Adaptive neural sampler speeds up monte carlo sampling tasks
Amortised adaptive importance sampling
Machine Learning
Summary
Sampling from complex distributions can be very slow because standard methods need a lot of work to get good results. The authors developed a way to train a small neural network to learn how to adapt the sampling process quickly for many similar tasks. After this training, the sampler can efficiently generate good samples for new but related problems without needing detailed knowledge beforehand. Their method improves speed and quality over both untrained and specially trained samplers for each problem. They also tested how well this trained sampler works on problems it wasn’t trained on.
What this means in practice
- •For machine learning engineers: Implement faster samplers within probabilistic models that share distribution characteristics without retraining for each new case.
- •For financial modelers: Generate efficient simulations for forecasting where model parameters vary within a known family without tuning samplers for each scenario.
Authors
Arran Carter, Víctor Elvira, Esmeralda S. Whitammer
Abstract
Monte Carlo sampling algorithms aim to produce samples from a target distribution with a given unnormalised probability density function. The high cost of running Monte Carlo algorithms, with many simulation steps or particles needed to obtain a good empirical approximation to the target, can be reduced by introducing learnable components into the sampler -- a form of amortisation. Once these components are trained, amortised samplers can produce high-quality samples with less computation at sampling time than training-free algorithms would require. We propose an amortised sampler built upon the framework of adaptive importance sampling -- a hierarchical importance sampling procedure where the proposal is iteratively adapted. Our amortised adaptive importance sampling algorithm fits a lightweight neural network that adapts the proposal using information obtained over the course of sampling. By training our sampler over many different targets taken from the same family of distributions, we obtain a sampler that can adapt to a specific target at sampling time without a priori access to the target's parameters. We show that our procedure can efficiently sample from targets within the family the sampler was trained on, giving improvements over target-specific amortised samplers and training-free adaptive importance sampling algorithms. We also explore the potential for generalisation, where the trained sampler is used to sample from targets outwith its training family.