|ICS-179, Algorithms for Reasoning and Learning in Probabilistic and Deterministic Graphical Models, Spring 2010
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Graphical models have become the primary approach for automated reasoning which evolved around two distinct ways of representing knowledge. The first is using hard and soft constraints. For example, a hard constraint might be, “a student cannot enroll in two courses if they meet at the same time,” and a soft constraint might be, “a student prefers that his first class on Monday will be after 10 am.” The second way of representing knowledge is probabilistic, recognizing that knowledge involves uncertainty. An example of a probabilistic information would be, “if a student has a solid math background, he or she is likely (but not certain) to do well in computer science classes.” Many real-life applications involve both types of information.
The class will focus on graphical models, such as constraint networks, Bayesian networks and Markov networks that have become a central paradigm for knowledge representation and reasoning in Artificial Intelligence and general computer science. These models are used in numerous applications in industrial and engineering tasks, such as scheduling, planning, diagnosis and prediction, design, hardware and software verification, and in bioinformatics applications. The primary tasks can be formalized as constraint satisfaction and satisfiability, combinatorial optimization and likelihood queries. While it is well known that computing an answer to any of the above queries is computationally hard, research during the past three decades has yielded a variety of principles and techniques for mitigating the computational challenge.
In this class I will teach the algorithmic principles that allow reasoning and learning for graphical models. We will study how those principles can address the complexity of solving problems within this framework, even though all are NP-hard. Students will also be exposed to the primary software developed in the community. This includes state of the art software for satisfiability and constraint satisfaction, counting and likelihood queries as well as constraint optimization. We will draw examples and engage in modeling in some applications including bio-informatics and planning.
Text books and class notes