ADAPTIVE IMPORTANCE SAMPLING VIA AUTO-REGRESSIVE GENERATIVE MODELS AND GAUSSIAN PROCESSES.

Area of Science:

• Computational Statistics
• Machine Learning

Background:

• Adaptive importance sampling (AIS) is crucial for efficient Monte Carlo methods.
• High-dimensional spaces present challenges for AIS due to sparse and complex target distributions.
• Effective proposal distributions must be expressive, adaptable, and evaluable.

Purpose of the Study:

• To introduce a novel class of AIS methods utilizing Gaussian processes.
• To enhance the adaptability and expressiveness of proposal distributions in AIS.
• To address the limitations of existing AIS techniques in high-dimensional settings.

Main Methods:

• Constructing proposal distributions by autoregressively combining Gaussian processes.
• Leveraging Gaussian processes for their non-parametric, expressive conditional density estimation capabilities.
• Implementing and evaluating the proposed method through numerical experiments.

Main Results:

• The proposed Gaussian process-based AIS method demonstrates high accuracy.
• The method shows significant efficiency gains compared to existing AIS techniques.
• Successful sampling from a high-dimensional target distribution was achieved.

Conclusions:

• Autoregressively combined Gaussian processes offer a powerful approach for constructing proposal distributions in AIS.
• The developed method provides an accurate and efficient solution for sampling in high-dimensional, sparse target distribution spaces.
• This work advances the field of adaptive importance sampling with a novel, robust methodology.