Gradient Importance Sampling
This work addresses a methodological bottleneck in Monte Carlo sampling for researchers in computational statistics and machine learning, offering an incremental improvement over existing importance sampling approaches.
The paper tackles the limitation of diminishing adaptation in adaptive Monte Carlo schemes by introducing a gradient-informed variant of Sequential Monte Carlo (SMC) and Population Monte Carlo for static problems, enabling continuous adaptation without ergodicity constraints.
Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case ergodicity can only be guaranteed if adaptation is diminished at a certain rate. Importance Sampling approaches offer a way to circumvent this limitation and design sampling algorithms that keep adapting. Here I present a gradient informed variant of SMC (and its special case Population Monte Carlo) for static problems.