We propose a novel a framework for deriving approximations for intractable probabilisticmodels. This framework is based on a free energy (negative log marginal likelihood) and can be seen as a generalization of adaptive TAP [1, 2, 3] and expectation propagation (EP) [4, 5]. The free energy is constructed from two approximating distributions which encode different aspects of the intractable model such a single node constraints andcouplings and are by construction consistent on a chosen set of moments. We test the framework on a difficult benchmark problem with binary variables on fully connected graphs and 2D grid graphs. We find good performance using sets of moments which either specify factorized nodesor a spanning tree on the nodes (structured approximation). Surprisingly, the Bethe approximation gives very inferior results even on grids.

We discuss an identification framework for noisy speech mixtures.

A generative probabilistic model for objects in images is presented. An object consists of a constellation of features. Feature appearance and pose are modeled probabilistically. Scene images are generated by drawing aset of objects from a given database, with random clutter sprinkled on the remaining image surface.

Coreference analysis, also known as record linkage or identity uncertainty, isa difficult and important problem in natural language processing, databases, citation matching and many other tasks. This paper introduces severaldiscriminative, conditional-probability models for coreference analysis,all examples of undirected graphical models. Unlike many historical approaches to coreference, the models presented here are relational--they do not assume that pairwise coreference decisions should be made independently from each other. Unlike other relational models of coreference that are generative, the conditional model here can incorporate a great variety of features of the input without having to be concerned about their dependencies--paralleling the advantages of conditional randomfields over hidden Markov models.

While clustering is usually an unsupervised operation, there are circumstances inwhich we believe (with varying degrees of certainty) that items A and B should be assigned to the same cluster, while items A and C should not. We would like such pairwise relations to influence cluster assignments of out-of-sample data in a manner consistent with the prior knowledge expressed in the training set. Our starting point is probabilistic clusteringbased on Gaussian mixture models (GMM) of the data distribution. We express clustering preferences in the prior distribution over assignments of data points to clusters. This prior penalizes cluster assignments according to the degree with which they violate the preferences.

We propose a new method for estimating intrinsic dimension of a dataset derived by applying the principle of maximum likelihood to the distances between close neighbors. We derive the estimator by a Poisson process approximation, assess its bias and variance theoretically andby simulations, and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.

We present a competitive analysis of Bayesian learning algorithms in the online learning setting and show that many simple Bayesian algorithms (such as Gaussian linear regression and Bayesian logistic regression) perform favorablywhen compared, in retrospect, to the single best model in the model class. The analysis does not assume that the Bayesian algorithms' modelingassumptions are "correct," and our bounds hold even if the data is adversarially chosen. For Gaussian linear regression (using logloss),our error bounds are comparable to the best bounds in the online learning literature, and we also provide a lower bound showing that Gaussian linear regression is optimal in a certain worst case sense. We also give bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

In this paper we present a framework for using multi-layer perceptron (MLP)networks in nonlinear generative models trained by variational Bayesian learning. The nonlinearity is handled by linearizing it using a Gauss-Hermite quadrature at the hidden neurons. Thisyields an accurate approximation for cases of large posterior variance.The method can be used to derive nonlinear counterparts forlinear algorithms such as factor analysis, independent component/factor analysis and state-space models. This is demonstrated witha nonlinear factor analysis experiment in which even 20 sources can be estimated from a real world speech data set.

Statistical approaches to language learning typically focus on either short-range syntactic dependencies or long-range semantic dependencies between words. We present a generative model that uses both kinds of dependencies, and can be used to simultaneously find syntactic classes and semantic topics despite having no representation of syntax or semantics beyondstatistical dependency. This model is competitive on tasks like part-of-speech tagging and document classification with models that exclusively use short-and long-range dependencies respectively.

We consider the semi-supervised learning problem, where a decision rule is to be learned from labeled and unlabeled data. In this framework, we motivate minimum entropy regularization, which enables to incorporate unlabeled data in the standard supervised learning. Our approach includes otherapproaches to the semi-supervised problem as particular or limiting cases. A series of experiments illustrates that the proposed solution benefitsfrom unlabeled data. The method challenges mixture models when the data are sampled from the distribution class spanned by the generative model. The performances are definitely in favor of minimum entropy regularization when generative models are misspecified, and the weighting of unlabeled data provides robustness to the violation of the "cluster assumption". Finally, we also illustrate that the method can also be far superior to manifold learning in high dimension spaces.