Signal processing and classification algorithms often have limited applicability resulting from an inaccurate model of the signal's underlying structure.We present here an efficient, Bayesian algorithm for modeling a signal composed of the superposition of brief, Poisson-distributed functions. This methodology is applied to the specific problem of modeling and classifying extracellular neural waveforms which are composed of a superposition of an unknown number of action potentials CAPs). Previous approaches have had limited success due largely to the problems of determining the spike shapes, deciding how many are shapes distinct, and decomposing overlapping APs. A Bayesian solution to each of these problems is obtained by inferring a probabilistic model of the waveform. This approach quantifies the uncertainty of the form and number of the inferred AP shapes and is used to obtain an efficient method for decomposing complex overlaps. This algorithm can extract many times more information than previous methods and facilitates the extracellular investigation of neuronal classes and of interactions within neuronal circuits.

MacKay's Bayesian framework for backpropagation is conceptually appealing as well as practical. It automatically adjusts the weight decay parameters during training, and computes the evidence for each trained network. The evidence is proportional to our belief in the model. In this paper, the framework is extended to pruned nets, leading to an Ockham Factor for "tuning the architecture to the data". A committee of networks, selected by their high evidence, is a natural Bayesian construction.

In solving these tasks, one is faced with a large variety of learning algorithms and a vast selection of possible network architectures. After all the training, how does one know which is the best network? This decision is further complicated by the fact that standard techniques can be severely limited by problems such as over-fitting, data sparsity and local optima. The usual solution to these problems is a winner-take-all cross-validatory model selection. However, recent experimental and theoretical work indicates that we can improve performance by considering methods for combining neural networks.

The past several years have seen a tremendous growth in the complexity of the recognition, estimation and control tasks expected of neural networks. In solving these tasks, one is faced with a large variety of learning algorithms and a vast selection of possible network architectures. After all the training, how does one know which is the best network? This decision is further complicated by the fact that standard techniques can be severely limited by problems such as over-fitting, data sparsity and local optima. The usual solution to these problems is a winner-take-all cross-validatory model selection.

Model-based object recognition solves the problem of invariant recognition by relying on stored prototypes at unit scale positioned at the origin of an object-centered coordinate system. Elastic matching techniques are used to find a correspondence between features of the stored model and the data and can also compute the parameters of the transformation the observed instance has undergone relative to the stored model.

Signal processing and classification algorithms often have limited applicability resulting from an inaccurate model of the signal's underlying structure. We present here an efficient, Bayesian algorithm for modeling a signal composed of the superposition of brief, Poisson-distributed functions. This methodology is applied to the specific problem of modeling and classifying extracellular neural waveforms which are composed of a superposition of an unknown number of action potentials CAPs). Previous approaches have had limited success due largely to the problems of determining the spike shapes, deciding how many are shapes distinct, and decomposing overlapping APs. A Bayesian solution to each of these problems is obtained by inferring a probabilistic model of the waveform. This approach quantifies the uncertainty of the form and number of the inferred AP shapes and is used to obtain an efficient method for decomposing complex overlaps. This algorithm can extract many times more information than previous methods and facilitates the extracellular investigation of neuronal classes and of interactions within neuronal circuits.

This paper describes probabilistic methods for novelty detection when using pattern recognition methods for fault monitoring of dynamic systems. The problem of novelty detection is particularly acute when prior knowledge and training data only allow one to construct an incomplete classification model. Allowance must be made in model design so that the classifier will be robust to data generated by classes not included in the training phase. For diagnosis applications one practical approach is to construct both an input density model and a discriminative class model. Using Bayes' rule and prior estimates of the relative likelihood of data of known and unknown origin the resulting classification equations are straightforward.

I propose a learning algorithm for learning hierarchical models for object recognition.The model architecture is a compositional hierarchy that represents part-whole relationships: parts are described in the local contextof substructures of the object. The focus of this report is learning hierarchical models from data, i.e. inducing the structure of model prototypes from observed exemplars of an object. At each node in the hierarchy, a probability distribution governing its parameters must be learned. The connections between nodes reflects the structure of the object. The formulation of substructures is encouraged such that their parts become conditionally independent.

To assess the state of the art and identify issues requiring further investigation, a workshop on qualitative and abstract probability was held during the third week of November 1993. This workshop brought together a mix of active researchers from academia, industry, and government interested in the practical and theoretical impact of these abstractions on techniques, methods, and tools for solving complex AI tasks. The result was a set of specific recommendations on the most promising and important avenues for future research.

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, andthe manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximizationalgorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing how some popular algorithms fall within the framework presented. The main original contributions here are the decompositiontechniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.