Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must consider sample-to-population inferential approaches. This paper deals with the distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean and an analytical approximation of the variance are reported. Asymptotic approximations of the distribution are proposed. The results are applied to the problem of selecting features for incremental learning and classification of the naive Bayes classifier. A fast, newly defined method is shown to outperform the traditional approach based on empirical mutual information on a number of real data sets. Finally, a theoretical development is reported that allows one to efficiently extend the above methods to incomplete samples in an easy and effective way.

Despite the significant progress in multiagent teamwork, existing research does not address the optimality of its prescriptions nor the complexity of the teamwork problem. Without a characterization of the optimality-complexity tradeoffs, it is impossible to determine whether the assumptions and approximations made by a particular theory gain enough efficiency to justify the losses in overall performance. To provide a tool for use by multiagent researchers in evaluating this tradeoff, we present a unified framework, the COMmunicative Multiagent Team Decision Problem (COM-MTDP). The COM-MTDP model combines and extends existing multiagent theories, such as decentralized partially observable Markov decision processes and economic team theory. In addition to their generality of representation, COM-MTDPs also support the analysis of both the optimality of team performance and the computational complexity of the agents' decision problem. In analyzing complexity, we present a breakdown of the computational complexity of constructing optimal teams under various classes of problem domains, along the dimensions of observability and communication cost. In analyzing optimality, we exploit the COM-MTDP's ability to encode existing teamwork theories and models to encode two instantiations of joint intentions theory taken from the literature. Furthermore, the COM-MTDP model provides a basis for the development of novel team coordination algorithms. We derive a domain-independent criterion for optimal communication and provide a comparative analysis of the two joint intentions instantiations with respect to this optimal policy. We have implemented a reusable, domain-independent software package based on COM-MTDPs to analyze teamwork coordination strategies, and we demonstrate its use by encoding and evaluating the two joint intentions strategies within an example domain.

An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of ``normal'' examples with only a small percentage of ``abnormal'' or ``interesting'' examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.

The recursive least-squares (RLS) algorithm is one of the most well-known algorithms used in adaptive filtering, system identification and adaptive control. Its popularity is mainly due to its fast convergence speed, which is considered to be optimal in practice. In this paper, RLS methods are used to solve reinforcement learning problems, where two new reinforcement learning algorithms using linear value function approximators are proposed and analyzed. The two algorithms are called RLS-TD(lambda) and Fast-AHC (Fast Adaptive Heuristic Critic), respectively. RLS-TD(lambda) can be viewed as the extension of RLS-TD(0) from lambda=0 to general lambda within interval [0,1], so it is a multi-step temporal-difference (TD) learning algorithm using RLS methods. The convergence with probability one and the limit of convergence of RLS-TD(lambda) are proved for ergodic Markov chains. Compared to the existing LS-TD(lambda) algorithm, RLS-TD(lambda) has advantages in computation and is more suitable for online learning. The effectiveness of RLS-TD(lambda) is analyzed and verified by learning prediction experiments of Markov chains with a wide range of parameter settings. The Fast-AHC algorithm is derived by applying the proposed RLS-TD(lambda) algorithm in the critic network of the adaptive heuristic critic method. Unlike conventional AHC algorithm, Fast-AHC makes use of RLS methods to improve the learning-prediction efficiency in the critic. Learning control experiments of the cart-pole balancing and the acrobot swing-up problems are conducted to compare the data efficiency of Fast-AHC with conventional AHC. From the experimental results, it is shown that the data efficiency of learning control can also be improved by using RLS methods in the learning-prediction process of the critic. The performance of Fast-AHC is also compared with that of the AHC method using LS-TD(lambda). Furthermore, it is demonstrated in the experiments that different initial values of the variance matrix in RLS-TD(lambda) are required to get better performance not only in learning prediction but also in learning control. The experimental results are analyzed based on the existing theoretical work on the transient phase of forgetting factor RLS methods.

We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limits for the space and time complexities of the compression algorithms. A scaling law is proposed for extrapolation from finite sample lengths. This is applied to sequences of dynamical systems in non-trivial chaotic regimes, a 1-D cellular automaton, and to written English texts.

This article is an edited transcript of a lecture given at IJCAI-99, Stockholm, Sweden, on 4 August 1999. The article summarizes concepts, principles, and tools that were found useful in applications involving causal modeling. The principles are based on structural-model semantics in which functional (or counterfactual) relationships representing autonomous physical processes are the fundamental building blocks. The article presents the conceptual basis of this semantics, illustrates its application in simple problems, and discusses its ramifications to computational and cognitive problems concerning causation.

Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) provide useful tools for modeling dynamical systems. They are particularly useful for representing the topology of environments such as road networks and office buildings, which are typical for robot navigation and planning. The work presented here describes a formal framework for incorporating readily available odometric information and geometrical constraints into both the models and the algorithm that learns them. By taking advantage of such information, learning HMMs/POMDPs can be made to generate better solutions and require fewer iterations, while being robust in the face of data reduction. Experimental results, obtained from both simulated and real robot data, demonstrate the effectiveness of the approach.

Learning of a smooth but nonparametric probability density can be regularized using methods of Quantum Field Theory. We implement a field theoretic prior numerically, test its efficacy, and show that the free parameter of the theory (,smoothness scale') can be determined self consistently by the data; this forms an infinite dimensional generalization of the MDL principle. Finally, we study the implications of one's choice of the prior and the parameterization and conclude that the smoothness scale determination makes density estimation very weakly sensitive to the choice of the prior, and that even wrong choices can be advantageous for small data sets. One of the central problems in learning is to balance'goodness of fit' criteria against the complexity of models. An important development in the Bayesian approach was thus the realization that there does not need to be any extra penalty for model complexity: if we compute the total probability that data are generated by a model, there is a factor from the volume in parameter space-the'Occam factor' -that discriminates against models with more parameters [1, 2].

In this paper we will discuss a variational mean-field theory and its application to BNs, sigmoidal BNs in particular. We present a variational derivation of the mean-field theory, proposed by Plefka[2].

Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoretical results for the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms can be used in the inference step of variational Bayesian learning. Applying these results to the Bayesian analysis of linear-Gaussian state-space models we obtain a learning procedure that exploits the Kalman smoothing propagation, while integrating over all model parameters. We demonstrate how this can be used to infer the hidden state dimensionality of the state-space model in a variety of synthetic problems and one real high-dimensional data set. 1 Introduction Bayesian approaches to machine learning have several desirable properties.