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 this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of classes assigned to the patterns by manual means or some other means in whose veracity there is confidence. Such measures are refered to as ``external'. Our measure also has the characteristic of allowing clusterings with different numbers of clusters to be compared in a quantitative and principled way. Our evaluation scheme quantitatively measures how useful the cluster labels of the patterns are as predictors of their class labels. In cases where all clusterings to be compared have the same number of clusters, the measure is equivalent to the mutual information between the cluster labels and the class labels. In cases where the numbers of clusters are different, however, it computes the reduction in the number of bits that would be required to encode (compress) the class labels if both the encoder and decoder have free acccess to the cluster labels. To achieve this encoding the estimated conditional probabilities of the class labels given the cluster labels must also be encoded. These estimated probabilities can be seen as a model for the class labels and their associated code length as a model cost.

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.

Bio-Inspired Algorithms on Road Traffic Congestion and safety is a very promising research problem. Searching for an efficient optimization method to increase the degree of speed optimization and thereby increasing the traffic Flow in an unplanned zone is a widely concerning issue. However, there has been a limited research effort on the optimization of the lane usage with speed optimization. The main objective of this article is to find avenues or techniques in a novel way to solve the problem optimally using the knowledge from analysis of speeds of vehicles, which, in turn will act as a guide for design of lanes optimally to provide better optimized traffic. The accident factors adjust the base model estimates for individual geometric design element dimensions and for traffic control features. The application of these algorithms in partially modified form in accordance of this novel Speed Optimization Technique in an Unplanned Traffic analysis technique is applied to the proposed design and speed optimization plan. The experimental results based on real life data are quite encouraging.

From a psychological point of view, a human being uses the notions of similarity and dissimilarity for problem solving, inductive reasoning, element categorization, or simply to search for information partially matching specific criteria. The ability to assess similarities between a newly given pattern and already known patterns is a distinctive feature of human thinking. It is therefore not strange that similarity and its dual concept dissimilarity are a fundamental part of many theories and applications in several fields, within or related to Artificial Intelligence, like Case Based Reasoning [1], Data Mining [2], Information Retrieval [3], Pattern Matching [4] or Neural Networks, as the Radial Basis Function network [5]. Many applications are characterized by the use of metrics for measuring differences between objects. Metric dissimilarities have been deeply studied but they are tied to a particular transitivity expression based on the triangle inequality. Very often metric (distance) functions are used due to our natural understanding of Euclidean spaces. However, not all metrics are Euclidean and many interesting dissimilarities are non-metric. 1 In a general sense, similarity and dissimilarity express a dual comparison between two elements. We argue that every property of a similarity should have a correspondence with one property of a dissimilarity and vice versa. This duality is commonly ignored, as well as some annoying properties (e.g.

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.

This presentation will introduce the audience to a new, emerging body of research on sequential Monte Carlo techniques in robotics. In recent years, particle filters have solved several hard perceptual robotic problems. Early successes were limited to low-dimensional problems, such as the problem of robot localization in environments with known maps. More recently, researchers have begun exploiting structural properties of robotic domains that have led to successful particle filter applications in spaces with as many as 100,000 dimensions. The presentation will discuss specific tricks necessary to make these techniques work in real - world domains,and also discuss open challenges for researchers IN the UAI community.