Real-world learning tasks may involve high-dimensional data sets with arbitrary patterns of missing data. In this paper we present a framework based on maximum likelihood density estimation for learning from such data set.s. VVe use mixture models for the density estimatesand make two distinct appeals to the Expectation Maximization (EM) principle (Dempster et al., 1977) in deriving a learning algorithm-EM is used both for the estimation of mixture componentsand for coping wit.h missing dat.a. The resulting algorithm is applicable t.o a wide range of supervised as well as unsupervised learning problems.

HoUand Dept. of Psychology University of Michigan Ann Arbor, MI 48109 StephanieForrest Dept. of Computer Science University of New Mexico Albuquerque, NM 87131 Abstract We analyze a simple hill-climbing algorithm (RMHC) that was previously shownto outperform a genetic algorithm (GA) on a simple "Royal Road" function. We then analyze an "idealized" genetic algorithm (IGA) that is significantly faster than RMHC and that gives a lower bound for GA speed. We identify the features of the IGA that give rise to this speedup, and discuss how these features can be incorporated into a real GA. 1 INTRODUCTION Our goal is to understand the class of problems for which genetic algorithms (GA) are most suited, and in particular, for which they will outperform other search algorithms. Several studies have empirically compared GAs with other search and optimization methods such as simple hill-climbing (e.g., Davis, 1991), simulated annealing (e.g., Ingber & Rosen, 1992), linear, nonlinear, and integer programming techniques, and other traditional optimization techniques (e.g., De Jong, 1975). However, such comparisons typically compare one version of the GA with a second algorithm on a single problem or set of problems, often using performance criteria which may not be appropriate.

Gentner and Markman (1992) suggested that the ability to deal with analogy will be a "Watershed or Waterloo" for connectionist models. They identified "structural alignment" as the central aspect of analogy making. They noted the apparent ease with which people can perform structural alignment in a wide variety of tasks and were pessimistic about the of a distributed connectionist model that could be useful inprospects for the development performing structural alignment. In this paper I describe how Holographic Reduced Representations (HRRs) (Plate, 1991; Plate, 1994), a fixed-width distributed representation for nested structures, can be used to obtain fast estimates of analogical similarity.

This paper introduces a new recognition-based segmentation approach torecognizing online cursive handwriting from a database of 10,000 English words. The original input stream of z, y pen coordinates isencoded as a sequence of uniform stroke descriptions that are processed by six feed-forward neural-networks, each designed to recognize letters of different sizes. Words are then recognized by performing best-first search over the space of all possible segmentations. Resultsdemonstrate that the method is effective at both writer dependent recognition (1.7% to 15.5% error rate) and writer independent recognition (5.2% to 31.1% error rate). 1 Introduction With the advent of pen-based computers, the problem of automatically recognizing handwriting from the motions of a pen has gained much significance. Progress has been made in reading disjoint block letters [Weissman et.

This fact provides a theoretical justification of the widely observed excellent robustness properties of the LMS and backpropagation algorithms. We further discuss some implications of these results.

Dynamic programming provides a methodology to plan trajectories and design controllers and estimators for nonlinear systems. However, general dynamic programming is computationally intractable. We have developed procedures that allow more complex planning problems to be solved. We have modified the State Increment Dynamic Programming approach of Larson (1968) in several ways: 1. In State Increment DP, a constant action is integrated to form a trajectory segment from the center of a cell to its boundary. We use second order local trajectory optimization (Differential Dynamic Programming) to generate an optimal trajectory and form an optimal policy in a tube surrounding the optimal trajectory within a cell. The trajectory segment and local policy are globally optimal, up to the resolution of the representation of the value function on the boundary of the cell.

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learning problems involving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DPbased learning algorithms to the powerful techniques of stochastic approximation via a new convergence theorem, enabling us to establish a class of convergent algorithms to which both TD("\) and Q-Iearning belong. 1 INTRODUCTION Learning to predict the future and to find an optimal way of controlling it are the basic goals of learning systems that interact with their environment. A variety of algorithms are currently being studied for the purposes of prediction and control in incompletely specified, stochastic environments. Here we consider learning algorithms defined in Markov environments. There are actions or controls (u) available for the learner that affect both the state transition probabilities, and the probability distribution for the immediate, state dependent costs (Ci(u)) incurred by the learner.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, can employ selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitude codes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitude information; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules and direct the flow of computation (attention) to effect transitions between two subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

Recently, Ott, Grebogi and Yorke (OGY) [6] found an effective method to control chaotic systems to unstable fixed points by using only small control forces; however, OGY's method is based on and limited to a linear theory and requires considerable knowledge of the dynamics of the system to be controlled. In this paper we use two radial basis function networks: one as a model of an unknown plant and the other as the controller. The controller is trained with a recurrent learning algorithm to minimize a novel objective function such that the controller can locate an unstable fixed point and drive the system into the fixed point with no a priori knowledge of the system dynamics. Our results indicate that the neural controller offers many advantages over OGY's technique.

We developed a system for finding address blocks on mail pieces that can process four images per second. Besides locating the address block, our system also determines the writing style, handwritten or machine printed, and moreover, it measures the skew angle of the text lines and cleans noisy images. A layout analysis of all the elements present in the image is performed in order to distinguish drawings and dirt from text and to separate text of advertisement from that of the destination address. A speed of more than four images per second is obtained on a modular hardware platform, containing a board with two of the NET32K neural net chips, a SP ARC2 processor board, and a board with 2 digital signal processors. The system has been tested with more than 100,000 images. Its performance depends on the quality of the images, and lies between 85% correct location in very noisy images to over 98% in cleaner images.