Nevin Lianwen Zhang

Exploiting contextual independence in probabilistic inference

Bayesian belief networks have grown to prominence because they provide compact representations for many problems for which probabilistic inference is appropriate, and there are algorithms to exploit this compactness. The next step is to allow compact representations of the conditional probabilities of a variable given its parents. In this paper we present such a representation that exploits contextual independence in terms of parent contexts; which variables act as parents may depend on the value of other variables. The internal representation is in terms of contextual factors (confactors) that is simply a pair of a context and a table. The algorithm, contextual variable elimination, is based on the standard variable elimination algorithm that eliminates the nonquery variables in turn, but when eliminating a variable, the tables that need to be multiplied can depend on the context. This algorithm reduces to standard variable elimination when there is no contextual independence structure to exploit. We show how this can be much more efficient than variable elimination when there is structure to exploit. We explain why this new method can exploit more structure than previous methods for structured belief network inference and an analogous algorithm that uses trees.

Speeding up the convergence of value iteration in partially observable Markov decision processes

Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding optimal policies for POMDPs. It typically takes a large number of iterations to converge. This paper proposes a method for accelerating the convergence of value iteration. The method has been evaluated on an array of benchmark problems and was found to be very effective: It enabled value iteration to converge after only a few iterations on all the test problems.

Probabilistic Inference in Influence Diagrams

This paper is about reducing influence diagram (ID) evaluation into Bayesian network (BN) inference problems that are as easy to solve as possible. Such reduction is interesting because it enables one to readily use ones favorite BN inference algorithm to efficiently evaluate IDs. Two such reduction methods have been proposed previously (Cooper 1988; Shachter and Peot 1992). This paper proposes a new method. The BN inference problems induced by the new method are much easier to solve than those induced by the two previous methods.

Latent tree models and diagnosis in traditional Chinese medicine

OBJECTIVE TCM (traditional Chinese medicine) is an important avenue for disease prevention and treatment for the Chinese people and is gaining popularity among others. However, many remain skeptical and even critical of TCM because of a number of its shortcomings. One key shortcoming is the lack of objective diagnosis standards. We endeavor to alleviate this shortcoming using machine learning techniques. METHOD TCM diagnosis consists of two steps, patient information gathering and syndrome differentiation. We focus on the latter. When viewed as a black box, syndrome differentiation is simply a classifier that classifies patients into different classes based on their symptoms. A fundamental question is: do those classes exist in reality? To seek an answer to the question from the machine learning perspective, one would naturally use cluster analysis. Previous clustering methods are unable to cope with the complexity of TCM. We have therefore developed a new clustering method in the form of latent tree models. We have conducted a case study where we first collected a data set about a TCM domain called kidney deficiency and then used latent tree models to analyze the data set. RESULTS Our analysis has found natural clusters in the data set that correspond well to TCM syndrome types. This is an important discovery because (1) it provides statistical validation to TCM syndrome types and (2) it suggests the possibility of establishing objective and quantitative diagnosis standards for syndrome differentiation. In this paper, we provide a summary of research work on latent tree models and report the aforementioned case study.

Model-based multidimensional clustering of categorical data

Existing models for cluster analysis typically consist of a number of attributes that describe the objects to be partitioned and one single latent variable that represents the clusters to be identified. When one analyzes data using such a model, one is looking for one way to cluster data that is jointly defined by all the attributes. In other words, one performs unidimensional clustering. This is not always appropriate. For complex data with many attributes, it is more reasonable to consider multidimensional clustering, i.e., to partition data along multiple dimensions. In this paper, we present a method for performing multidimensional clustering on categorical data and show its superiority over unidimensional clustering.

Efficient learning of hierarchical latent class models

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are hidden. In earlier work, we have demonstrated in principle the possibility of reconstructing HLC models from data. We address the scalability issue and develop a search-based algorithm that can efficiently learn high-quality HLC models for realistic domains. There are three technical contributions: (1) the identification of a set of search operators; (2) the use of improvement in BIC score per unit of increase in model complexity, rather than BIC score itself, for model selection; and (3) the adaptation of structural EM for situations where candidate models contain different variables than the current model. The algorithm was tested on the COIL Challenge 2000 data set and an interesting model was found.

A model approximation scheme for planning in partially observable stochastic domains

Partially observable Markov decision processes (POMDPs) are a natural model for planning problems where effects of actions are nondeterministic and the state of the world is not completely observable. It is difficult to solve POMDPs exactly. This paper proposes a new approximation scheme. The basic idea is to transform a POMDP into another one where additional information is provided by an oracle. The oracle informs the planning agent that the current state of the world is in a certain region. The transformed POMDP is consequently said to be region observable. It is easier to solve than the original POMDP. We propose to solve the transformed POMDP and use its optimal policy to construct an approximate policy for the original POMDP. By controlling the amount of additional information that the oracle provides, it is possible to find a proper tradeoff between computational time and approximation quality. In terms of algorithmic contributions, we study in details how to exploit region observability in solving the transformed POMDP. To facilitate the study, we also propose a new exact algorithm for general POMDPs. The algorithm is conceptually simple and yet is significantly more efficient than all previous exact algorithms.

Latent tree models and approximate inference in Bayesian networks

We propose a novel method for approximate inference in Bayesian networks (BNs). The idea is to sample data from a BN, learn a latent tree model (LTM) from the data offline, and when online, make inference with the LTM instead of the original BN. Because LTMs are tree-structured, inference takes linear time. In the meantime, they can represent complex relationship among leaf nodes and hence the approximation accuracy is often good. Empirical evidence shows that our method can achieve good approximation accuracy at low online computational cost.

A survey on latent tree models and applications

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic graphical models, deserves attention. Its simple structure - a tree - allows simple and efficient inference, while its latent variables capture complex relationships. In the past decade, the latent tree model has been subject to significant theoretical and methodological developments. In this review, we propose a comprehensive study of this model. First we summarize key ideas underlying the model. Second we explain how it can be efficiently learned from data. Third we illustrate its use within three types of applications: latent structure discovery, multidimensional clustering, and probabilistic inference. Finally, we conclude and give promising directions for future researches in this field.

Latent variable discovery in classification models

The naive Bayes model makes the often unrealistic assumption that the feature variables are mutually independent given the class variable. We interpret a violation of this assumption as an indication of the presence of latent variables, and we show how latent variables can be detected. Latent variable discovery is interesting, especially for medical applications, because it can lead to a better understanding of application domains. It can also improve classification accuracy and boost user confidence in classification models.