Stephen M. Omohundro

Inducing Probabilistic Grammars by Bayesian Model Merging

We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are incorporated by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or nonterminals) are merged to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a trade-off between a close fit to the data and a default preference for simpler models (‘Occams Razor’). The general scheme is illustrated using three types of probabilistic grammars: Hidden Markov models, class-based n-grams, and stochastic context-free grammars.

Nonlinear manifold learning for visual speech recognition

A technique for representing and learning smooth nonlinear manifolds is presented and applied to several lip reading tasks. Given a set of points drawn from a smooth manifold in an abstract feature space, the technique is capable of determining the structure of the surface and of finding the closest manifold point to a given query point. We use this technique to learn the space of lips in a visual speech recognition task. The learned manifold is used for tracking and extracting the lips, for interpolating between frames in an image sequence and for providing features for recognition. We describe a system based on hidden Markov models and this learned lip manifold that significantly improves the performance of acoustic speech recognizers in degraded environments. We also present preliminary results on a purely visual lip reader.<<ETX>>

Modelling cellular automata with partial differential equations

A system of 10 coupled nonlinear partial differential equations is exhibited which simulates an arbitrary two-dimensional, nine-neighbor, square-lattice cellular automata. A number of theoretical implications of the result and the techniques used in its construction as well as possible practical consequences are discussed.

Engineering a Programming Language: The Type and Class System of Sather

Sather 1.0 is a programming language whose design has resulted from the interplay of many criteria. It attempts to support a powerful object-oriented paradigm without sacrificing either the computational performance of traditional procedural languages or support for safety and correctness checking. Much of the engineering effort went into the design of the class and type system. This paper describes some of these design decisions and relates them to approaches taken in other languages. We particularly focus on issues surrounding inheritance and subtyping and the decision to explicitly separate them in Sather.

Iteration abstraction in Sather

Sather extends the notion of an iterator in a powerful new way. We argue that iteration abstractions belong in class interfaces on an equal footing with routines. Sather iterators were derived from CLU iterators but are much more flexible and better suited for object-oriented programming. We retain the property that iterators are structured, i.e., strictly bound to a controlling structured statement. We motivate and describe the construct along with several simple examples. We compare it with iteration based on CLU iterators, cursors, riders, streams, series, generators, coroutines, blocks, closures, and lambda expressions. Finally, we describe experiences with iterators in the Sather compiler and libraries.

Geometric learning algorithms

Abstract Emergent computation in the form of geometric learning is central to the development of motor and perceptual systems in biological organisms and promises to have a similar impact on emerging technologies including robotics, vision, speech, and graphics. This paper examines some of the trade-offs involved in different implementation strategies, focusing on the tasks of learning discrete classifications and smooth nonlinear mappings. The trade-offs between local and global representations are discussed, a spectrum of distributed network implementations are examined, and an important source of computational inefficiency is identified. Efficient algorithms based on k -d trees and the Delaunay triangulation are presented and the relevance to biological networks is discussed. Finally, extensions of both the tasks and the implementations are given.

A hybrid approach to bimodal speech recognition

We explore multimodal recognition by combining visual lipreading with acoustic speech recognition. We show that combining visual and acoustic speech information improves the recognition performance significantly, especially in noisy environments. This is achieved with a hybrid speech recognition architecture, consisting of a new visual learning and tracking mechanism, a channel robust acoustic front end, a connectionist phone classifier, and a HMM based sentence classifier. Our focus in this paper is on the visual subsystem based on surface-learning and active vision models. Our bimodal hybrid speech recognition system has already been applied to a multi-speaker spelling task, and work is in progress to apply it to a speaker independent spontaneous speech task, the Berkeley Restaurant Project (BeRP).<<ETX>>

On the global structure of period doubling flows

Abstract For a wide class of period doubling flows on R3, we analyze the global structure of the invariant manifolds and the topology of the bifurcating periodic orbits. We emphasize aspects of the dynamics which are not visible in an analysis of the associated Poincare return map. The global manifold structure implies constraints for the subsequent bifurcational behavior of the flow. The period doubled orbits are classified using the theory of iterated torus knots. This classification reveals an infinite number of topologically distinct period doubling flows and raises the important question as to which sequences of torus knots appear in the asymptotic limit of a period doubling cascade. If the asymptotic sequence of torus knots produced is not unique, then the self-similarity of the Poincare map does not imply a self-similar structure for the flow. In particular, at the accumulation point for the cascade, one would not expect to observe a universal power spectrum for the flow. This possibility is of some experimental interest.

Building Faster Connectionist Systems With Bumptrees

This paper describes “bumptrees”, a new approach to improving the computational efficiency of a wide variety of connectionist algorithms. We describe the use of these structures for representing, learning, and evaluating smooth mappings, smooth constraints, classification regions, and probability densities. We present an empirical comparison of a bumptree approach to more traditional connectionist approaches for learning the mapping between the kinematic and visual representations of the state of a 3 joint robot arm. Simple networks based on backpropagation with sigmoidal units are unable to perform the task at all. Radial basis function networks perform the task but by using bumptrees, the learning rate is hundreds of times faster at reasonable error levels and the retrieval time is over fifty times faster with 10,000 samples. Bumptrees are a natural generalization of oct-trees, k-d trees, balltrees and boxtrees and are useful in a variety of circumstances. We describe both the underlying ideas and extensions to constraint and classification learning that are under current investigation.