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David Grimes

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NeurIPS Conference 2006 Conference Paper

Learning Nonparametric Models for Probabilistic Imitation

David Grimes
Daniel Rashid
Rajesh Rao

Learning by imitation represents an important mechanism for rapid acquisition of new behaviors in humans and robots. A critical requirement for learning by imitation is the ability to handle uncertainty arising from the observation process as well as the imitator's own dynamics and interactions with the environment. In this paper, we present a new probabilistic method for inferring imitative actions that takes into account both the observations of the teacher as well as the imitator's dynamics. Our key contribution is a nonparametric learning method which generalizes to systems with very different dynamics. Rather than relying on a known forward model of the dynamics, our approach learns a nonparametric forward model via exploration. Leveraging advances in approximate inference in graphical models, we show how the learned forward model can be directly used to plan an imitating sequence. We provide experimental results for two systems: a biomechanical model of the human arm and a 25-degrees-of-freedom humanoid robot. We demonstrate that the proposed method can be used to learn appropriate motor inputs to the model arm which imitates the desired movements. A second set of results demonstrates dynamically stable full-body imitation of a human teacher by the humanoid robot.

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NeurIPS Conference 2002 Conference Paper

A Bilinear Model for Sparse Coding

David Grimes
Rajesh Rao

Recent algorithms for sparse coding and independent component analy- sis (ICA) have demonstrated how localized features can be learned from natural images. However, these approaches do not take image transfor- mations into account. As a result, they produce image codes that are redundant because the same feature is learned at multiple locations. We describe an algorithm for sparse coding based on a bilinear generative model of images. By explicitly modeling the interaction between im- age features and their transformations, the bilinear approach helps reduce redundancy in the image code and provides a basis for transformation- invariant vision. We present results demonstrating bilinear sparse coding of natural images. We also explore an extension of the model that can capture spatial relationships between the independent features of an ob- ject, thereby providing a new framework for parts-based object recogni- tion.

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NeurIPS Conference 2000 Conference Paper

The Interplay of Symbolic and Subsymbolic Processes in Anagram Problem Solving

David Grimes
Michael Mozer

Although connectionist models have provided insights into the nature of perception and motor control, connectionist accounts of higher cognition seldom go beyond an implementation of traditional symbol-processing theories. We describe a connectionist constraint satisfaction model of how people solve anagram problems. The model exploits statistics of English orthography, but also addresses the interplay of sub symbolic and symbolic computation by a mechanism that extracts approximate symbolic representations (partial orderings of letters) from sub symbolic structures and injects the extracted representation back into the model to assist in the solution of the anagram. We show the computational benefit of this extraction-injection process and discuss its relationship to conscious mental processes and working memory. We also account for experimental data concerning the difficulty of anagram solution based on the orthographic structure of the anagram string and the target word. Historically, the mind has been viewed from two opposing computational perspectives. The symbolic perspective views the mind as a symbolic information processing engine. According to this perspective, cognition operates on representations that encode logical relationships among discrete symbolic elements, such as stacks and structured trees, and cognition involves basic operations such as means-ends analysis and best-first search. In contrast, the subsymbolic perspective views the mind as performing statistical inference, and involves basic operations such as constraint-satisfaction search. The data structures on which these operations take place are numerical vectors. In some domains of cognition, significant progress has been made through analysis from one computational perspective or the other. The thesis of our work is that many of these do(cid: 173) mains might be understood more completely by focusing on the interplay of subsymbolic and symbolic information processing. Consider the higher-cognitive domain of problem solving. At an abstract level of description, problem solving tasks can readily be formal(cid: 173) ized in terms of symbolic representations and operations. However, the neurobiological hardware that underlies human cognition appears to be subsymbolic-representations are noisy and graded, and the brain operates and adapts in a continuous fashion that is diffi(cid: 173) cult to characterize in discrete symbolic terms. At some level-between the computational level of the task description and the implementation level of human neurobiology-the symbolic and subsymbolic accounts must come into contact with one another. We focus on this point of contact by proposing mechanisms by which symbolic representations can modulate sub symbolic processing, and mechanisms by which subsymbolic representations are made symbolic. We conjecture that these mechanisms can not only provide an account for the interplay of symbolic and sub symbolic processes in cognition, but that they form a sensible computational strategy that outperforms purely subsymbolic computation, and hence, symbolic reasoning makes sense from an evolutionary perspective. In this paper, we apply our approach to a high-level cognitive task, anagram problem solv(cid: 173) ing. An anagram is a nonsense string of letters whose letters can be rearranged to form a word. For example, the solution to the anagram puzzle RYTEHO is THEORY. Anagram solving is a interesting task because it taps higher cognitive abilities and issues of aware(cid: 173) ness, it has a tractable state space, and interesting psychological data is available to model. 1 A Sub symbolic Computational Model We start by presenting a purely subsymbolic model of anagram processing. By subsym(cid: 173) bolic, we mean that the model utilizes only English orthographic statistics and does not have access to an English lexicon. We will argue that this model proves insufficient to ex(cid: 173) plain human performance on anagram problem solving. However, it is a key component of a hybrid symbolic-subsymbolic model we propose, and is thus described in detail. 1. 1 Problem Representation A computational model of anagram processing must represent letter orderings. For ex(cid: 173) ample, the model must be capable of representing a solution such as, or any permutation of the letters such as. (The symbols " " will be used to delimit the beginning and end of a string, respectively. ) We adopted a representation of letter strings in which a string is encoded by the set of letter pairs (hereafter, bigrams) contained in the string; for example, the bigrams in are: . The delimiters are treated as ordinary symbols of the alphabet. We capture letter pairings in a symbolic letter-ordering matrix, or symbolic ordering for short. Figure lea) shows the matrix, in which the rows indicate the first letter of the bigram, and the columns indicate the second. A cell of the matrix contains a value of I if the corre(cid: 173) sponding bigram is present in the string. (This matrix formalism and all procedures in the paper can be extended to handle strings with repeated letters, which we do not have space to discuss. ) The matrix columns and rows can be thought of as consisting of all letters from A to z, along with the delimiters. However, in the Figure we have omitted rows and columns corresponding to letters not present in the anagram. Similarly, we have omitted the from row space, as they could not by definition be part of any bigram. The seven bigrams indicated by the seven ones in the Figure uniquely specify the string THEORY. As we've described the matrix, cells contain the truth value of the proposition that a par(cid: 173) ticular bigram appears in the string being represented. However, the cell values have an interesting alternative interpretation: as the probability that a particular bigram is present. Figure l(b) illustrates a matrix of this sort, which we call a subsymbolic letter ordering matrix, or subsymbolic ordering for short. In the Figure, the bigram TH occurs with prob(cid: 173) ability 0. 8. Although the symbolic orderings are obviously a subset of the sub symbolic orderings, the two representations play critically disparate roles in our model, and thus are treated as separate entities. To formally characterize symbolic and subsymbolic ordering matrices, we define a mask vector, /-£, having N = 28 elements, corresponding to the 26 letters of the alphabet plus the two delimiters. Element i of the mask, /-£i, is set to one if the corresponding letter appears in the anagram string and zero if it does not. In both the symbolic and sub symbolic orderings, the matrices are constrained such that elements in row i and column i must sum E H 0 R T Y > 1 0 0 < 0 0 0 0 E H

