We address in this paper the question of how the knowledge of the marginal distribution P (x) can be incorporated in a learning algorithm. We suggest three theoretical methods for taking into account this distribution for regularization and provide links to existing graph-based semi-supervised learning algorithms. We also propose practical implementations.

We present and empirically test a novel approach for categorizing 3-D free form object shapes represented by range data. In contrast to traditional surface-signature based systems that use alignment to match specific objects, we adapted the newly introduced symbolic-signature representation to classify deformable shapes [10]. Our approach constructs an abstract description of shape classes using an ensemble of classifiers that learn object class parts and their corresponding geometrical relationships from a set of numeric and symbolic descriptors. We used our classification engine in a series of large scale discrimination experiments on two well-defined classes that share many common distinctive features. The experimental results suggest that our method outperforms traditional numeric signature-based methodologies.

We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statistical problem of model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathematical definition of randomness given by Kolmogorov complexity, we characterize regularity in terms of a hierarchy of automata that augment a finite controller with different forms of memory. We find that the regularities detected in binary sequences depend upon presentation format, and that the kinds of automata that can identify these regularities are informative about the cognitive processes engaged by different formats.

Autonomous helicopter flight represents a challenging control problem, with complex, noisy, dynamics. In this paper, we describe a successful application of reinforcement learning to autonomous helicopter flight.

We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data.

The E-step boils down to computing probabilities of the hidden variables given the observed variables (evidence) and current set of parameters. The M-step then, given these probabilities, yields a new set of parameters guaranteed to increase the likelihood. In Bayesian networks, that will be the focus of this article, the M-step is usually relatively straightforward. A complication may arise in the E-step, when computing the probability of the hidden variables given the evidence becomes intractable. An often used approach is to replace the exact yet intractable inference in the E step with approximate inference, either through sampling or using a deterministic variational method. The use of a "mean-field" variational method in this context leads to an algorithm known as variational EM and can be given theinterpretation of minimizing a free energy with respect to both a tractable approximate distribution (approximate E-step) and the parameters (M-step) [2]. Loopy belief propagation [3] and variants thereof, such as generalized belief propagation [4] and expectation propagation [5], have become popular alternatives to the "mean-field" variational approaches, often yielding somewhat better approximations. And indeed, they can and have been applied for approximate inference in the E-step of the EM algorithm (see e.g.

This paper presents VLSI circuits with continuous-valued probabilistic behaviour realized by injecting noise into each computing unit(neuron). Interconnecting the noisy neurons forms a Continuous Restricted Boltzmann Machine (CRBM), which has shown promising performance in modelling and classifying noisy biomedical data.

When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. In this paper we present an improved algorithm for learning k while clustering. The G-means algorithm is based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution. G-means runs k-means with increasing k in a hierarchical fashion until the test accepts the hypothesis that the data assigned to each k-means center are Gaussian. Two key advantages are that the hypothesis test does not limit the covariance of the data and does not compute a full covariance matrix. Additionally, G-means only requires one intuitive parameter, the standard statistical significance level α. We present results from experiments showing that the algorithm works well, and better than a recent method based on the BIC penalty for model complexity. In these experiments, we show that the BIC is ineffective as a scoring function, since it does not penalize strongly enough the model's complexity.

We describe a pattern acquisition algorithm that learns, in an unsupervised fashion, a streamlined representation of linguistic structures from a plain natural-language corpus. This paper addresses the issues of learning structured knowledge from a large-scale natural language data set, and of generalization to unseen text. The implemented algorithm represents sentences as paths on a graph whose vertices are words (or parts of words). Significant patterns, determined by recursive context-sensitive statistical inference, form new vertices. Linguistic constructions are represented by trees composed of significant patterns and their associated equivalence classes. An input module allows the algorithm to be subjected to a standard test of English as a Second Language (ESL) proficiency. The results are encouraging: the model attains a level of performance considered to be "intermediate" for 9th-grade students, despite having been trained on a corpus (CHILDES) containing transcribed speech of parents directed to small children.

Recent developments in grid-based and point-based approximation algorithms for POMDPs have greatly improved the tractability of POMDP planning. These approaches operate on sets of belief points by individually learning a value function for each point. In reality, belief points exist in a highly-structured metric simplex, but current POMDP algorithms do not exploit this property. This paper presents a new metric-tree algorithm which can be used in the context of POMDP planning to sort belief points spatially, and then perform fast value function updates over groups of points. We present results showing that this approach can reduce computation in point-based POMDP algorithms for a wide range of problems.