Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more "focused" predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense does not necessarily perform well in supervised domains. In particular, the standard marginal likelihood score is a criterion for the unsupervised task, and, although frequently used for supervised model selection also, does not perform well in such tasks. In this paper we study the performance of the marginal likelihood score empirically in supervised Bayesian network selection tasks by using a large number of publicly available classification data sets, and compare the results to those obtained by alternative model selection criteria, including empirical crossvalidation methods, an approximation of a supervised marginal likelihood measure, and a supervised version of Dawid's prequential (predictive sequential) principle. The results demonstrate that the marginal likelihood score does not perform well for supervised model selection, while the best results are obtained by using Dawid's prequential approach.

We consider the problem of finding good finite-horizon policies for POMDPs under the expected reward metric. The policies considered are {em free finite-memory policies with limited memory}; a policy is a mapping from the space of observation-memory pairs to the space of action-memeory pairs (the policy updates the memory as it goes), and the number of possible memory states is a parameter of the input to the policy-finding algorithms. The algorithms considered here are preliminary implementations of three search heuristics: local search, simulated annealing, and genetic algorithms. We compare their outcomes to each other and to the optimal policies for each instance. We compare run times of each policy and of a dynamic programming algorithm for POMDPs developed by Hansen that iteratively improves a finite-state controller --- the previous state of the art for finite memory policies. The value of the best policy can only improve as the amount of memory increases, up to the amount needed for an optimal finite-memory policy. Our most surprising finding is that more memory helps in another way: given more memory than is needed for an optimal policy, the algorithms are more likely to converge to optimal-valued policies.

Let \phi(G) be the minimum conductance of an undirected graph G, and let 0=\lambda_1 <= \lambda_2 <=... <= \lambda_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, \phi(G) = O(k) \lambda_2 / \sqrt{\lambda_k}, and this performance guarantee is achieved by the spectral partitioning algorithm. This improves Cheeger's inequality, and the bound is optimal up to a constant factor for any k. Our result shows that the spectral partitioning algorithm is a constant factor approximation algorithm for finding a sparse cut if \lambda_k$ is a constant for some constant k. This provides some theoretical justification to its empirical performance in image segmentation and clustering problems. We extend the analysis to other graph partitioning problems, including multi-way partition, balanced separator, and maximum cut.

In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be described by a Bayesian network that evolve dynamically over time and the observations taken are not necessarily Gaussian. It uses recent developments in approximate Bayesian forecasting methods in combination with more familiar Gaussian propagation algorithms on junction trees. The procedure for learning state parameters from data is given explicitly for common sampling distributions and the methodology is illustrated through a real application. The efficiency of the dynamic approximation is explored by using the Hellinger divergence measure and theoretical bounds for the efficacy of such a procedure are discussed.

Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents muscle actions. We present a mixed-state dynamic graphical model in which a hidden Markov model drives a linear dynamic system. This combination allows us to model both the discrete and continuous causes of trajectories such as human gestures. The number of computations needed for exact inference is exponential in the sequence length, so we derive an approximate variational inference technique that can also be used to learn the parameters of the discrete and continuous models. We show how the mixed-state model and the variational technique can be used to classify human hand gestures made with a computer mouse.

Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There are instances in which this method is slow to converge. Therefore, several accelerations have been proposed to improve the method. None of the proposed acceleration methods are theoretically dominant and experimental comparisons are lacking. In this paper, we present the different proposed accelerations and try to compare them experimentally. From the results of the experiments, we argue that some acceleration of EM is always possible, but that which acceleration is superior depends on properties of the problem.

Probabilistic Latent Semantic Analysis is a novel statistical technique for the analysis of two-mode and co-occurrence data, which has applications in information retrieval and filtering, natural language processing, machine learning from text, and in related areas. Compared to standard Latent Semantic Analysis which stems from linear algebra and performs a Singular Value Decomposition of co-occurrence tables, the proposed method is based on a mixture decomposition derived from a latent class model. This results. in a more principled approach which has a solid foundation in statistics. In order to avoid overfitting, we propose a widely applicable generalization of maximum likelihood model fitting by tempered EM.

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior distributions over the parameters remains a difficult problem. Moreover, learning the structure of models with latent variables, for which the Bayesian approach is crucial, is yet a harder problem. In this paper I present the Variational Bayes framework, which provides a solution to these problems. This approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner without resorting to sampling methods. Unlike in the Laplace approximation, these posteriors are generally non-Gaussian and no Hessian needs to be computed. The resulting algorithm generalizes the standard Expectation Maximization algorithm, and its convergence is guaranteed. I demonstrate that this algorithm can be applied to a large class of models in several domains, including unsupervised clustering and blind source separation.

It is well-known that the notion of (strong) conditional independence (CI) is too restrictive to capture independencies that only hold in certain contexts. This kind of contextual independency, called context-strong independence (CSI), can be used to facilitate the acquisition, representation, and inference of probabilistic knowledge. In this paper, we suggest the use of contextual weak independence (CWI) in Bayesian networks. It should be emphasized that the notion of CWI is a more general form of contextual independence than CSI. Furthermore, if the contextual strong independence holds for all contexts, then the notion of CSI becomes strong CI. On the other hand, if the weak contextual independence holds for all contexts, then the notion of CWI becomes weak independence (WI) nwhich is a more general noncontextual independency than strong CI. More importantly, complete axiomatizations are studied for both the class of WI and the class of CI and WI together. Finally, the interesting property of WI being a necessary and sufficient condition for ensuring consistency in granular probabilistic networks is shown.

The AGM theory of belief revision has become an important paradigm for investigating rational belief changes. Unfortunately, researchers working in this paradigm have restricted much of their attention to rather simple representations of belief states, namely logically closed sets of propositional sentences. In our opinion, this has resulted in a too abstract categorisation of belief change operations: expansion, revision, or contraction. Occasionally, in the AGM paradigm, also probabilistic belief changes have been considered, and it is widely accepted that the probabilistic version of expansion is conditioning. However, we argue that it may be more correct to view conditioning and expansion as two essentially different kinds of belief change, and that what we call constraining is a better candidate for being considered probabilistic expansion.