# Efficient Incremental Belief Updates Using Weighted Virtual Observations

arXiv: https://arxiv.org/abs/2402.06940 · HTML: https://mlsanity.com/paper/2402.06940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 10 Feb 2024.

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

- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [Inference Compilation and Universal Probabilistic Programming](https://mlsanity.com/paper/1610.09900/) (2016)
- [Sparse Variational Inference: Bayesian Coresets from Scratch](https://mlsanity.com/paper/1906.03329/) (2019)
- [A New Approach to Probabilistic Programming Inference](https://mlsanity.com/paper/1507.00996/) (2015)
- [Bayesian Federated Learning: A Survey](https://mlsanity.com/paper/2304.13267/) (2023)
- [Etalumis: Bringing Probabilistic Programming to Scientific Simulators at Scale](https://mlsanity.com/paper/1907.03382/) (2019)
- [A Critical Review of Communications in Multi-Robot Systems](https://mlsanity.com/paper/2206.09484/) (2022)
- [Probabilistic Programs with Stochastic Conditioning](https://mlsanity.com/paper/2010.00282/) (2020)
- [Uncertain Evidence in Probabilistic Models and Stochastic Simulators](https://mlsanity.com/paper/2210.12236/) (2022)
- [Learning Probabilistic Programs](https://mlsanity.com/paper/1407.2646/) (2014)
- [Inference Over Programs That Make Predictions](https://mlsanity.com/paper/1810.01190/) (2018)

## Abstract (arXiv)

We present an algorithmic solution to the problem of incremental belief updating in the context of Monte Carlo inference in Bayesian statistical models represented by probabilistic programs. Given a model and a sample-approximated posterior, our solution constructs a set of weighted observations to condition the model such that inference would result in the same posterior. This problem arises e.g. in multi-level modelling, incremental inference, inference in presence of privacy constraints. First, a set of virtual observations is selected, then, observation weights are found through a computationally efficient optimization procedure such that the reconstructed posterior coincides with or closely approximates the original posterior. We implement and apply the solution to a number of didactic examples and case studies, showing efficiency and robustness of our approach. The provided reference implementation is agnostic to the probabilistic programming language or the inference algorithm, and can be applied to most mainstream probabilistic programming environments.