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.

The three-dimensional motion of humans is underdetermined when the observation is limited to a single camera, due to the inherent 3D ambiguity of 2D video. We present a system that reconstructs the 3D motion of human subjects from single-camera video, relying on prior knowledge about human motion, learned from training data, to resolve those ambiguities. After initialization in 2D, the tracking and 3D reconstruction is automatic; we show results for several video sequences. The results show the power of treating 3D body tracking as an inference problem.

We present a new learning architecture: the Decision Directed Acyclic Graph (DDAG), which is used to combine many two-class classifiers into a multiclass classifier. For an N -class problem, the DDAG contains N(N - 1)/2 classifiers, one for each pair of classes. We present a VC analysis of the case when the node classifiers are hyperplanes; the resulting bound on the test error depends on N and on the margin achieved at the nodes, but not on the dimension of the space. This motivates an algorithm, DAGSVM, which operates in a kernel-induced feature space and uses two-class maximal margin hyperplanes at each decision-node of the DDAG. The DAGSVM is substantially faster to train and evaluate than either the standard algorithm or Max Wins, while maintaining comparable accuracy to both of these algorithms. 1 Introduction The problem of multiclass classificatIon, especially for systems like SVMs, doesn't present an easy solution. It is generally simpler to construct classifier theory and algorithms for two mutually-exclusive classes than for N mutually-exclusive classes.

In many classification tasks, recognition accuracy is low because input patterns are corrupted by noise or are spatially or temporally overlapping. We propose an approach to overcoming these limitations based on a model of human selective attention. The model, an early selection filter guided by top-down attentional control, entertains each candidate output class in sequence and adjusts attentional gain coefficients in order to produce a strong response for that class. The chosen class is then the one that obtains the strongest response with the least modulation of attention. We present simulation results on classification of corrupted and superimposed handwritten digit patterns, showing a significant improvement in recognition rates.

A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-tenn predict and to locate the outlines of the attractor by a new way of nonlinear principal component analysis. Closed-loop predictions are constrained to stay within these outlines, to prevent divergence from the attractor. Learning is exceptionally fast: parameter estimation for the 1000 sample laser data from the 1991 Santa Fe time series competition took less than a minute on a 166 MHz Pentium PC.

For many problems, the correct behavior of a model depends not only on its input-output mapping but also on properties of its Jacobian matrix, the matrix of partial derivatives of the model's outputs with respect to its inputs. We introduce the J-prop algorithm, an efficient general method for computing the exact partial derivatives of a variety of simple functions of the Jacobian of a model with respect to its free parameters. The algorithm applies to any parametrized feedforward model, including nonlinear regression, multilayer perceptrons, and radial basis function networks.