# Importance Weighting Approach in Kernel Bayes' Rule

arXiv: https://arxiv.org/abs/2202.02474 · HTML: https://mlsanity.com/paper/2202.02474/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 5 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)
- [Hilbert Space Embeddings of Predictive State Representations](https://mlsanity.com/paper/1309.6819/) (2013)
- [Kernel-Based Just-In-Time Learning for Passing Expectation Propagation Messages](https://mlsanity.com/paper/1503.02551/) (2015)
- [Filtering with State-Observation Examples via Kernel Monte Carlo Filter](https://mlsanity.com/paper/1312.4664/) (2013)
- [Kernel Bayesian Inference with Posterior Regularization](https://mlsanity.com/paper/1607.02011/) (2016)

## Built on by (most cited first, 1 of 1)

- [Regularized f-Divergence Kernel Tests](https://mlsanity.com/paper/2601.19755/) (2026)

## Abstract (arXiv)

We study a nonparametric approach to Bayesian computation via feature means, where the expectation of prior features is updated to yield expected kernel posterior features, based on regression from learned neural net or kernel features of the observations. All quantities involved in the Bayesian update are learned from observed data, making the method entirely model-free. The resulting algorithm is a novel instance of a kernel Bayes' rule (KBR), based on importance weighting. This results in superior numerical stability to the original approach to KBR, which requires operator inversion. We show the convergence of the estimator using a novel consistency analysis on the importance weighting estimator in the infinity norm. We evaluate KBR on challenging synthetic benchmarks, including a filtering problem with a state-space model involving high dimensional image observations. Importance weighted KBR yields uniformly better empirical performance than the original KBR, and competitive performance with other competing methods.