# Stratified Splitting for Efficient Monte Carlo Integration

## TL;DR

This paper introduces Stratified Splitting, a new Sequential Monte Carlo method that efficiently estimates high-dimensional integrals, including rare-event probabilities, with unbiasedness and polynomial complexity.

## Contribution

The paper presents a novel Stratified Splitting technique that improves Monte Carlo integration efficiency and handles indicator functions, with proven polynomial complexity.

## Key findings

- Accurate estimates for high-dimensional integrals.
- Handles indicator functions in rare-event problems.
- Achieves polynomial complexity in certain variants.

## Abstract

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the curse of dimensionality. However, due to the curse of dimensionality, deterministic numerical methods are inefficient in high-dimensional settings. Consequentially, for many practical problems, one must resort to Monte Carlo estimation. In this paper, we introduce a novel Sequential Monte Carlo technique called Stratified Splitting. The method provides unbiased estimates and can handle various integrand types including indicator functions, which are used in rare-event probability estimation problems. Moreover, we demonstrate that a variant of the algorithm can achieve polynomial complexity. The results of our numerical experiments suggest that the Stratified Splitting method is capable of delivering accurate results for a variety of integration problems.