# Nonlinear Kalman Filtering with Reparametrization Gradients

arXiv: https://arxiv.org/abs/2303.04450 · HTML: https://mlsanity.com/paper/2303.04450/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 8 Mar 2023.

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

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Black-box α-divergence Minimization](https://mlsanity.com/paper/1511.03243/) (2015)
- [Wasserstein Variational Inference](https://mlsanity.com/paper/1805.11284/) (2018)
- [Online Forecasting Matrix Factorization](https://mlsanity.com/paper/1712.08734/) (2017)
- [A Linear Dynamical System Model for Text](https://mlsanity.com/paper/1502.04081/) (2015)
- [Nonlinear Kalman Filtering with Divergence Minimization](https://mlsanity.com/paper/1705.00722/) (2017)
- [A Collaborative Kalman Filter for Time-Evolving Dyadic Processes](https://mlsanity.com/paper/1501.05624/) (2015)

## Abstract (arXiv)

We introduce a novel nonlinear Kalman filter that utilizes reparametrization gradients. The widely used parametric approximation is based on a jointly Gaussian assumption of the state-space model, which is in turn equivalent to minimizing an approximation to the Kullback-Leibler divergence. It is possible to obtain better approximations using the alpha divergence, but the resulting problem is substantially more complex. In this paper, we introduce an alternate formulation based on an energy function, which can be optimized instead of the alpha divergence. The optimization can be carried out using reparametrization gradients, a technique that has recently been utilized in a number of deep learning models.