Double-Loop Quasi-Monte Carlo Estimator for Nested Integration

핵심 개념

Introducing a novel DLQMC estimator for nested integration problems to improve efficiency and reduce computational costs.

초록

1. Introduction

• Evaluating Expected Information Gain (EIG) is crucial in computational science and statistics.
• Techniques based on Quasi-Monte Carlo (QMC) methods have focused on enhancing inner integral approximation efficiency.
• A novel approach, DLQMC estimator, extends efforts to address inner and outer expectations simultaneously.

2. Brief Overview of Monte Carlo and Randomized Quasi-Monte Carlo Integration

• MC method approximates integrals using random points.
• QMC method achieves better convergence rates for certain integrands.
• RQMC method improves efficiency while maintaining a low-discrepancy structure.

3. Nested Integration

• DLQMC estimator defined for nested integrals.
• DLMC estimator for nested integrals has limitations due to bias and variance.
• DLQMC estimator aims to reduce required samples and improve efficiency.

4. Numerical Results

• DLQMC estimator's bias and variance analyzed.
• Optimal work for DLQMC estimator derived for specified error tolerance.

통계

"The total work of the optimized DLQMC estimator for a specified error tolerance TOL > 0 is given by W ∗ DLQ ∝ TOL−(2/(1+β) + 1/(1+δ + γη))"

인용구

"The DLQMC estimator for nested integration problems to improve efficiency and reduce computational costs."
"DLQMC estimator aims to reduce required samples and improve efficiency."

핵심 통찰 요약

Double-loop quasi-Monte Carlo estimator for nested integration

by Arve... 게시일 arxiv.org 02-29-2024

https://arxiv.org/pdf/2302.14119.pdf

더 깊은 질문

질문 1

DLQMC 추정자를 다른 계산 문제에 어떻게 적용할 수 있습니까?
답변 1 여기에

질문 2

실제 응용 프로그램에서 DLQMC 추정자의 잠재적인 제한 사항은 무엇입니까?
답변 2 여기에

질문 3

DLQMC의 원칙을 확장하여 다른 계산 알고리즘을 최적화하는 방법은 무엇입니까?
답변 3 여기에