# Importance sampling for online variational learning

arXiv: https://arxiv.org/abs/2402.02859 · HTML: https://mlsanity.com/paper/2402.02859/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Online Variational Filtering and Parameter Learning](https://mlsanity.com/paper/2110.13549/) (2021)
- [Variational Message Passing with Structured Inference Networks](https://mlsanity.com/paper/1803.05589/) (2018)
- [A General Method for Amortizing Variational Filtering](https://mlsanity.com/paper/1811.05090/) (2018)
- [Real-Time Variational Method for Learning Neural Trajectory and its Dynamics](https://mlsanity.com/paper/2305.11278/) (2023)

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

- [Latent Inference-Time Guidance of Time Series Foundation Models](https://mlsanity.com/paper/2609.38058/) (2026)

## Abstract (arXiv)

This article addresses online variational estimation in state-space models. We focus on learning the smoothing distribution, i.e. the joint distribution of the latent states given the observations, using a variational approach together with Monte Carlo importance sampling. We propose an efficient algorithm for computing the gradient of the evidence lower bound (ELBO) in the context of streaming data, where observations arrive sequentially. Our contributions include a computationally efficient online ELBO estimator, demonstrated performance in offline and true online settings, and adaptability for computing general expectations under joint smoothing distributions.