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Paul E. Johnson
Senior Data Scientist, H&R Block Corporate Headquarters
Professor Emeritus, University of Kansas
On October 20, 2022 1:11:50 PM CDT, glen e ropella <gepr@agent-based-modeling.com> wrote:
https://arxiv.org/abs/2210.08572
Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded
by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin
with probability of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters (p)
is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased
and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our
code is available at
this https URL.