[Research] Thesis proposal tomorrow

[Sajid M. Siddiqi]

Dear Autonites,

My thesis proposal is tomorrow (Friday) at 11:00 in Wean 4623, and you are all cordially invited to attend :) I am told that refreshments will be served.

Sajid

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Latent Variable and Predictive Models of Dynamical Systems

Sajid Siddiqi
Robotics Institute
Carnegie Mellon University

Place and Time

WEH 4623
11:00 AM

Abstract

We propose to investigate new models and algorithms for inference, structure and parameter learning that extend our capabilities of modeling uncontrolled discrete-time dynamical systems. Our work is grounded in existing generative models for dynamical systems that are based on latent variable representations. Hidden Markov Models (HMMs) and Linear Dynamical Systems (LDSs) are popular choices for modeling dynamical systems because of their balance of simplicity and expressive power, and because of the existence of efficient inference and learning algorithms for these models.

Recently proposed predictive models of dynamical systems, such as linear Predictive State Representations (PSRs) and Predictive Linear Gaussians (PLGs) have been shown to be equally powerful as (and often more compact than) HMMs and LDSs. Instead of modeling state by a latent variable, however, predictive models model the state of the dynamical system by a set of statistics defined on future observable events. This dependence on observable quantities and avoidance of latent variables makes it easier to learn consistent parameter settings and avoid local minima in predictive models, though they have other problems such as a paucity of well-developed learning algorithms. However, one interesting class of algorithms for learning models such as LDSs and PSRs is based on factoring matrices containing statistics about observations using techniques such as the singular value decomposition (SVD). This class of algorithms is especially popular in the control theory literature, under !
 the area of subspace identification.

A restriction of most current models is that they are restricted to either discrete, Gaussian, or mixture-of-Gaussian observation distributions. Recently, Wingate and Singh (2007) proposed a predictive model that aims to generalize PLGs to exponential family distributions. This allows us to exploit structure in the observations using exponential family graphical models. It also exposes us to problems of intractable inference, structure and parameter learning inherent in conventional algorithms for graphical models, necessitating the use of approximate inference techniques.

Our goal is to formulate models and algorithms that unify disparate elements of this set of tools. The ultimate aim of this thesis is to devise predictive models that unify HMM-style and LDS-style models in a way that captures the advantages of both and generalize them to exponential families, and to investigate efficient and stable structure and parameter learning algorithms for these models based on matrix decomposition techniques.

Further Details

Thesis Committee

    * Geoffrey Gordon, Chair
    * Andrew Moore
    * Jeff Schneider
    * Zoubin Ghahramani, University of Cambridge
    * David Wingate, University of Michigan