In this paper we introduce a new sparseness inducing prior which does not involve any (hyper)parameters that need to be adjusted or estimated. Although other applications are possible, we focus here on supervised learning problems: regression and classification. Experiments with several publicly available benchmark data sets show that the proposed approach yields state-of-the-art performance. In particular, our method outperforms support vector machines and performs competitively with the best alternative techniques, both in terms of error rates and sparseness, although it involves no tuning or adjusting of sparsenesscontrolling hyper-parameters.

The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka's expectation propagation. Lastly, we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classification and density estimation with Gaussian processes and on an independent component analysis problem.

SMC is often referred to as particle filtering (PF) in the context of computing filtering distributions for statistical inference and learning. It is known that the performance of PF often deteriorates in high-dimensional state spaces. In the past, we have shown that if a model admits partial analytical tractability, it is possible to combine PF with exact algorithms (Kalman filters, HMM filters, junction tree algorithm) to obtain efficient high dimensional filters (Doucet, de Freitas, Murphy and Russell 2000, Doucet, Godsill and Andrieu 2000). In particular, we exploited a marginalisation technique known as Rao-Blackwellisation (RB). Here, we attack a more complex model that does not admit immediate analytical tractability.

We study properties of popular near-uniform (Dirichlet) priors for learning undersampled probability distributions on discrete nonmetric spaces and show that they lead to disastrous results. However, an Occam-style phase space argument expands the priors into their infinite mixture and resolves most of the observed problems. This leads to a surprisingly good estimator of entropies of discrete distributions. Learning a probability distribution from examples is one of the basic problems in data analysis. Common practical approaches introduce a family of parametric models, leading to questions about model selection. In Bayesian inference, computing the total probability of the data arising from a model involves an integration over parameter space, and the resulting "phase space volume" automatically discriminates against models with larger numbers of parameters--hence the description of these volume terms as Occam factors [1, 2]. As we move from finite parameterizations to models that are described by smooth functions, the integrals over parameter space become functional integrals and methods from quantum field theory allow us to do these integrals asymptotically; again the volume in model space consistent with the data is larger for models that are smoother and hence less complex [3]. Further, at least under some conditions the relevant degree of smoothness can be determined self-consistently from the data, so that we approach something like a model independent method for learning a distribution [4]. The results emphasizing the importance of phase space factors in learning prompt us to look back at a seemingly much simpler problem, namely learning a distribution on a discrete, nonmetric space.

We derive an equivalence between AdaBoost and the dual of a convex optimization problem, showing that the only difference between minimizing the exponential loss used by AdaBoost and maximum likelihood for exponential models is that the latter requires the model to be normalized to form a conditional probability distribution over labels. In addition to establishing a simple and easily understood connection between the two methods, this framework enables us to derive new regularization procedures for boosting that directly correspond to penalized maximum likelihood. Experiments on UCI datasets support our theoretical analysis and give additional insight into the relationship between boosting and logistic regression.

Statistical learning and probabilistic inference techniques are used to infer the hand position of a subject from multi-electrode recordings of neural activity in motor cortex. First, an array of electrodes provides training data of neural firing conditioned on hand kinematics. We learn a nonparametric representation of this firing activity using a Bayesian model and rigorously compare it with previous models using cross-validation. Second, we infer a posterior probability distribution over hand motion conditioned on a sequence of neural test data using Bayesian inference. The learned firing models of multiple cells are used to define a non-Gaussian likelihood term which is combined with a prior probability for the kinematics. A particle filtering method is used to represent, update, and propagate the posterior distribution over time. The approach is compared with traditional linear filtering methods; the results suggest that it may be appropriate for neural prosthetic applications.

Multisensory response enhancement (MRE) is the augmentation of the response of a neuron to sensory input of one modality by simultaneous input from another modality. The maximum likelihood (ML) model presented here modifies the Bayesian model for MRE (Anastasio et al.) by incorporating a decision strategy to maximize the number of correct decisions. Thus the ML model can also deal with the important tasks of stimulus discrimination and identification in the presence of incongruent visual and auditory cues. It accounts for the inverse effectiveness observed in neurophysiological recording data, and it predicts a functional relation between uni-and bimodal levels of discriminability that is testable both in neurophysiological and behavioral experiments.

In this paper we explore two quantitative approaches to the modelling of counterfactual reasoning - a linear and a noisy-OR model - based on information contained in conceptual dependency networks. Empirical data is acquired in a study and the fit of the models compared to it. We conclude by considering the appropriateness of nonparametric approaches to counterfactual reasoning, and examining the prospects for other parametric approaches in the future.

A theory of categorization is presented in which knowledge of causal relationships between category features is represented as a Bayesian network. Referred to as causal-model theory, this theory predicts that objects are classified as category members to the extent they are likely to have been produced by a categorys causal model. On this view, people have models of the world that lead them to expect a certain distribution of features in category members (e.g., correlations between feature pairs that are directly connected by causal relationships), and consider exemplars good category members when they manifest those expectations. These expectations include sensitivity to higher-order feature interactions that emerge from the asymmetries inherent in causal relationships. Research on the topic of categorization has traditionally focused on the problem of learning new categories given observations of category members.

Narayanan and Jurafsky (1998) proposed that human language comprehension can be modeled by treating human comprehenders as Bayesian reasoners, and modeling the comprehension process with Bayesian decision trees. In this paper we extend the Narayanan and Jurafsky model to make further predictions about reading time given the probability of difference parses or interpretations, and test the model against reading time data from a psycholinguistic experiment.