Forexample, in the Options framework [1,2], the programmer defines a set of macro actions ("options") and provides a policy for each. Learning algorithms (such as semi-Markov Q learning) can then treat these temporally abstract actions as if they were primitives and learn a policy for selecting among them. Closely related is the HAM framework, in which the programmer constructs a hierarchy of finitestate controllers[3]. Each controller can include non-deterministic states (where the programmer was not sure what action to perform). The HAMQ learning algorithm can then be applied to learn a policy for making choices in the non-deterministic states.

The statistics of photographic images, when represented using multiscale (wavelet) bases, exhibit two striking types of non Gaussian behavior. First, the marginal densities of the coefficients have extended heavy tails. Second, the joint densities exhibit variance dependenciesnot captured by second-order models. We examine propertiesof the class of Gaussian scale mixtures, and show that these densities can accurately characterize both the marginal and joint distributions of natural image wavelet coefficients. This class of model suggests a Markov structure, in which wavelet coefficients arelinked by hidden scaling variables corresponding to local image structure.

However, designing a net to have a given set of attractors is notoriously tricky; training procedures are CPU intensive and often produce spurious afuactors andill-conditioned attractor basins. These difficulties occur because each connection in the network participates in the encoding ofmultiple attractors. We describe an alternative formulation of attractor networks in which the encoding of knowledge is local, not distributed. Although localist attractor networks have similar dynamics to their distributed counterparts, they are much easier to work with and interpret. Attractor networks map an input space, usually continuous, to a sparse output space composed of a discrete set of alternatives.

The three-dimensional motion of humans is underdetermined when the observation is limited to a single camera, due to the inherent 3D ambiguity of2D 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. Afterinitialization 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.

Local "belief propagation" rules of the sort proposed by Pearl [15] are guaranteed to converge to the correct posterior probabilities in singly connected graphical models. Recently, a number of researchers have empirically demonstratedgood performance of "loopy belief propagation" using these same rules on graphs with loops. Perhaps the most dramatic instance is the near Shannon-limit performance of "Turbo codes", whose decoding algorithm is equivalent to loopy belief propagation. Except for the case of graphs with a single loop, there has been little theoretical understandingof the performance of loopy propagation. Here we analyze belief propagation in networks with arbitrary topologies when the nodes in the graph describe jointly Gaussian random variables.

Independent component analysis of natural images leads to emergence ofsimple cell properties, Le. linear filters that resemble wavelets or Gabor functions. In this paper, we extend ICA to explain further properties of VI cells.

We present a new technique for time series analysis based on dynamic probabilisticnetworks. In this approach, the observed data are modeled in terms of unobserved, mutually independent factors, as in the recently introduced technique of Independent Factor Analysis (IFA).However, unlike in IFA, the factors are not Li.d.; each factor has its own temporal statistical characteristics. We derive a family of EM algorithms that learn the structure of the underlying factors and their relation to the data. These algorithms perform source separation and noise reduction in an integrated manner, and demonstrate superior performance compared to IFA. 1 Introduction The technique of independent factor analysis (IFA) introduced in [1] provides a tool for modeling L'-dim data in terms of L unobserved factors. These factors are mutually independent and combine linearly with added noise to produce the observed data.

A latent variable generative model with finite noise is used to describe severaldifferent algorithms for Independent Components Analysis (lCA). In particular, the Fixed Point ICA algorithm is shown to be equivalent to the Expectation-Maximization algorithm for maximum likelihood under certain constraints, allowing the conditions for global convergence to be elucidated. The algorithms can also be explained by their generic behavior near a singular point where the size of the optimal generativebases vanishes. An expansion of the likelihood about this singular point indicates the role of higher order correlations in determining thefeatures discovered by ICA. The application and convergence of these algorithms are demonstrated on a simple illustrative example.

In this paper, we use mutual information to characterize the distributions ofphonetic and speaker/channel information in a timefrequency space. The mutual information (MI) between the phonetic label and one feature, and the joint mutual information (JMI) between the phonetic label and two or three features are estimated. The Miller's bias formulas for entropy and mutual information estimates areextended to include higher order terms. The MI and the JMI for speaker/channel recognition are also estimated. The results are complementary to those for phonetic classification. Our results show how the phonetic information is locally spread and how the speaker/channel information is globally spread in time and frequency.

In this work, we formulate a hierarchical systemof interconnected modules consisting in populations of neurons formodeling the underlying mechanisms involved in selective visual attention. We demonstrate that our neural system for visual search works across the visual field in parallel but due to the different intrinsic dynamics can show the two experimentally observed modes of visual attention, namely: the serial and the parallel search mode. In other words, neither explicit model of a focus of attention nor saliencies maps are used. The focus of attention appears as an emergent property of the dynamic behavior of the system. The neural population dynamics are handled in the framework of the mean-field approximation. Consequently, thewhole process can be expressed as a system of coupled differential equations.