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.

We investigate a learning algorithm for the classification of nonnegative data by mixture models. Multiplicative update rules are derived that directly optimize the performance of these models as classifiers. The update rules have a simple closed form and an intuitive appeal. Our algorithm retains the main virtues of the Expectation-Maximization (EM) algorithm--its guarantee of monotonic improvement, andits absence of tuning parameters--with the added advantage of optimizing a discriminative objective function. The algorithm reduces as a special caseto the method of generalized iterative scaling for log-linear models. The learning rate of the algorithm is controlled by the sparseness of the training data. We use the method of nonnegative matrix factorization (NMF) to discover sparse distributed representations of the data. This form of feature selection greatly accelerates learning and makes the algorithm practical on large problems. Experiments showthat discriminatively trained mixture models lead to much better classification than comparably sized models trained by EM.

Yuille's algorithm is based on a certain decomposition of the Bethe

Common wisdom has it that small distinctions in the probabilities (parameters) quantifying a belief network do not matter much for the results of probabilistic queries. Yet, one can develop realistic scenarios under which small variations in network parameters can lead to significant changes in computed queries. A pending theoretical question is then to analytically characterize parameter changes that do or do not matter. In this paper, we study the sensitivity of probabilistic queries to changes in network parameters and prove some tight bounds on the impact that such parameters can have on queries. Our analytic results pinpoint some interesting situations under which parameter changes do or do not matter. These results are important for knowledge engineers as they help them identify influential network parameters. They also help explain some of the previous experimental results and observations with regards to network robustness against parameter changes.