We present a framework for sparse Gaussian process (GP) methods which uses forward selection with criteria based on informationtheoretic principles, previously suggested for active learning. Our goal is not only to learn d-sparse predictors (which can be evaluated in O(d) rather than O(n), d n, n the number of training points), but also to perform training under strong restrictions on time and memory requirements.

An essential step in understanding the function of sensory nervous systems is to characterize as accurately as possible the stimulus-response function (SRF) of the neurons that relay and process sensory information. One increasingly common experimental approach is to present a rapidly varying complex stimulus to the animal while recording the responses of one or more neurons, and then to directly estimate a functional transformation of the input that accounts for the neuronal firing. The estimation techniques usually employed, such as Wiener filtering or other correlation-based estimation of the Wiener or Volterra kernels, are equivalent to maximum likelihood estimation in a Gaussian-output-noise regression model. We explore the use of Bayesian evidence-optimization techniques to condition these estimates. We show that by learning hyperparameters that control the smoothness and sparsity of the transfer function it is possible to improve dramatically the quality of SRF estimates, as measured by their success in predicting responses to novel input.

In this paper, we study a special kind of learning problem in which each training instance is given a set of (or distribution over) candidate class labels and only one of the candidate labels is the correct one. Such a problem can occur, e.g., in an information retrieval setting where a set of words is associated with an image, or if classes labels are organized hierarchically. We propose a novel discriminative approach for handling the ambiguity of class labels in the training examples. The experiments with the proposed approach over five different UCI datasets show that our approach is able to find the correct label among the set of candidate labels and actually achieve performance close to the case when each training instance is given a single correct label. In contrast, naIve methods degrade rapidly as more ambiguity is introduced into the labels. 1 Introduction Supervised and unsupervised learning problems have been extensively studied in the machine learning literature. In supervised classification each training instance is associated with a single class label, while in unsupervised classification (i.e.

We propose a dynamic Bayesian model for motifs in biopolymer sequences which captures rich biological prior knowledge and positional dependencies in motif structure in a principled way. Our model posits that the position-specific multinomial parameters for monomer distribution are distributed as a latent Dirichlet-mixture random variable, and the position-specific Dirichlet component is determined by a hidden Markov process. Model parameters can be fit on training motifs using a variational EM algorithm within an empirical Bayesian framework. Variational inference is also used for detecting hidden motifs. Our model improves over previous models that ignore biological priors and positional dependence. It has much higher sensitivity to motifs during detection and a notable ability to distinguish genuine motifs from false recurring patterns.

In this paper, we consider Tipping's relevance vector machine (RVM) [1] and formalize an incremental training strategy as a variant of the expectation-maximization (EM) algorithm that we call Subspace EM (SSEM). Working with a subset of active basis functions, the sparsity of the RVM solution will ensure that the number of basis functions and thereby the computational complexity is kept low. We also introduce a mean field approach to the intractable classification model that is expected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case.

We present a simple direct approach for solving the ICA problem, using density estimation and maximum likelihood. Given a candidate orthogonal frame, we model each of the coordinates using a semi-parametric density estimate based on cubic splines. Since our estimates have two continuous derivatives, we can easily run a second order search for the frame parameters. Our method performs very favorably when compared to state-of-the-art techniques. 1 Introduction Independent component analysis (ICA) is a popular enhancement over principal component analysis (PCA) and factor analysis. IRP which is assumed to arise from a linear mixing of a latent random source vector S E IRP, (1) X AS; the components Sj, j 1,...,p of S are assumed to be independently distributed.

The information bottleneck (IB) method is an information-theoretic formulation for clustering problems.

Gaussian process regression allows a simple analytical treatment of exact Bayesian inference and has been found to provide good performance, yet scales badly with the number of training data. In this paper we compare several approaches towards scaling Gaussian processes regression to large data sets: the subset of representers method, the reduced rank approximation, online Gaussian processes, and the Bayesian committee machine. Furthermore we provide theoretical insight into some of our experimental results. We found that subset of representers methods can give good and particularly fast predictions for data sets with high and medium noise levels. On complex low noise data sets, the Bayesian committee machine achieves significantly better accuracy, yet at a higher computational cost.

People routinely make sophisticated causal inferences unconsciously, effortlessly, and from very little data - often from just one or a few observations. We argue that these inferences can be explained as Bayesian computations over a hypothesis space of causal graphical models, shaped by strong top-down prior knowledge in the form of intuitive theories.

We consider Bayesian mixture approaches, where a predictor is constructed by forming a weighted average of hypotheses from some space of functions. While such procedures are known to lead to optimal predictors in several cases, where sufficiently accurate prior information is available, it has not been clear how they perform when some of the prior assumptions are violated. In this paper we establish data-dependent bounds for such procedures, extending previous randomized approaches such as the Gibbs algorithm to a fully Bayesian setting. The finite-sample guarantees established in this work enable the utilization of Bayesian mixture approaches in agnostic settings, where the usual assumptions of the Bayesian paradigm fail to hold. Moreover, the bounds derived can be directly applied to non-Bayesian mixture approaches such as Bagging and Boosting.