Active Importance Sampling for Variational Objectives Dominated by Rare
Events: Consequences for Optimization and Generalization
- URL: http://arxiv.org/abs/2008.06334v2
- Date: Fri, 12 Mar 2021 03:06:51 GMT
- Title: Active Importance Sampling for Variational Objectives Dominated by Rare
Events: Consequences for Optimization and Generalization
- Authors: Grant M. Rotskoff and Andrew R. Mitchell and Eric Vanden-Eijnden
- Abstract summary: We introduce an approach that combines rare events sampling techniques with neural network optimization to optimize objective functions dominated by rare events.
We show that importance sampling reduces the variance of the solution to a learning problem, suggesting benefits for generalization.
Our numerical experiments demonstrate that we can successfully learn even with the compounding difficulties of high-dimensional and rare data.
- Score: 12.617078020344618
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Deep neural networks, when optimized with sufficient data, provide accurate
representations of high-dimensional functions; in contrast, function
approximation techniques that have predominated in scientific computing do not
scale well with dimensionality. As a result, many high-dimensional sampling and
approximation problems once thought intractable are being revisited through the
lens of machine learning. While the promise of unparalleled accuracy may
suggest a renaissance for applications that require parameterizing
representations of complex systems, in many applications gathering sufficient
data to develop such a representation remains a significant challenge. Here we
introduce an approach that combines rare events sampling techniques with neural
network optimization to optimize objective functions that are dominated by rare
events. We show that importance sampling reduces the asymptotic variance of the
solution to a learning problem, suggesting benefits for generalization. We
study our algorithm in the context of learning dynamical transition pathways
between two states of a system, a problem with applications in statistical
physics and implications in machine learning theory. Our numerical experiments
demonstrate that we can successfully learn even with the compounding
difficulties of high-dimension and rare data.
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