# Deep Kalman Filters

arXiv: https://arxiv.org/abs/1511.05121 · HTML: https://mlsanity.com/paper/1511.05121/

## Key facts

- Cited by 166 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2015.

## Built on by (most cited first, 30 of 166)

- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Criteria for Classifying Forecasting Methods](https://mlsanity.com/paper/2212.03523/) (2022)
- [Clockwork Variational Autoencoders](https://mlsanity.com/paper/2102.09532/) (2021)
- [Universal Approximation Theorems for Differentiable Geometric Deep Learning](https://mlsanity.com/paper/2101.05390/) (2021)
- [Contrastively Disentangled Sequential Variational Autoencoder](https://mlsanity.com/paper/2110.12091/) (2021)
- [Uncertainty-aware State Space Transformer for Egocentric 3D Hand Trajectory Forecasting](https://mlsanity.com/paper/2307.08243/) (2023)
- [Time Series Anomaly Detection for Cyber-Physical Systems via Neural System Identification and Bayesian Filtering](https://mlsanity.com/paper/2106.07992/) (2021)
- [Action-Sufficient State Representation Learning for Control with Structural Constraints](https://mlsanity.com/paper/2110.05721/) (2021)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2102.00397/) (2021)
- [Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2301.11308/) (2023)
- [Unsupervised Speech Enhancement using Dynamical Variational Auto-Encoders](https://mlsanity.com/paper/2106.12271/) (2021)
- [Roto-translated Local Coordinate Frames For Interacting Dynamical Systems](https://mlsanity.com/paper/2110.14961/) (2021)
- [Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis](https://mlsanity.com/paper/2210.13300/) (2022)
- [Generative Recursive Reasoning](https://mlsanity.com/paper/2605.19376/) (2026)
- [Unsupervised Representation Learning in Deep Reinforcement Learning: A Review](https://mlsanity.com/paper/2208.14226/) (2022)
- [MADiff: Motion-Aware Mamba Diffusion Models for Hand Trajectory Prediction on Egocentric Videos](https://mlsanity.com/paper/2409.02638/) (2024)
- [Unsupervised Learned Kalman Filtering](https://mlsanity.com/paper/2110.09005/) (2021)
- [ACE-NODE: Attentive Co-Evolving Neural Ordinary Differential Equations](https://mlsanity.com/paper/2105.14953/) (2021)
- [SSDNet: State Space Decomposition Neural Network for Time Series Forecasting](https://mlsanity.com/paper/2112.10251/) (2021)
- [An Adaptive Deep RL Method for Non-Stationary Environments with Piecewise Stable Context](https://mlsanity.com/paper/2212.12735/) (2022)
- [Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Models](https://mlsanity.com/paper/2101.07046/) (2021)
- [Automatically Learning Hybrid Digital Twins of Dynamical Systems](https://mlsanity.com/paper/2410.23691/) (2024)
- [Latent State Marginalization as a Low-cost Approach for Improving Exploration](https://mlsanity.com/paper/2210.00999/) (2022)
- [On Uncertainty in Deep State Space Models for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2210.09256/) (2022)
- [Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty](https://mlsanity.com/paper/2110.08607/) (2021)
- [Information is Power: Intrinsic Control via Information Capture](https://mlsanity.com/paper/2112.03899/) (2021)

## Abstract (arXiv)

Kalman Filters are one of the most influential models of time-varying phenomena. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption in a variety of disciplines. Motivated by recent variational methods for learning deep generative models, we introduce a unified algorithm to efficiently learn a broad spectrum of Kalman filters. Of particular interest is the use of temporal generative models for counterfactual inference. We investigate the efficacy of such models for counterfactual inference, and to that end we introduce the "Healing MNIST" dataset where long-term structure, noise and actions are applied to sequences of digits. We show the efficacy of our method for modeling this dataset. We further show how our model can be used for counterfactual inference for patients, based on electronic health record data of 8,000 patients over 4.5 years.