Massive transaction data sets are recorded in a routine manner in telecommunications, retail commerce, and Web site management. In this paper we address the problem of inferring predictive individual profiles from such historical transaction data. We describe a generative mixture model for count data and use an an approximate Bayesian estimation framework that effectively combines an individual's specific history with more general population patterns. We use a large real-world retail transaction data set to illustrate how these profiles consistently outperform non-mixture and non-Bayesian techniques in predicting customer behavior in out-of-sample data.

Discriminative classifiers model the posterior p(ylx) directly, or learn a direct map from inputs x to the class labels. There are several compelling reasons for using discriminative rather than generative classifiers, one of which, succinctly articulated by Vapnik [6], is that "one should solve the [classification] problem directly and never solve a more general problem as an intermediate step [such as modeling p(xly)]." Indeed, leaving aside computational issues and matters such as handling missing data, the prevailing consensus seems to be that discriminative classifiers are almost always to be preferred to generative ones. Another piece of prevailing folk wisdom is that the number of examples needed to fit a model is often roughly linear in the number of free parameters of a model. This has its theoretical basis in the observation that for "many" models, the VC dimension is roughly linear or at most some low-order polynomial in the number of parameters (see, e.g., [1, 3]), and it is known that sample complexity in the discriminative setting is linear in the VC dimension [6]. In this paper, we study empirically and theoretically the extent to which these beliefs are true. A parametric family of probabilistic models p(x, y) can be fit either to optimize the joint likelihood of the inputs and the labels, or fit to optimize the conditional likelihood p(ylx), or even fit to minimize the 0-1 training error obtained by thresholding p(ylx) to make predictions.

The hierarchical hidden Markov model (HHMM) is a generalization of the hidden Markov model (HMM) that models sequences with structure at many length/time scales [FST98].

We describe the application of kernel methods to Natural Language Processing (NLP) problems. In many NLP tasks the objects being modeled are strings, trees, graphs or other discrete structures which require some mechanism to convert them into feature vectors. We describe kernels for various natural language structures, allowing rich, high dimensional representations of these structures. We show how a kernel over trees can be applied to parsing using the voted perceptron algorithm, and we give experimental results on the ATIS corpus of parse trees.

In previous work on "transformed mixtures of Gaussians" and "transformed hidden Markov models", we showed how the EM algorithm in a discrete latent variable model can be used to jointly normalize data (e.g., center images, pitch-normalize spectrograms) and learn a mixture model of the normalized data. The only input to the algorithm is the data, a list of possible transformations, and the number of clusters to find. The main criticism of this work was that the exhaustive computation of the posterior probabilities over transformations would make scaling up to large feature vectors and large sets of transformations intractable. Here, we describe how a tremendous speedup is acheived through the use of a variational technique for decoupling transformations, and a fast Fourier transform method for computing posterior probabilities.

We present a probabilistic generative model for timing deviations in expressive music. The structure of the proposed model is equivalent to a switching state space model. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. The inferences are carried out using sequential Monte Carlo integration (particle filtering) techniques. For this purpose, we have derived a novel Viterbi algorithm for Rao-Blackwellized particle filters, where a subset of the hidden variables is integrated out.

Multisensory response enhancement (MRE) is the augmentation of the response of a neuron to sensory input of one modality by simultaneous input from another modality. The maximum likelihood (ML) model presented here modifies the Bayesian model for MRE (Anastasio et al.) by incorporating a decision strategy to maximize the number of correct decisions. Thus the ML model can also deal with the important tasks of stimulus discrimination and identification in the presence of incongruent visual and auditory cues. It accounts for the inverse effectiveness observed in neurophysiological recording data, and it predicts a functional relation between uni-and bimodal levels of discriminability that is testable both in neurophysiological and behavioral experiments.

In this paper we explore two quantitative approaches to the modelling of counterfactual reasoning - a linear and a noisy-OR model - based on information contained in conceptual dependency networks. Empirical data is acquired in a study and the fit of the models compared to it. We conclude by considering the appropriateness of nonparametric approaches to counterfactual reasoning, and examining the prospects for other parametric approaches in the future.

High dimensional data that lies on or near a low dimensional manifold can be described by a 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" of these 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 systems are aligned in a consistent way. As a result, the internal coordinates change smoothly 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 inference in intractable probabilistic models, but to learn more useful internal representations in tractable ones.

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 and adaptation. 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 and experimental chip results demonstrating the operation in learning and calibration mode, and show how to use our synapse to implement various learning rules in silicon.