# Fundamental limits for weighted empirical approximations of tilted distributions

arXiv: https://arxiv.org/abs/2512.23979 · HTML: https://mlsanity.com/paper/2512.23979/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [Generating DDPM-based Samples from Tilted Distributions](https://mlsanity.com/paper/2604.03015/) (2026)

## Abstract (arXiv)

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.