A phenomenon as complex as protein folding requires a complex model to approximate it. This thesis presents a bottom-up approach for building complex probabilistic models of protein secondary structure by incorporating the multiple information sources which we call experts. Expert opinions are represented by probability distributions over the set of possible structures. Bayesian treatment of a group of experts results in a consensus opinion that combines the experts' probability distributions using the operators of normalized product, quotient and exponentiation. The expression of this consensus opinion simplifiesto a product of the expert opinions with two assumptions: (1) balanced training of experts, i. e. , uniform prior probability over all structures, and (2) conditional independence between expert opinions,given the structure. This research also studies how Markov chains and hidden Markov models may be used to represent expert opinion. Closure properties areproven, and construction algorithms are given for product of hidden Markov models, and product, quotient and exponentiation of Markovchains. Algorithms for extracting single-structure predictions from these models are also given. Current product-of-experts approaches in machine learning are top-down modeling strategies that assume expert independence, and require simultaneous training of all experts. This research describes a bottom-up modeling strategy that can incorporate conditionally dependent experts, and assumes separately trained experts.

A phenomenon as complex as protein folding requires a complex model to approximate it. This thesis presents a bottom-up approach for building complex probabilistic models of protein secondary structure by incorporating the multiple information sources which we call experts. Expert opinions are represented by probability distributions over the set of possible structures. Bayesian treatment of a group of experts results in a consensus opinion that combines the experts' probability distributions using the operators of normalized product, quotient and exponentiation. The expression of this consensus opinion simplifiesto a product of the expert opinions with two assumptions: (1) balanced training of experts, i. e. , uniform prior probability over all structures, and (2) conditional independence between expert opinions,given the structure. This research also studies how Markov chains and hidden Markov models may be used to represent expert opinion. Closure properties areproven, and construction algorithms are given for product of hidden Markov models, and product, quotient and exponentiation of Markovchains. Algorithms for extracting single-structure predictions from these models are also given. Current product-of-experts approaches in machine learning are top-down modeling strategies that assume expert independence, and require simultaneous training of all experts. This research describes a bottom-up modeling strategy that can incorporate conditionally dependent experts, and assumes separately trained experts.