Stable Mixing of Complete and Incomplete Information

An increasing number of parameter estimation tasks involve the use of at least two information sources, one complete but limited, the other abundant but incomplete. Standard algorithms such as EM (or em) used in this context are unfortunately not stable in the sense that they can lead to a dramatic loss of accuracy with the inclusion of incomplete observations. We provide a more controlled solution to this problem through differential equations that govern the evolution of locally optimal solutions (fixed points) as a function of the source weighting. This approach permits us to explicitly identify any critical (bifurcation) points leading to choices unsupported by the available complete data. The approach readily applies to any graphical model in O(n^3) time where n is the number of parameters. We use the naive Bayes model to illustrate these ideas and demonstrate the effectiveness of our approach in the context of text classification problems.

Syntax-Based Analytic Reading of Musical Scores

As part of a larger research project in musical structure, a program has been written which "reads" scores encoded in an input language isomorphic to music notation. The program is believed to be the first of its kind. From a small number of parsing rules the program derives complex configurations, each of which is associated with a set of reference points in a numerical representation of a time-continuum. The logical structure of the program is such that all and only the defined classes of events are represented in the output. Because the basis of the program is syntactic (in the sense that parsing operations are performed on formal structures in the input string), many extensions and refinements can be made without excessive difficulty. The program can be applied to any music which can be represented in the input language. At present, however, it constitutes the first stage in the development of a set of analytic tools for the study of so-called atonal music, the revolutionary and little understood music which has exerted a decisive influence upon contemporary practice of the art. The program and the approach to automatic data-structuring may be of interest to linguists and scholars in other fields concerned with basic studies of complex structures produced by human beings.

The Definition and Implementation of a Computer Programming Language Based on Constraints

The constraint paradigm is a model of computation in which values are deduced whenever possible, under the limitation that deductions be local in a certain sense. One may visualize a constraint 'program' as a network of devices connected by wires. Data values may flow along the wires, and computation is performed by the devices. A device computes using only locally available information (with a few exceptions), and places newly derived values on other, locally attached wires. In this way computed values are propagated. An advantage of the constraint paradigm (not unique to it) is that a single relationship can be used in more than one direction. The connections to a device are not labelled as inputs and outputs; a device will compute with whatever values are available, and produce as many new values as it can. General theorem provers are capable of such behavior, but tend to suffer from combinatorial explosion; it is not usually useful to derive all the possible consequences of a set of hypotheses. The constraint paradigm places a certain kind of limitation on the deduction process. The limitations imposed by the constraint paradigm are not the only one possible. It is argued, however, that they are restrictive enough to forestall combinatorial explosion in many interesting computational situations, yet permissive enough to allow useful computations in practical situations. Moreover, the paradigm is intuitive: It is easy to visualize the computational effects of these particular limitations, and the paradigm is a natural way of expressing programs for certain applications, in particular relationships arising in computer-aided design. A number of implementations of constraint-based programming languages are presented. A progression of ever more powerful languages is described, complete implementations are presented and design difficulties and alternatives are discussed. The goal approached, though not quite reached, is a complete programming system which will implicitly support the constraint paradigm to the same extent that LISP, say, supports automatic storage management.