Fundamental limits for weighted empirical approximations of tilted distributions

Sarvesh Ravichandran Iyer; Himadri Mandal; Dhruman Gupta; Rushil Gupta; Agniv Bandhyopadhyay; Achal Bassamboo; Varun Gupta; Sandeep Juneja

arXiv · 2512.23979

Fundamental limits for weighted empirical approximations of tilted distributions

Sarvesh Ravichandran Iyer·Himadri Mandal·Dhruman Gupta·Rushil Gupta·Agniv Bandhyopadhyay·Achal Bassamboo·Varun Gupta·Sandeep Juneja

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Abstract

Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in rare event simulation. In this article, we discuss the asymptotic efficiency of a self-normalized importance sampler of the tilted distribution. We provide a sharp characterization of its accuracy, given the number of samples and the degree of tilt. Our findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions.

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Sarvesh Ravichandran Iyer, Himadri Mandal, Dhruman Gupta, Rushil Gupta, Agniv Bandhyopadhyay, Achal Bassamboo, Varun Gupta, Sandeep Juneja. 2025-12-30. Fundamental limits for weighted empirical approximations of tilted distributions. https://arxiv.org/abs/2512.23979

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