Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distributions in the exponential domain, that is applicable to an arbitrary undirected graphical model. In the special case of convex combinations of tree-structured distributions, we obtain a family of variational problems, similar to the Bethe free energy, but distinguished by the following desirable properties: i. they are cnvex, and have a unique global minimum; and ii. the global minimum gives an upper bound on the log partition function. The global minimum is defined by stationary conditions very similar to those defining fixed points of belief propagation or tree-based reparameterization Wainwright et al., 2001. As with BP fixed points, the elements of the minimizing argument can be used as approximations to the marginals of the original model. The analysis described here can be extended to structures of higher treewidth e.g., hypertrees, thereby making connections with more advanced approximations e.g., Kikuchi and variants Yedidia et al., 2001; Minka, 2001.

Active learning is a powerful approach to analyzing data effectively. We show that the feasibility of active learning depends crucially on the choice of measure with respect to which the query is being optimized. The standard information gain, for example, does not permit an accurate evaluation with a small committee, a representative subset of the model space. We propose a surrogate measure requiring only a small committee and discuss the properties of this new measure. We devise, in addition, a bootstrap approach for committee selection. The advantages of this approach are illustrated in the context of recovering (regulatory) network models.

In this paper, we introduce and evaluate a data-driven staged mixture modeling technique for building density, regression, and classification models. Our basic approach is to sequentially add components to a finite mixture model using the structural expectation maximization (SEM) algorithm. We show that our technique is qualitatively similar to boosting. This correspondence is a natural byproduct of the fact that we use the SEM algorithm to sequentially fit the mixture model. Finally, in our experimental evaluation, we demonstrate the effectiveness of our approach on a variety of prediction and density estimation tasks using real-world data.

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When hidden variables are present, however, standard dimension might no longer be appropriate. One should instead use effective dimension (Geiger et al. 1996). This paper is concerned with the computation of effective dimension. First we present an upper bound on the effective dimension of a latent class (LC) model. This bound is tight and its computation is easy. We then consider a generalization of LC models called hierarchical latent class (HLC) models (Zhang 2002). We show that the effective dimension of an HLC model can be obtained from the effective dimensions of some related LC models. We also demonstrate empirically that using effective dimension in place of standard dimension improves the quality of models learned from data.

In probabilistic approaches to classification and information extraction, one typically builds a statistical model of words under the assumption that future data will exhibit the same regularities as the training data. In many data sets, however, there are scope-limited features whose predictive power is only applicable to a certain subset of the data. For example, in information extraction from web pages, word formatting may be indicative of extraction category in different ways on different web pages. The difficulty with using such features is capturing and exploiting the new regularities encountered in previously unseen data. In this paper, we propose a hierarchical probabilistic model that uses both local/scope-limited features, such as word formatting, and global features, such as word content. The local regularities are modeled as an unobserved random parameter which is drawn once for each local data set. This random parameter is estimated during the inference process and then used to perform classification with both the local and global features--- a procedure which is akin to automatically retuning the classifier to the local regularities on each newly encountered web page. Exact inference is intractable and we present approximations via point estimates and variational methods. Empirical results on large collections of web data demonstrate that this method significantly improves performance from traditional models of global features alone.

We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. Treating the problem as a semiparametric statistical problem, we show that the optimal transform is found by minimizing a contrast function based on mutual information, a function that directly extends the contrast function used for classical ICA. We provide two approximations of this contrast function, one using kernel density estimation, and another using kernel generalized variance. This tree-dependent component analysis framework leads naturally to an efficient general multivariate density estimation technique where only bivariate density estimation needs to be performed.

Building models, or maps, of robot environments is a highly active research area; however, most existing techniques construct unstructured maps and assume static environments. In this paper, we present an algorithm for learning object models of non-stationary objects found in office-type environments. Our algorithm exploits the fact that many objects found in office environments look alike (e.g., chairs, recycling bins). It does so through a two-level hierarchical representation, which links individual objects with generic shape templates of object classes. We derive an approximate EM algorithm for learning shape parameters at both levels of the hierarchy, using local occupancy grid maps for representing shape. Additionally, we develop a Bayesian model selection algorithm that enables the robot to estimate the total number of objects and object templates in the environment. Experimental results using a real robot equipped with a laser range finder indicate that our approach performs well at learning object-based maps of simple office environments. The approach outperforms a previously developed non-hierarchical algorithm that models objects but lacks class templates.

Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define as a wide class of discrete variable models including undirected graphical models and Bayesian networks, but also chain graphs and sigmoid belief networks. The second one is for conditional likelihood maximization in standard undirected models and Bayesian networks. In both algorithms, the iteration steps are expressed in closed form. Numerical simulations show that the algorithms are competitive with state of the art methods.

This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s classical result, AND can therefore be applied TO ANY finite Bayesian network.It neither requires linear utility AS did de Finetti s classical result, AND r ntherefore allows FOR the empirically AND normatively desirable risk r naversion.Finally, BY identifying AND fixing utility IN an elementary r nmanner, our result can readily be applied TO identify methods OF r nprobability updating.Thus, a decision - theoretic foundation IS given r nto the computationally efficient method OF inductive reasoning r ndeveloped BY Rudolf Carnap.Finally, recent empirical findings ON r nprobability assessments are discussed.It leads TO suggestions FOR r ncorrecting biases IN probability assessments, AND FOR an alternative r nto the Dempster - Shafer belief functions that avoids the reduction TO r ndegeneracy after multiple updatings.r n

We propose an efficient method for Bayesian network inference in models with functional dependence. We generalize the multiplicative factorization method originally designed by Takikawa and D Ambrosio(1999) FOR models WITH independence OF causal influence.Using a hidden variable, we transform a probability potential INTO a product OF two - dimensional potentials.The multiplicative factorization yields more efficient inference. FOR example, IN junction tree propagation it helps TO avoid large cliques. IN ORDER TO keep potentials small, the number OF states OF the hidden variable should be minimized.We transform this problem INTO a combinatorial problem OF minimal base IN a particular space.We present an example OF a computerized adaptive test, IN which the factorization method IS significantly more efficient than previous inference methods.