Fundamental Limits for Weighted Empirical Approximations of Exponentially Tilted Distributions

Sarvesh Ravichandran Iyer, Himadri Mandal, Dhruman Gupta, Rushil Gupta, Agniv Bandyopadhyay, Achal Bassamboo, Sandeep Kumar Juneja, Varun Gupta
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:5239-5247, 2026.

Abstract

Generating samples from exponentially tilting a given distribution of random vectors when samples from the given distribution are available finds applications in fields such as finance and climate science and in the broad area of rare event simulation. In this article, we discuss the asymptotic efficiency of an estimator obtained by exponentially tilting the empirical distribution. We provide a sharp characterization of how much one can accurately tilt distributions given a certain number of samples. Our findings reveal a surprising dichotomy: While twisting unbounded distributions is a fundamentally hard task, for bounded distributions, one can accurately tilt by a large amount using much fewer samples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-iyer26a, title = { Fundamental Limits for Weighted Empirical Approximations of Exponentially Tilted Distributions }, author = {Iyer, Sarvesh Ravichandran and Mandal, Himadri and Gupta, Dhruman and Gupta, Rushil and Bandyopadhyay, Agniv and Bassamboo, Achal and Juneja, Sandeep Kumar and Gupta, Varun}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {5239--5247}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/iyer26a/iyer26a.pdf}, url = {https://proceedings.mlr.press/v300/iyer26a.html}, abstract = { Generating samples from exponentially tilting a given distribution of random vectors when samples from the given distribution are available finds applications in fields such as finance and climate science and in the broad area of rare event simulation. In this article, we discuss the asymptotic efficiency of an estimator obtained by exponentially tilting the empirical distribution. We provide a sharp characterization of how much one can accurately tilt distributions given a certain number of samples. Our findings reveal a surprising dichotomy: While twisting unbounded distributions is a fundamentally hard task, for bounded distributions, one can accurately tilt by a large amount using much fewer samples. } }
Endnote
%0 Conference Paper %T Fundamental Limits for Weighted Empirical Approximations of Exponentially Tilted Distributions %A Sarvesh Ravichandran Iyer %A Himadri Mandal %A Dhruman Gupta %A Rushil Gupta %A Agniv Bandyopadhyay %A Achal Bassamboo %A Sandeep Kumar Juneja %A Varun Gupta %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-iyer26a %I PMLR %P 5239--5247 %U https://proceedings.mlr.press/v300/iyer26a.html %V 300 %X Generating samples from exponentially tilting a given distribution of random vectors when samples from the given distribution are available finds applications in fields such as finance and climate science and in the broad area of rare event simulation. In this article, we discuss the asymptotic efficiency of an estimator obtained by exponentially tilting the empirical distribution. We provide a sharp characterization of how much one can accurately tilt distributions given a certain number of samples. Our findings reveal a surprising dichotomy: While twisting unbounded distributions is a fundamentally hard task, for bounded distributions, one can accurately tilt by a large amount using much fewer samples.
APA
Iyer, S.R., Mandal, H., Gupta, D., Gupta, R., Bandyopadhyay, A., Bassamboo, A., Juneja, S.K. & Gupta, V.. (2026). Fundamental Limits for Weighted Empirical Approximations of Exponentially Tilted Distributions . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:5239-5247 Available from https://proceedings.mlr.press/v300/iyer26a.html.

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