Hierarchical learning machines are non-regular and non-identifiable statistical models, whose true parameter sets are analytic sets with singularities. Using algebraic analysis, we rigorously prove that the stochastic complexity of a non-identifiable learning machine is asymptotically equal to '1 log n - (ml - 1) log log n

An important issue in neural computing concerns the description of learning dynamics with macroscopic dynamical variables. Recent progress on online learning only addresses the often unrealistic case of an infinite training set. We introduce a new framework to model batch learning of restricted sets of examples, widely applicable to any learning cost function, and fully taking into account the temporal correlations introduced by the recycling of the examples. For illustration we analyze the effects of weight decay and early stopping during the learning of teacher-generated examples.

However, most models have simply ignored these data; the few that have attempted to address them have failed by at least an order of magnitude. We discuss key data on the speed of acquisition, and show how to account for them using a statistically sound model of learning, in which differential reliabilities of stimuli playa crucial role. 1 Introduction Conditioning experiments probe the ways that animals make predictions about rewards and punishments and how those predictions are used to their advantage. Substantial quantitative data are available as to how pigeons and rats acquire conditioned responses during autoshaping, which is one of the simplest paradigms of classical conditioning.

We present a class of approximate inference algorithms for graphical models of the QMR-DT type. We give convergence rates for these algorithms and for the Jaakkola and Jordan (1999) algorithm, and verify these theoretical predictions empirically.

A novel learning approach for human face detection using a network of linear units is presented. The SNoW learning architecture is a sparse network of linear functions over a predefined or incrementally learned feature space and is specifically tailored for learning in the presence of a very large number of features. A wide range of face images in different poses, with different expressions and under different lighting conditions are used as a training set to capture the variations of human faces. Experimental results on commonly used benchmark data sets of a wide range of face images show that the SNoW-based approach outperforms methods that use neural networks, Bayesian methods, support vector machines and others. Furthermore, learning and evaluation using the SNoW-based method are significantly more efficient than with other methods. 1 Introduction Growing interest in intelligent human computer interactions has motivated a recent surge in research on problems such as face tracking, pose estimation, face expression and gesture recognition. Most methods, however, assume human faces in their input images have been detected and localized.

Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified

We develop a hierarchical generative model to study cue combination. The model maps a global shape parameter to local cuespecific parameters, which in tum generate an intensity image. Inferring shape from images is achieved by inverting this model. Inference produces a probability distribution at each level; using distributions rather than a single value of underlying variables at each stage preserves information about the validity of each local cue for the given image. This allows the model, unlike standard combination models, to adaptively weight each cue based on general cue reliability and specific image context.

Everybody "knows" that neural networks need more than a single layer of nonlinear units to compute interesting functions. We show that this is false if one employs winner-take-all as nonlinear unit: - Any boolean function can be computed by a single k-winner-takeall unit applied to weighted sums of the input variables.

Model Predictive Control was developed in the late 70's and came into widespread use, particularly in the refining industry, in the 80's. The economic benefit of this approach to control has been documented [1,2].

Dual estimation refers to the problem of simultaneously estimating the state of a dynamic system and the model which gives rise to the dynamics. Algorithms include expectation-maximization (EM), dual Kalman filtering, and joint Kalman methods. These methods have recently been explored in the context of nonlinear modeling, where a neural network is used as the functional form of the unknown model. Typically, an extended Kalman filter (EKF) or smoother is used for the part of the algorithm that estimates the clean state given the current estimated model. An EKF may also be used to estimate the weights of the network. This paper points out the flaws in using the EKF, and proposes an improvement based on a new approach called the unscented transformation (UT) [3]. A substantial performance gain is achieved with the same order of computational complexity as that of the standard EKF. The approach is illustrated on several dual estimation methods.