Data Structures for Efficient Inference and Optimization in Expressive Continuous Domains

Опубликовано 9 августа 2016, 7:34

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 (c) 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.).