Most machine learning researchers perform quantitative experiments to estimate generalization error and compare algorithm performances. In order to draw statistically convincing conclusions, it is important to estimate the uncertainty of such estimates. This paper studies the estimation of uncertainty around the K-fold cross-validation estimator. The main theorem shows that there exists no universal unbiased estimator of the variance of K-fold cross-validation. An analysis based on the eigendecomposition of the covariance matrix of errors helps to better understand the nature of the problem and shows that naive estimators may grossly underestimate variance, as con£rmed by numerical experiments.

The so-called "experts algorithms" constitute a methodology for choosing actions repeatedly, when the rewards depend both on the choice of action and on the unknown current state of the environment. An experts algorithm has access to a set of strategies ("experts"), each of which may recommend which action to choose. The algorithm learns how to combine the recommendations of individual experts so that, in the long run, for any fixed sequence of states of the environment, it does as well as the best expert would have done relative to the same sequence. This methodology may not be suitable for situations where the evolution of states of the environment depends on past chosen actions, as is usually the case, for example, in a repeated nonzero-sum game. A new experts algorithm is presented and analyzed in the context of repeated games. It is shown that asymptotically, under certain conditions, it performs as well as the best available expert. This algorithm is quite different from previously proposed experts algorithms. It represents a shift from the paradigms of regret minimization and myopic optimization to consideration of the long-term effect of a player's actions on the opponent's actions or the environment. The importance of this shift is demonstrated by the fact that this algorithm is capable of inducing cooperation in the repeated Prisoner's Dilemma game, whereas previous experts algorithms converge to the suboptimal non-cooperative play.

A novel approach to combining clustering and feature selection is presented. It implements a wrapper strategy for feature selection, in the sense that the features are directly selected by optimizing the discriminative power of the used partitioning algorithm. On the technical side, we present an efficient optimization algorithm with guaranteed local convergence property. The only free parameter of this method is selected by a resampling-based stability analysis. Experiments with real-world datasets demonstrate that our method is able to infer both meaningful partitions and meaningful subsets of features.

A recent area of significant progress in speaker recognition is the use of high level features--idiolect, phonetic relations, prosody, discourse structure, etc. A speaker not only has a distinctive acoustic sound but uses language in a characteristic manner. Large corpora of speech data available in recent years allow experimentation with long term statistics of phone patterns, word patterns, etc. of an individual. We propose the use of support vector machines and term frequency analysis of phone sequences to model a given speaker. To this end, we explore techniques for text categorization applied to the problem. We derive a new kernel based upon a linearization of likelihood ratio scoring. We introduce a new phone-based SVM speaker recognition approach that halves the error rate of conventional phone-based approaches.

A common way of image denoising is to project a noisy image to the subspace of admissible images made for instance by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion.

This paper devises a novel kernel function for structured natural language data. In the field of Natural Language Processing, feature extraction consists of the following two steps: (1) syntactically and semantically analyzing raw data, i.e., character strings, then representing the results as discrete structures, such as parse trees and dependency graphs with part-of-speech tags; (2) creating (possibly high-dimensional) numerical feature vectors from the discrete structures. The new kernels, called Hierarchical Directed Acyclic Graph (HDAG) kernels, directly accept DAGs whose nodes can contain DAGs. HDAG data structures are needed to fully reflect the syntactic and semantic structures that natural language data inherently have. In this paper, we define the kernel function and show how it permits efficient calculation. Experiments demonstrate that the proposed kernels are superior to existing kernel functions, e.g., sequence kernels, tree kernels, and bag-of-words kernels.

Loopy belief propagation (BP) has been successfully used in a number of difficult graphical models to find the most probable configuration of the hidden variables. In applications ranging from protein folding to image analysis one would like to find not just the best configuration but rather the top M. While this problem has been solved using the junction tree formalism, in many real world problems the clique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configurations when exact inference is impossible. We start by developing a new exact inference algorithm for calculating the best configurations that uses only max-marginals. For approximate inference, we replace the max-marginals with the beliefs calculated using max-product BP and generalized BP. We show empirically that the algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.

In this paper we obtain convergence bounds for the concentration of Bayesian posterior distributions (around the true distribution) using a novel method that simplifies and enhances previous results. Based on the analysis, we also introduce a generalized family of Bayesian posteriors, and show that the convergence behavior of these generalized posteriors is completely determined by the local prior structure around the true distribution. This important and surprising robustness property does not hold for the standard Bayesian posterior in that it may not concentrate when there exist "bad" prior structures even at places far away from the true distribution.

This paper presents a method for learning a distance metric from relative comparison such as "A is closer to B than A is to C". Taking a Support Vector Machine (SVM) approach, we develop an algorithm that provides a flexible way of describing qualitative training data as a set of constraints. We show that such constraints lead to a convex quadratic programming problem that can be solved by adapting standard methods for SVM training. We empirically evaluate the performance and the modelling flexibility of the algorithm on a collection of text documents.

Spike timing plasticity (STDP) is a special form of synaptic plasticity where the relative timing of post-and presynaptic activity determines the change of the synaptic weight. On the postsynaptic side, active backpropagating spikes in dendrites seem to play a crucial role in the induction of spike timing dependent plasticity. We argue that postsynaptically the temporal change of the membrane potential determines the weight change. Coming from the presynaptic side induction of STDP is closely related to the activation of NMDA channels. Therefore, we will calculate analytically the change of the synaptic weight by correlating the derivative of the membrane potential with the activity of the NMDA channel.