Source separation, or computational auditory scene analysis, attempts to extract individual acoustic objects from input which contains a mixture of sounds from different sources, altered by the acoustic environment. Unmixing algorithms such as lCA and its extensions recover sources by reweighting multiple observation sequences,and thus cannot operate when only a single observation signal is available. I present a technique called refiltering which recovers sources by a nonstationary reweighting ("masking") of frequency sub-bands from a single recording, and argue for the application of statistical algorithms to learning this masking function. I present results of a simple factorial HMM system which learns on recordings of single speakers and can then separate mixtures using only one observation signal by computing the masking function and then refiltering.

We use graphical models to explore the question of how people learn simple causalrelationships from data. The two leading psychological theories canboth be seen as estimating the parameters of a fixed graph. We argue that a complete account of causal induction should also consider how people learn the underlying causal graph structure, and we propose to model this inductive process as a Bayesian inference. Our argument is supported through the discussion of three data sets. 1 Introduction Causality plays a central role in human mental life. Our behavior depends upon our understanding ofthe causal structure of our environment, and we are remarkably good at inferring causation from mere observation. Constructing formal models of causal induction is currently a major focus of attention in computer science [7], psychology [3,6], and philosophy [5].This paper attempts to connect these literatures, by framing the debate between two major psychological theories in the computational language of graphical models. We show that existing theories equate human causal induction with maximum likelihood parameter estimationon a fixed graphical structure, and we argue that to fully account for human behavioral data, we must also postulate that people make Bayesian inferences about the underlying causal graph structure itself.

We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m.

A central issue in principal component analysis (PCA) is choosing the number of principal components to be retained. By interpreting PCA as density estimation, we show how to use Bayesian model selection to estimate thetrue dimensionality of the data. The resulting estimate is simple to compute yet guaranteed to pick the correct dimensionality, given enough data. The estimate involves an integral over the Steifel manifold of k-frames, which is difficult to compute exactly. But after choosing an appropriate parameterization and applying Laplace's method, an accurate andpractical estimator is obtained. In simulations, it is convincingly better than cross-validation and other proposed algorithms, plus it runs much faster.

Algebraic geometry is essential to learning theory. In hierarchical learning machines such as layered neural networks and gaussian mixtures, the asymptotic normality does not hold, since Fisher information matricesare singular. In this paper, the rigorous asymptotic form of the stochastic complexity is clarified based on resolution of singularities and two different problems are studied.

This paper presents a unified probabilistic framework for denoising and dereverberation of speech signals. The framework transforms the denoising anddereverberation problems into Bayes-optimal signal estimation. The key idea is to use a strong speech model that is pre-trained on a large data set of clean speech. Computational efficiency is achieved by using variational EM, working in the frequency domain, and employing conjugate priors. The framework covers both single and multiple microphones. Weapply this approach to noisy reverberant speech signals and get results substantially better than standard methods.

We present an algorithm that samples the hypothesis space of kernel classifiers.Given a uniform prior over normalised weight vectors and a likelihood based on a model of label noise leads to a piecewise constantposterior that can be sampled by the kernel Gibbs sampler (KGS). The KGS is a Markov Chain Monte Carlo method that chooses a random direction in parameter space and samples from the resulting piecewise constant density along the line chosen. The KGS can be used as an analytical tool for the exploration of Bayesian transduction, Bayes point machines, active learning, and evidence-based model selection on small data sets that are contaminated withlabel noise. For a simple toy example we demonstrate experimentally how a Bayes point machine based on the KGS outperforms anSVM that is incapable of taking into account label noise. 1 Introduction Two great ideas have dominated recent developments in machine learning: the application ofkernel methods and the popularisation of Bayesian inference. Focusing on the task of classification, various connections between the two areas exist: kernels havelong been a part of Bayesian inference in the disguise of covariance nmctions thatcharacterise priors over functions [9].

We propose a method of approximate dynamic programming for Markov decision processes (MDPs) using algebraic decision diagrams (ADDs). We produce near-optimal value functions and policies with much lower time and space requirements than exact dynamic programming. Our method reduces the sizes of the intermediate value functions generated during value iteration by replacing the values at the terminals of the ADD with ranges of values. Our method is demonstrated on a class of large MDPs (with up to 34 billion states), and we compare the results with the optimal value functions.

Recent work has exploited boundedness of data in the unsupervised learning of new types of generative model. For nonnegative data it was recently shown that the maximum-entropy generative model is a Nonnegative BoltzmannDistribution not a Gaussian distribution, when the model is constrained to match the first and second order statistics of the data. Learning for practical sized problems is made difficult by the need to compute expectations under the model distribution. The computational costof Markov chain Monte Carlo methods and low fidelity of naive mean field techniques has led to increasing interest in advanced mean field theories and variational methods. Here I present a secondorder mean-fieldapproximation for the Nonnegative Boltzmann Machine model, obtained using a "high-temperature" expansion. The theory is tested on learning a bimodal 2-dimensional model, a high-dimensional translationally invariant distribution, and a generative model for handwritten digits.

In this article, I describe agent-centered search (also called real-time search or local search) and illustrate this planning paradigm with examples. Agent-centered search methods interleave planning and plan execution and restrict planning to the part of the domain around the current state of the agent, for example, the current location of a mobile robot or the current board position of a game. These methods can execute actions in the presence of time constraints and often have a small sum of planning and execution cost, both because they trade off planning and execution cost and because they allow agents to gather information early in nondeterministic domains, which reduces the amount of planning they have to perform for unencountered situations. These advantages become important as more intelligent systems are interfaced with the world and have to operate autonomously in complex environments. Agent-centered search methods have been applied to a variety of domains, including traditional search, strips-type planning, moving-target search, planning with totally and partially observable Markov decision process models, reinforcement learning, constraint satisfaction, and robot navigation. I discuss the design and properties of several agent-centered search methods, focusing on robot exploration and localization.