Statistical dependence estimation for object interaction and matching

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 97-103).This dissertation shows how statistical dependence estimation underlies two key problems in visual surveillance and wide-area tracking. The first problem is to detect and describe interactions between moving objects. The goal is to measure the influence objects exert on one another. The second problem is to match objects between non-overlapping cameras. There, the goal is to pair the departures in one camera with the arrivals in a different camera so that the resulting distribution of relationships best models the data. Both problems have become important for scaling up surveillance systems to larger areas and expanding the monitoring to more interesting behaviors. We show how statistical dependence estimation generalizes previous work and may have applications in other areas. The two problems represent different applications of our thesis that statistical dependence estimation underlies the learning of the structure of probabilistic models. First, we analyze the relationship between Bayesian, information-theoretic, and classical statistical methods for statistical dependence estimation. Then, we apply these ideas to formulate object interaction in terms of dependency structure model selection.(cont.) We describe experiments on simulated and real interaction data to validate our approach. Second, we formulate the matching problem in terms of maximizing statistical dependence. This allows us to generalize previous work on matching, and we show improved results on simulated and real data for non-overlapping cameras. We also prove an intractability result on exact maximally dependent matching.by Kinh Tieu.Ph.D

Modeling and inference of changing dependence among multiple time-series

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 183-190).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.(cont.) 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. The modular nature of the prior we define allows one to reason over a super-exponential number of structures in exponential-time in general. Furthermore, by imposing simple local or global structural constraints we show that one can reduce the exponential-time complexity to polynomial-time complexity while still reasoning over a super-exponential number of candidate structures. We cast the problem of reasoning over temporally evolving structures as inference over a latent state sequence which indexes structure over time in a dynamic Bayesian network. This model allows one to utilize standard algorithms such as Expectation Maximization, Viterbi decoding, forward-backward messaging and Gibbs sampling in order to efficiently reasoning over an exponential number of structural sequences. We demonstrate the utility of our methodology on two tasks: audio-visual association and moving object interaction analysis. We achieve state-of-the-art performance on a standard audio-visual dataset and show how our model allows one to tractably make exact probabilistic statements about interactions among multiple moving objects.by Michael Richard Siracusa.Ph.D