Inference with new hierarchical stochastic grammar models

Wiley Huaili Wang, Purdue University

Abstract

We develop a new class of hierarchical stochastic models called spatial random trees (SRTs) which admit polynomial-complexity exact inference algorithms. SRTs are stochastic hidden tree models whose leaves are associated with image data. The states at the tree nodes are random variables, and, in addition, the structure of the tree is random and is generated by a stochastic grammar. We describe an efficient recursive algorithm for obtaining the maximum a posteriori estimate of both the tree structure and the tree states given an image. We also develop an efficient procedure for performing one iteration of the expectation-maximization algorithm and use it to estimate the model parameters from a set of training images. We address other inference problems arising in applications such as maximization of posterior marginals and hypothesis testing. We illustrate our models and algorithms through several image classification and segmentation experiments. We also propose a stochastic context-free grammar model whose structure can alternatively be viewed as a graphical model, and use it to model time series. We use the inside-outside algorithm to estimate the model parameters. We assume that the time series is a finite-order Markov process generated by our model, and develop an algorithm to forecast the conditional variance of the process. We use this algorithm to forecast the volatility of the S&P 500 index, achieving results that outperform both standard and more recent approaches.

Degree

Ph.D.

Advisors

Pollak, Purdue University.

Subject Area

Electrical engineering

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