Over the last years, particle filters have been applied with great success to a variety of state estimation problems. We present a statistical approach to increasing the efficiency of particle filters by adapting the size of sample sets on-the-fly. The key idea of the KLD-sampling method is to bound the approximation error introduced by the sample-based representation of the particle filter. The name KLD-sampling is due to the fact that we measure the approximation error by the Kullback-Leibler distance. Our adaptation approach chooses a small number of samples if the density is focused on a small part of the state space, and it chooses a large number of samples if the state uncertainty is high. Both the implementation and computation overhead of this approach are small. Extensive experiments using mobile robot localization as a test application show that our approach yields drastic improvements over particle filters with fixed sample set sizes and over a previously introduced adaptation technique.

Recent approaches have used uncertainty over the vocabulary of symbols in a multinomial distribution as a means of accounting for sparsity. We present a Bayesian approach that allows weak prior knowledge, in the form of a small set of approximate candidate vocabularies, to be used to dramatically improve the resulting estimates. We demonstrate these improvements in applications to text compression andestimating distributions over words in newsgroup data. 1 Introduction Sparse multinomial distributions arise in many statistical domains, including natural languageprocessing and graphical models. Consequently, a number of approaches toparameter estimation for sparse multinomial distributions have been suggested [3]. These approaches tend to be domain-independent: they make little use of prior knowledge about a specific domain. In many domains where multinomial distributionsare estimated there is often at least weak prior knowledge about' the potential structure of distributions, such as a set of hypotheses about restricted vocabularies from which the symbols might be generated. Such knowledge can be solicited from experts or obtained from unlabeled data. We present a method for Bayesian_parameter estimation in sparse discrete domains that exploits this weak form of prior knowledge to improve estimates over knowledge-free approaches.

The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka's expectation propagation. Lastly,we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classification anddensity estimation with Gaussian processes and on an independent componentanalysis problem.

We derive an equivalence between AdaBoost and the dual of a convex optimization problem, showing that the only difference between minimizing theexponential loss used by AdaBoost and maximum likelihood for exponential models is that the latter requires the model to be normalized toform a conditional probability distribution over labels. In addition to establishing a simple and easily understood connection between the two methods, this framework enables us to derive new regularization procedures for boosting that directly correspond to penalized maximum likelihood. Experiments on UCI datasets support our theoretical analysis andgive additional insight into the relationship between boosting and logistic regression.

A theory of categorization is presented in which knowledge of causal relationships between category features is represented as a Bayesian network. Referred to as causal-model theory, this theory predicts that objects are classified as category members to the extent they are likely to have been produced by a categorys causal model. On this view, people have models of the world that lead them to expect a certain distribution of features in category members (e.g., correlations between feature pairs that are directly connected by causal relationships), and consider exemplars good category members when they manifest those expectations. These expectations include sensitivity to higher-order feature interactions that emerge from the asymmetries inherent in causal relationships. Research on the topic of categorization has traditionally focused on the problem of learning new categories given observations of category members.

Our analysis has shown the following: 1. As a function of an individual hyperparameter ai, £(a) has a unique maximum computable in closed-form.

Many domains are naturally organized in an abstraction hierarchy or taxonomy, where the instances in "nearby" classes in the taxonomy are similar. In this paper, weprovide a general probabilistic framework for clustering data into a set of classes organized as a taxonomy, where each class is associated with a probabilistic modelfrom which the data was generated. The clustering algorithm simultaneously optimizes three things: the assignment of data instances to clusters, themodels associated with the clusters, and the structure of the abstraction hierarchy. A unique feature of our approach is that it utilizes global optimization algorithms for both of the last two steps, reducing the sensitivity to noise and the propensity to local maxima that are characteristic of algorithms such as hierarchical agglomerativeclustering that only take local steps. We provide a theoretical analysis for our algorithm, showing that it converges to a local maximum of the joint likelihood of model and data.

High dimensional data that lies on or near a low dimensional manifold can be described bya collection of local linear models. Such a description, however, does not provide a global parameterization of the manifold--arguably an important goal of unsupervised learning. In this paper, we show how to learn a collection of local linear models that solves this more difficult problem. Our local linear models are represented by a mixture of factor analyzers, and the "global coordination" ofthese models is achieved by adding a regularizing term to the standard maximum likelihood objective function. The regularizer breaks a degeneracy in the mixture model's parameter space, favoring models whose internal coordinate systemsare aligned in a consistent way. As a result, the internal coordinates changesmoothly and continuously as one traverses a connected path on the manifold--even when the path crosses the domains of many different local models. The regularizer takes the form of a Kullback-Leibler divergence and illustrates an unexpected application of variational methods: not to perform approximate inferencein intractable probabilistic models, but to learn more useful internal representations in tractable ones.

Singularities are ubiquitous in the parameter space of hierarchical models such as multilayer perceptrons. At singularities, the Fisher information matrix degenerates, and the Cramer-Rao paradigm does no more hold, implying that the classical model selection theory suchas AIC and MDL cannot be applied. It is important to study the relation between the generalization error and the training error at singularities. The present paper demonstrates a method of analyzing these errors both for the maximum likelihood estimator andthe Bayesian predictive distribution in terms of Gaussian random fields, by using simple models. 1 Introduction A neural network is specified by a number of parameters which are synaptic weights and biases. Learning takes place by modifying these parameters from observed input-output examples.

We have designed and fabricated a VLSI synapse that can learn a conditional probability or correlation between spike-based inputs and feedback signals. The synapse is low power, compact, provides nonvolatile weight storage, and can perform simultaneous multiplication andadaptation. We can calibrate arrays of synapses to ensure uniform adaptation characteristics. Finally, adaptation in our synapse does not necessarily depend on the signals used for computation. Consequently,our synapse can implement learning rules that correlate past and present synaptic activity. We provide analysis andexperimental chip results demonstrating the operation in learning and calibration mode, and show how to use our synapse to implement various learning rules in silicon.