A central issue in principal component analysis (PCA) is choosing the number of principal components to be retained. By interpreting PCA as density estimation, we show how to use Bayesian model selection to estimate thetrue dimensionality of the data. The resulting estimate is simple to compute yet guaranteed to pick the correct dimensionality, given enough data. The estimate involves an integral over the Steifel manifold of k-frames, which is difficult to compute exactly. But after choosing an appropriate parameterization and applying Laplace's method, an accurate andpractical estimator is obtained. In simulations, it is convincingly better than cross-validation and other proposed algorithms, plus it runs much faster.

Algebraic geometry is essential to learning theory. In hierarchical learning machines such as layered neural networks and gaussian mixtures, the asymptotic normality does not hold, since Fisher information matricesare singular. In this paper, the rigorous asymptotic form of the stochastic complexity is clarified based on resolution of singularities and two different problems are studied.

We propose a method of approximate dynamic programming for Markov decision processes (MDPs) using algebraic decision diagrams (ADDs). We produce near-optimal value functions and policies with much lower time and space requirements than exact dynamic programming. Our method reduces the sizes of the intermediate value functions generated during value iteration by replacing the values at the terminals of the ADD with ranges of values. Our method is demonstrated on a class of large MDPs (with up to 34 billion states), and we compare the results with the optimal value functions.

The problem of reinforcement learning in large factored Markov decision processes is explored. The Q-value of a state-action pair is approximated by the free energy of a product of experts network. Network parameters are learned online using a modified SARSA algorithm which minimizes the inconsistency of the Q-values of consecutive state-action pairs. Actions arechosen based on the current value estimates by fixing the current state and sampling actions from the network using Gibbs sampling. The algorithm is tested on a cooperative multi-agent task. The product of experts model is found to perform comparably to table-based Q-Iearning for small instances of the task, and continues to perform well when the problem becomes too large for a table-based representation.

Many approaches to reinforcement learning combine neural networks orother parametric function approximators with a form of temporal-difference learning to estimate the value function of a Markov Decision Process. A significant disadvantage of those procedures isthat the resulting learning algorithms are frequently unstable. In this work, we present a new, kernel-based approach to reinforcement learning which overcomes this difficulty and provably converges to a unique solution. By contrast to existing algorithms, our method can also be shown to be consistent in the sense that its costs converge to the optimal costs asymptotically. Our focus is on learning in an average-cost framework and on a practical application tothe optimal portfolio choice problem. 1 Introduction Temporal-difference (TD) learning has been applied successfully to many real-world applications that can be formulated as discrete state Markov Decision Processes (MDPs) with unknown transition probabilities.

Prior knowledge about video structure can be used both as a means to improve the peiformance of content analysis and to extract features that allow semantic classification. We introduce statistical models for two important components of this structure, shot duration and activity, and demonstrate the usefulness of these models by introducing a Bayesian formulation for the shot segmentation problem. The new formulations is shown to extend standard thresholding methods in an adaptive and intuitive way, leading to improved segmentation accuracy.

A Bayes network based classifier for distinguishing terrestrial rocks from meteorites is implemented onboard the Nomad robot. Equipped with a camera, spectrometer and eddy current sensor, this robot searched the ice sheets of Antarctica and autonomously made the first robotic identification of a meteorite, in January 2000 at the Elephant Moraine. This paper discusses rock classification from a robotic platform, and describes the system onboard Nomad. 1 Introduction Figure 1: Human meteorite search with snowmobiles on the Antarctic ice sheets, and on foot in the moraines. Antarctica contains the most fertile meteorite hunting grounds on Earth. The pristine, dry and cold environment ensures that meteorites deposited there are preserved for long periods.

The human figure exhibits complex and rich dynamic behavior that is both nonlinear and time-varying. Effective models of human dynamics can be learned from motion capture data using switching linear dynamic system (SLDS) models. We present results for human motion synthesis, classification,and visual tracking using learned SLDS models. Since exact inference in SLDS is intractable, we present three approximate inference algorithmsand compare their performance. In particular, a new variational inference algorithm is obtained by casting the SLDS model as a Dynamic Bayesian Network. Classification experiments show the superiority of SLDS over conventional HMM's for our problem domain.

In this work, we introduce an Interactive Parts (IP) model as an alternative to Hidden Markov Models (HMMs). We tested both models on a database of online cursive script. We show that implementations ofHMMs and the IP model, in which all letters are assumed to have the same average width, give comparable results. However, in contrast to HMMs, the IP model can handle duration modeling without an increase in computational complexity. 1 Introduction Hidden Markov models [9] have been a dominant paradigm in speech and handwriting recognitionover the past several decades. The success of HMMs is primarily due to their ability to model the statistical and sequential nature of speech and handwriting data.

We propose a novel probabilistic framework for semantic video indexing. Wedefine probabilistic multimedia objects (multijects) to map low-level media features to high-level semantic labels.