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.

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.

We present a growing dimension asymptotic formalism. The perspective in this paper is classification theory and we show that it can accommodate probabilistic networks classifiers, including naive Bayes model and its augmented version. When represented as a Bayesian network these classifiers have an important advantage: The corresponding discriminant function turns out to be a specialized case of a generalized additive model, which makes it possible to get closed form expressions for the asymptotic misclassification probabilities used here as a measure of classification accuracy. Moreover, in this paper we propose a new quantity for assessing the discriminative power of a set of features which is then used to elaborate the augmented naive Bayes classifier. The result is a weighted form of the augmented naive Bayes that distributes weights among the sets of features according to their discriminative power. We derive the asymptotic distribution of the sample based discriminative power and show that it is seriously overestimated in a high dimensional case. We then apply this result to find the optimal, in a sense of minimum misclassification probability, type of weighting.

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 present a language for finite state continuous time Bayesian networks (CTBNs), which describe structured stochastic processes that evolve over continuous time. The state of the system is decomposed into a set of local variables whose values change over time. The dynamics of the system are described by specifying the behavior of each local variable as a function of its parents in a directed (possibly cyclic) graph. The model specifies, at any given point in time, the distribution over two aspects: when a local variable changes its value and the next value it takes. These distributions are determined by the variable s CURRENT value AND the CURRENT VALUES OF its parents IN the graph.More formally, each variable IS modelled AS a finite state continuous time Markov process whose transition intensities are functions OF its parents.We present a probabilistic semantics FOR the language IN terms OF the generative model a CTBN defines OVER sequences OF events.We list types OF queries one might ask OF a CTBN, discuss the conceptual AND computational difficulties associated WITH exact inference, AND provide an algorithm FOR approximate inference which takes advantage OF the structure within the process.

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.

A popular approach to solving a decision process with non-Markovian rewards (NMRDP) is to exploit a compact representation of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable to our favorite MDP solution method. The contribution of this paper is a representation of non-Markovian reward functions and a translation into MDP aimed at making the best possible use of state-based anytime algorithms as the solution method. By explicitly constructing and exploring only parts of the state space, these algorithms are able to trade computation time for policy quality, and have proven quite effective in dealing with large MDPs. Our representation extends future linear temporal logic (FLTL) to express rewards. Our translation has the effect of embedding model-checking in the solution method. It results in an MDP of the minimal size achievable without stepping outside the anytime framework, and consequently in better policies by the deadline.

Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such models can be very computationally expensive when there are many datapoints and many continuous variables with complex nonlinear relationships, particularly when no good ways of decomposing the joint distribution are known a priori. In such situations, previous research has generally focused on the use of discretization techniques in which each continuous variable has a single discretization that is used throughout the entire network. \ In this paper, we present and compare a wide variety of tree-based algorithms for learning and evaluating conditional density estimates over continuous variables. These trees can be thought of as discretizations that vary according to the particular interactions being modeled; however, the density within a given leaf of the tree need not be assumed constant, and we show that such nonuniform leaf densities lead to more accurate density estimation. We have developed Bayesian network structure-learning algorithms that employ these tree-based conditional density representations, and we show that they can be used to practically learn complex joint probability models over dozens of continuous variables from thousands of datapoints. We focus on finding models that are simultaneously accurate, fast to learn, and fast to evaluate once they are learned.

We introduce a new Bayesian network (BN) scoring metric called the Global Uniform (GU) metric. This metric is based on a particular type of default parameter prior. Such priors may be useful when a BN developer is not willing or able to specify domain-specific parameter priors. The GU parameter prior specifies that every prior joint probability distribution P consistent with a BN structure S is considered to be equally likely. Distribution P is consistent with S if P includes just the set of independence relations defined by S. We show that the GU metric addresses some undesirable behavior of the BDeu and K2 Bayesian network scoring metrics, which also use particular forms of default parameter priors. A closed form formula for computing GU for special classes of BNs is derived. Efficiently computing GU for an arbitrary BN remains an open problem.

MAP is the problem of finding a most probable instantiation of a set of nvariables in a Bayesian network, given some evidence. MAP appears to be a significantly harder problem than the related problems of computing the probability of evidence Pr, or MPE a special case of MAP. Because of the complexity of MAP, and the lack of viable algorithms to approximate it,MAP computations are generally avoided by practitioners. This paper investigates the complexity of MAP. We show that MAP is complete for NP. We also provide negative complexity results for elimination based algorithms. It turns out that MAP remains hard even when MPE, and Pr are easy. We show that MAP is NPcomplete when the networks are restricted to polytrees, and even then can not be effectively approximated. Because there is no approximation algorithm with guaranteed results, we investigate best effort approximations. We introduce a generic MAP approximation framework. As one instantiation of it, we implement local search coupled with belief propagation BP to approximate MAP. We show how to extract approximate evidence retraction information from belief propagation which allows us to perform efficient local search. This allows MAP approximation even on networks that are too complex to even exactly solve the easier problems of computing Pr or MPE. Experimental results indicate that using BP and local search provides accurate MAP estimates in many cases.