Backpropagation of Approximate Gradients for Stochastic Lattice Models
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2023-07-12
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en
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Abstract
Stochastic lattice models (s-LMs) are efficient computational tools for simulating non-equilibrium
and morphogenetic systems. Yet, to date, no efficient method for fitting s-LM parameters to a set of
objectives has been devised. The current state-of-the-art method for fitting s-LMs is Approximate-
Bayesian Computation, a gradient-free general-purpose Bayesian inference method for estimating
posterior distributions. While powerful, it is computationally expensive and quickly becomes intractable
for high-dimensional parameter spaces. Gradient-based methods, particularly gradient
descent algorithms making use of backpropagation could be significantly more efficient by directly fitting
the parameters without needing to estimate the posterior. However, s-LMs are non-differentiable
due to stochasticity and discreteness, preventing the use of backpropagation. Recent advances in
Artificial Intelligence have introduced methods to circumvent this issue. The reparameterization
trick re-enables backpropagation for stochastic models. Straight-through Estimation, on the other
hand, enables backpropagation of approximate gradients for discrete models. We investigate the
application of these methods for fitting four different s-LMs with respect to four common types of
objectives. The results are promising, showing that backpropagation of approximate gradients can
successfully be applied to various s-LM tasks. However, some challenges remain that will require
further investigation.
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Faculteit der Sociale Wetenschappen