Abstract
I will introduce an extension of the algebraic decision diagram (ADD) to continuous variables -- termed the extended ADD (XADD) -- to represent arbitrary piecewise functions and show how to define and efficiently compute elementary arithmetic operations, integrals, and maximization for various restrictions of these functions. Following this, I will briefly cover a wide range of applications where the XADD has yielded novel closed-form solutions: (a) probabilistic inference in hybrid graphical models, (b) parametric constrained optimization, (c) sequential decision-making and transfer in continuous state and action domains, and (d) joint prediction+optimization in machine learning.