# Black-box Importance Sampling

arXiv: https://arxiv.org/abs/1610.05247 · HTML: https://mlsanity.com/paper/1610.05247/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2016.

## Built on by (most cited first, 13 of 13)

- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Positively Weighted Kernel Quadrature via Subsampling](https://mlsanity.com/paper/2107.09597/) (2021)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Data Optimization in Deep Learning: A Survey](https://mlsanity.com/paper/2310.16499/) (2023)
- [Probabilistic Inference and Learning with Stein's Method](https://mlsanity.com/paper/2603.07467/) (2026)
- [Improved Stein Variational Gradient Descent with Importance Weights](https://mlsanity.com/paper/2210.00462/) (2022)
- [Tractable Computation of Expected Kernels](https://mlsanity.com/paper/2102.10562/) (2021)
- [Asymptotic Inference for Multi-Stage Stationary Treatment Policy with Variable Selection](https://mlsanity.com/paper/2301.12553/) (2023)
- [Importance Sampling for Nonlinear Models](https://mlsanity.com/paper/2505.12353/) (2025)
- [A Black-Box Debiasing Framework for Conditional Sampling](https://mlsanity.com/paper/2510.11071/) (2025)
- [On two ways to use determinantal point processes for Monte Carlo integration](https://mlsanity.com/paper/2604.19698/) (2026)
- [λ-PSD: Scalable Approximate SNR-Optimised Polynomial Stein Discrepancies](https://mlsanity.com/paper/2606.26621/) (2026)

## Abstract (arXiv)

Importance sampling is widely used in machine learning and statistics, but its power is limited by the restriction of using simple proposals for which the importance weights can be tractably calculated. We address this problem by studying black-box importance sampling methods that calculate importance weights for samples generated from any unknown proposal or black-box mechanism. Our method allows us to use better and richer proposals to solve difficult problems, and (somewhat counter-intuitively) also has the additional benefit of improving the estimation accuracy beyond typical importance sampling. Both theoretical and empirical analyses are provided.