Fast Monte-Carlo
TLDR
This paper introduces an eigenvalue-based Monte Carlo approximation that significantly reduces sample paths while maintaining accuracy and robustness.
Key contributions
- Proposes an eigenvalue-based small-sample approximation for Markov Chain Monte Carlo (MCMC).
- Reduces required simulation paths from millions to as few as 10, depending on time horizon.
- Achieves comparable, distributionally robust results, validated by Wasserstein distance.
- Delivers a significant reduction in variance for the steady-state distribution.
Why it matters
This paper offers a revolutionary approach to Monte Carlo simulations, drastically cutting down computational costs. By requiring far fewer samples, it makes complex simulations more accessible and efficient for various applications. This could accelerate research and development in fields relying on MCMC.
Original Abstract
This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed eigenvalue-based methodology reduces the number of paths required for Monte Carlo from as many as 1,000,000 to as few as 10 (depending on the simulation time horizon $T$), and delivers comparable, distributionally robust results, as measured by the Wasserstein distance. The proposed methodology also produces a significant variance reduction in the steady-state distribution.
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