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NeurIPS Conference 1999 Conference Paper

Churn Reduction in the Wireless Industry

Michael Mozer
Richard Wolniewicz
David Grimes
Eric Johnson
Howard Kaushansky

Competition in the wireless telecommunications industry is rampant. To main(cid: 173) tain profitability, wireless carriers must control chum, the loss of subscribers who switch from one carrier to another. We explore statistical techniques for chum prediction and, based on these predictions. an optimal policy for identify(cid: 173) ing customers to whom incentives should be offered to increase retention. Our experiments are based on a data base of nearly 47, 000 U. S. domestic subscrib(cid: 173) ers, and includes information about their usage, billing, credit, application, and complaint history. We show that under a wide variety of assumptions concerning the cost of intervention and the retention rate resulting from intervention, chum prediction and remediation can yield significant savings to a carrier. We also show the importance of a data representation crafted by domain experts. Competition in the wireless telecommunications industry is rampant. As many as seven competing carriers operate in each market. The industry is extremely dynamic, with new services, technologies, and carriers constantly altering the landscape. Carriers announce new rates and incentives weekly, hoping to entice new subscribers and to lure subscribers away from the competition. The extent of rivalry is reflected in the deluge of advertise(cid: 173) ments for wireless service in the daily newspaper and other mass media. The United States had 69 million wireless subscribers in 1998, roughly 25% of the population. Some markets are further developed; for example, the subscription rate in Fin(cid: 173) land is 53%. Industry forecasts are for a U. S. penetration rate of 48% by 2003. Although there is significant room for growth in most markets, the industry growth rate is declining and competition is rising. Consequently, it has become crucial for wireless carriers to con(cid: 173) trol chum-the loss of customers who switch from one carrier to another. At present, domestic monthly chum rates are 2-3% of the customer base. At an average cost of $400 to acquire a subscriber, churn cost the industry nearly $6. 3 bilIion in 1998; the total annual loss rose to nearly $9. 6 billion when lost monthly revenue from subscriber cancellations is considered (Luna, 1998). It costs roughly five times as much to sign on a new subscriber as to retain an existing one. Consequently, for a carrier with 1. 5 milIion subscribers, reduc(cid: 173) ing the monthly churn' rate from 2% to 1 % would yield an increase in annual earnings of at least $54 milIion, and an increase in shareholder value of approximately $150 million. (Estimates are even higher when lost monthly revenue is considered; see Fowlkes, Madan, Andrew, & Jensen, 1999; Luna, 1998. ) The goal of our research is to evaluate the benefits of predicting churn using tech(cid: 173) niques from statistical machine learning. We designed models that predict the probability 936 M. C. Mozer, R. Wolniewicz. D. B. Grimes. E. Johnson and H. Kaushansky of a subscriber churning within a short time window, and we evaluated how well these pre(cid: 173) dictions could be used for decision making by estimating potential cost savings to the wireless carrier under a variety of assumptions concerning subscriber behavior.

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