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Data Structures for Efficient Inference and Optimization in Expressive Continuous Domains
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This talk is in two parts. In the first part, I introduce an extension of the algebraic decision diagram (ADD) to continuous variables—termed the extended ADD (XADD)—to represent arbitrary piecewise functions (nb, arbitrary pieces, not just hyper-rectangular) over discrete and continuous variables and show how to define and efficiently compute elementary arithmetic operations, integrals, and maximization for various restrictions of these functions. In the second part, I cover a wide range of novel applications where the XADD may be applied: (a) exact inference in expressive discrete and continuous variable graphical models, (b) factored, parameterized linear and quadratic optimization (a generalization of LP and QP solving), and© exact solutions to continuous state, action, and observation sequential decision-making problems.
This is joint work with Zahra Zamani & Ehsan Abbasnejad (Australian National University), Karina Valdivia Delgado & Leliane Nunes de Barros (University of Sao Paulo), and Simon Fang (M.I.T.).
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