# Accession Number:

## ADA595664

# Title:

## Dynamic Dependence Analysis : Modeling and Inference of Changing Dependence Among Multiple Time-Series

# Descriptive Note:

## Doctoral thesis

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

# Personal Author(s):

# Report Date:

## 2009-06-01

# Pagination or Media Count:

## 192.0

# Abstract:

In this dissertation we investigate the problem of reasoning over evolving structures which describe the dependence among multiple, possibly vector-valued, time-series. Such problems arise naturally in variety of settings. Consider the problem of object interaction analysis. Given tracks of multiple moving objects one may wish to describe if and how these objects are interacting over time. Alternatively, consider a scenario in which one observes multiple video streams representing participants in a conversation. Given a single audio stream, one may wish to determine with which video stream the audio stream is associated as a means of indicating who is speaking at any point in time. Both of these problems can be cast as inference over dependence structures. In the absence of training data, such reasoning is challenging for several reasons. If one is solely interested in the structure of dependence as described by a graphical model, there is the question of how to account for unknown parameters. Additionally the set of possible structures is generally super-exponential in the number of time series. Furthermore, if one wishes to reason about structure which varies over time, the number of structural sequences grows exponentially with the length of time being analyzed. We present tractable methods for reasoning in such scenarios. We consider two approaches for reasoning over structure while treating the unknown parameters as nuisance variables. First, we develop a generalized likelihood approach in which point estimates of parameters are used in place of the unknown quantities. We explore this approach in scenarios in which one considers a small enumerated set of specified structures. Second we develop a Bayesian approach and present a conjugate prior on the parameters and structure of a model describing the dependence among time-series. This allows for Bayesian reasoning over structure while integrating over parameters.

# Descriptors:

# Subject Categories:

- Psychology
- Numerical Mathematics