This chapter covers the Bayesian filtering algorithms that deploy deep learning to build state‐space models from raw data. Variational inference and amortized variational inference are reviewed, which are used to estimate an approximate posterior through reformulating the inference problem as an optimization problem aimed at minimizing the Kullback–Leibler divergence between the true and the approximate posteriors. A number of deep learning‐based filtering algorithms are inspired by variational autoencoders. Such filters are trained by optimizing the evidence lower bound. The presented deep learning‐based filtering algorithms include deep Kalman filter, backpropagation Kalman filter, differentiable particle filter, deep Rao–Blackwellized particle filter, deep variational Bayes filter, and Kalman variational autoencoder. Then, deep variational information bottleneck is reviewed, which aims at providing an optimal representation in terms of a trade‐off between complexity of the representation and its predictive power. The issue of robustness is discussed by presenting the Wasserstein distributionally robust Kalman filter. Hierarchical invertible neural transport is presented, which can provide both the joint and the conditional densities. The reviewed applications of deep learning‐based filters include predicting the effect of anti‐diabetic drugs based on the electronic health records and autonomous driving using the KITTI Vision Benchmark.


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