Sarthak Ghosh will defend his PhD Dissertation, Optimizing Value of Information in Probabilistic Systems
Abstract: Decision-making based on probabilistic reasoning typically involves selecting a subset of several expensive observations that best predict the system state. The contribution of an observation to the overall utility of the system is referred to as its value of information (VoI). Non-myopically (non-greedily) choosing the optimal observations is wildly intractable even in simple probabilistic graphical models. This work includes four distinct contributions.

First, we present a framework, based on the Markov Decision Process (MDP), for optimally choosing observations in general dynamic Bayesian networks (DBNs), based on non-myopic VoI. The framework involves a notion for utilities, which incorporates a wide range of information metrics and uses a filtering strategy of choosing observations. The framework results in state-of-the-art time complexities for selecting observations in chain graphical models. 

Second, we use the MDP-based framework to formulate efficient approximation algorithms that offer absolute, deterministic, a posteriori approximation bounds. The algorithms come with a parameter, which can be tuned to adjust the amount of computational resources used. We show that affording more computational resources lead to better results, and tighter approximation bounds. We leverage this fact to create useful anytime algorithms. 

Third, the preceding MDP-based framework, as well as all other works that have used the generic notion of VoI considered here, require a graphical model with a finite number of variables. We present a restricted setting for non-myopically optimizing VoI in graphical models of unbounded size. We also discuss how the related concepts can be adapted for the more general setting considered in the first two parts. 

And last, we present a setting for optimally choosing observations, based on the generic notion of VoI, in probabilistic logic programs (PLPs), a generic framework for modeling probabilistic systems. We present a greedy algorithm for choosing observations in the PLP setting, which, unlike other algorithms in this work chooses observations based on myopic VoI.

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