We consider the problem of reconstructing a temporal discrete sequence of multidimensional real vectors when part of the data is missing, under the assumption that the sequence was generated by a continuous process. A particular case of this problem is multivariate regression, which is very difficult when the underlying mapping is one-to-many. We propose an algorithm based on a joint probability model of the variables of interest, implemented using a nonlinear latent variable model. Each point in the sequence is potentially reconstructed as any of the modes of the conditional distribution of the missing variables given the present variables (computed using an exhaustive mode search in a Gaussian mixture). Mode selection is determined by a dynamic programming search that minimises a geometric measure of the reconstructed sequence, derived from continuity constraints. We illustrate the algorithm with a toy example and apply it to a real-world inverse problem, the acoustic-toarticulatory mapping. The results show that the algorithm outperforms conditional mean imputation and multilayer perceptrons. 1 Definition of the 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 demonstrated good 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 understanding of 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.

Three contributions to developing an algorithm for assisting engineers in designing analog circuits are provided in this paper. First, a method for representing highly nonlinear and noncontinuous analog circuits using Kirchoff current law potential functions within the context of a Markov field is described. Second, a relatively efficient algorithm for optimizing the Markov field objective function is briefly described and the convergence proof is briefly sketched. And third, empirical results illustrating the strengths and limitations of the approach are provided within the context of a JFET transistor design problem. The proposed algorithm generated a set of circuit components for the JFET circuit model that accurately generated the desired characteristic curves. 1 Analog circuit design using Markov random fields

He intended to build a model mimicking the behavior of the autistic savant without the need either to develop arithmetical skills or to encode explicit knowledge about regularities in the structure of dates. A standard multilayer network trained with backpropagation [6] was not able to solve the date-calculation task. Although the network was able to learn the examples used for training, it did not manage to generalize to novel date-day combinations.

We formulate the problem of retrieving images from visual databases as a problem of Bayesian inference. This leads to natural and effective solutions for two of the most challenging issues in the design of a retrieval system: providing support for region-based queries without requiring prior image segmentation, and accounting for user-feedback during a retrieval session. We present a new learning algorithm that relies on belief propagation to account for both positive and negative examples of the user's interests.

The complexity of cortical circuits may be characterized by the number of synapses per neuron. We study the dependence of complexity on the fraction of the cortical volume that is made up of "wire" (that is, ofaxons and dendrites), and find that complexity is maximized when wire takes up about 60% of the cortical volume. This prediction is in good agreement with experimental observations. A consequence of our arguments is that any rearrangement of neurons that takes more wire would sacrifice computational power.

Psychophysical and physiological evidence shows that sound localization of acoustic signals is strongly influenced by their synchrony with visual signals. This effect, known as ventriloquism, is at work when sound coming from the side of a TV set feels as if it were coming from the mouth of the actors. The ventriloquism effect suggests that there is important information about sound location encoded in the synchrony between the audio and video signals. In spite of this evidence, audiovisual synchrony is rarely used as a source of information in computer vision tasks. In this paper we explore the use of audio visual synchrony to locate sound sources. We developed a system that searches for regions of the visual landscape that correlate highly with the acoustic signals and tags them as likely to contain an acoustic source.

We propose a new and efficient technique for incorporating contextual information into object classification. Most of the current techniques face the problem of exponential computation cost. In this paper, we propose a new general framework that incorporates partial context at a linear cost. This technique is applied to microscopic urinalysis image recognition, resulting in a significant improvement of recognition rate over the context free approach. This gain would have been impossible using conventional context incorporation techniques.

We present a variational Bayesian method for model selection over families of kernels classifiers like Support Vector machines or Gaussian processes. The algorithm needs no user interaction and is able to adapt a large number of kernel parameters to given data without having to sacrifice training cases for validation. This opens the possibility to use sophisticated families of kernels in situations where the small "standard kernel" classes are clearly inappropriate. We relate the method to other work done on Gaussian processes and clarify the relation between Support Vector machines and certain Gaussian process models.

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.