set and kernel in a geometric fashion, (2) to help in model selection, and to (3) de-noise in feature space in order to yield better classification results.

Independent Component Analysis (ICA) is a popular method for extracting independent features from visual data. However, as a fundamentally linear technique, there is always nonlinear residual redundancy that is not captured by ICA. Hence there have been many attempts to try to create a hierarchical version of ICA, but so far none of the approaches have a natural way to apply them more than once. Here we show that there is a relatively simple technique that transforms the absolute values of the outputs of a previous application of ICA into a normal distribution, to which ICA maybe applied again. This results in a recursive ICA algorithm that may be applied any number of times in order to extract higher order structure from previous layers.

We propose a new technique for sampling the solutions of combinatorial problems in a near-uniform manner. We focus on problems specified as a Boolean formula, i.e., on SAT instances. Sampling for SAT problems has been shown to have interesting connections with probabilistic reasoning, making practical sampling algorithms for SAT highly desirable. The best current approaches are based on Markov Chain Monte Carlo methods, which have some practical limitations.

Establishing correspondence between distinct objects is an important and nontrivial task: correctness of the correspondence hinges on properties which are difficult to capture in an a priori criterion. While previous work has used a priori criteria which in some cases led to very good results, the present paper explores whether it is possible to learn a combination of features that, for a given training set of aligned human heads, characterizes the notion of correct correspondence. By optimizing this criterion, we are then able to compute correspondence and morphs for novel heads.

In this paper, we propose a novel exemplar-based approach to extract dynamic foreground regions from a changing background within a collection of images or a video sequence. By using image segmentation as a pre-processing step, we convert this traditional pixel-wise labeling problem into a lower-dimensional supervised, binary labeling procedure on image segments. Our approach consists of three steps. First, a set of random image patches are spatially and adaptively sampled within each segment. Second, these sets of extracted samples are formed into two "bags of patches" to model the foreground/background appearance, respectively.

This paper proposes a PAC-Bayes bound to measure the performance of Support Vector Machine (SVM) classifiers. The bound is based on learning a prior over the distribution of classifiers with a part of the training samples. Experimental work shows that this bound is tighter than the original PAC-Bayes, resulting in an enhancement of the predictive capabilities of the PAC-Bayes bound. In addition, it is shown that the use of this bound as a means to estimate the hyperparameters of the classifier compares favourably with cross validation in terms of accuracy of the model, while saving a lot of computational burden.

Online convex programming has recently emerged as a powerful primitive for designing machine learning algorithms. For example, OCP can be used for learning a linear classifier, dynamically rebalancing a binary search tree, finding the shortest path in a graph with unknown edge lengths, solving a structured classification problem, or finding a good strategy in an extensive-form game. Several researchers have designed no-regret algorithms for OCP. But, compared to algorithms for special cases of OCP such as learning from expert advice, these algorithms are not very numerous or flexible. In learning from expert advice, one tool which has proved particularly valuable is the correspondence between no-regret algorithms and convex potential functions: by reasoning about these potential functions, researchers have designed algorithms with a wide variety of useful guarantees such as good performance when the target hypothesis is sparse. Until now, there has been no such recipe for the more general OCP problem, and therefore no ability to tune OCP algorithms to take advantage of properties of the problem or data. In this paper we derive a new class of no-regret learning algorithms for OCP. These Lagrangian Hedging algorithms are based on a general class of potential functions, and are a direct generalization of known learning rules like weighted majority and external-regret matching. In addition to proving regret bounds, we demonstrate our algorithms learning to play one-card poker.

We present a method for localizing and separating sound sources in stereo recordings that is robust to reverberation and does not make any assumptions about the source statistics. The method consists of a probabilistic model of binaural multisource recordings and an expectation maximization algorithm for finding the maximum likelihood parameters of that model. These parameters include distributions over delays and assignments of time-frequency regions to sources. We evaluate this method against two comparable algorithms on simulations of simultaneous speech from two or three sources. Our method outperforms the others in anechoic conditions and performs as well as the better of the two in the presence of reverberation.

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 propose a highly efficient framework for kernel multi-class models with a large and structured set of classes. Kernel parameters are learned automatically by maximizing the cross-validation log likelihood, and predictive probabilities are estimated. We demonstrate our approach on large scale text classification tasks with hierarchical class structure, achieving state-of-the-art results in an order of magnitude less time than previous work.