Influence modeling of complex stochastic processes

Abstract

A complex stochastic process involving human behaviors or human group behaviors is computationally hard to model with a hidden Markov process. This is because the state space of such behaviors is often a Cartesian product of a large number of constituent probability spaces, and is exponentially large. A sample for those stochastic processes is normally composed of a large collection of heterogeneous constituent samples. How to combine those heterogeneous constituent samples in a consistent and stable way is another difficulty for the hidden Markov process modeling. A latent structure influence process models human behaviors and human group behaviors by emulating the work of a team of experts. In such a team, each expert concentrates on one constituent probability space, investigates one type of constituent samples, and/or employ one type of technique. An expert improves his work by considering the results from the other experts, instead of the raw data for them. Compared with the hidden Markov process, the latent structure influence process is more expressive, more stable to outliers, and less likely to overfit. It can be used to study the interaction of over 100 persons and get good results.

(cont.) This thesis is organized in the following way. Chapter 0 reviews the notation and the background concepts necessary to develop this thesis. Chapter 1 describes the intuition behind the latent structure influence process and the situations where it outperforms the other dynamic models. In Chapter 2, we give inference algorithms based on two different interpretations of the influence model. Chapter 3 applies the influence algorithms to various toy data sets and real-world data sets. We hope our demonstrations of the influence modeling could serve as templates for the readers to develop other applications. In Chapter 4, we conclude with the rationale and other considerations for influence modeling.