We propose a learning algorithm for a variable memory length Markov process. Human communication, whether given as text, handwriting, or speech, has multi characteristic time scales. On short scales it is characterized mostly by the dynamics that generate the process, whereas on large scales, more syntactic and semantic information is carried. For that reason the conventionally used fixed memory Markov models cannot capture effectively the complexity of such structures. On the other hand using long memory models uniformly is not practical even for as short memory as four.

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.

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.

The conventional Bayesian justification of backprop is that it finds the MAP weight vector. As this paper shows, to find the MAP io function instead one must add a correction tenn to backprop. That tenn biases one towards io functions with small description lengths, and in particular favors (some kinds of) feature-selection, pruning, and weight-sharing.

We propose a learning algorithm for a variable memory length Markov process. Human communication, whether given as text, handwriting, or speech, has multi characteristic time scales. On short scales it is characterized mostly by the dynamics that generate theprocess, whereas on large scales, more syntactic and semantic informationis carried. For that reason the conventionally used fixed memory Markov models cannot capture effectively the complexity of such structures. On the other hand using long memory modelsuniformly is not practical even for as short memory as four.

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.

We introduce a new approach for online recognition of handwritten wordswritten in unconstrained mixed style. The preprocessor performs a word-level normalization by fitting a model of the word structure using the EM algorithm. Words are then coded into low resolution "annotated images" where each pixel contains information abouttrajectory direction and curvature. The recognizer is a convolution network which can be spatially replicated. From the network output, a hidden Markov model produces word scores.

Spotting tasks require detection of target patterns from a background of richly varied non-target inputs. The performance measure of interest for these tasks, called the figure of merit (FOM), is the detection rate for target patterns when the false alarm rate is in an acceptable range. A new approach to training spotters is presented which computes the FOM gradient for each input pattern and then directly maximizes the FOM using backpropagation. This eliminates the need for thresholds during training. It also uses network resources to model Bayesian a posteriori probability functions accurately only for patterns which have a significant effect on the detection accuracy over the false alarm rate of interest.

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.

To control such complex systems it is computationally moreefficient to decompose the problem into smaller subtasks, with different control strategies for different operating points. When detailed information about the plant is available, gain scheduling has proven a successful method for designing a global control (Shamma and Athans, 1992). The system is partitioned by choosing several operating points and a linear model for each operating point. A controller is designed for each linear model and a method for interpolating or'scheduling' the gains of the controllers is chosen. The control problem becomes even more challenging when the system to be controlled isnon-stationary, and the mode of the system is not explicitly observable.