Deep Kalman Filters

By Rahul G. Krishnan, Uri Shalit, David A. Sontag. 2015

435 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Generative Models, Probabilistic & Bayesian Methods

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Citations in the corpus

Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, methodology): “[59], and models optimized with this bound have been successfully used to model data such as natural images [58, 38, 11, 26], speech and music time-series [12, 23, 39], and video [2, 28, 17].”
Learning Latent Dynamics for Planning from Pixels (2018, background): “…Ha and Schmidhuber, 2018; Wayne et al., 2018; Igl et al., 2018; Srinivas et al., 2018), and pure video prediction without planning (Oh et al., 2015; Krishnan et al., 2015; Karl et al., 2016; Chiappa et al., 2017; Babaeizadeh et al., 2017; Gemici et al., 2017; Denton and Fergus, 2018; Buesing et…”
Learning and Querying Fast Generative Models for Reinforcement Learning (2018, methodology): “Multiple studies investigate the graphical model structure of the prior and posterior graphs and stress the possible importance of smoothing over ﬁltering inference distributions (e.g. Krishnan et al., 2015); in our investigations we did not ﬁnd a difference between these distributions.”
Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI (2019, neutral): “Deep formulation of classical ML models has been done, e.g. in Deep Kalman ﬁlters (DKFs) [302] , Deep Variational Bayes Filters (DVBFs) [303] , Structural Variational Autoencoders (SVAE) [304] , or conditional random ﬁelds as RNNs [305] .”
Deconfounding Reinforcement Learning in Observational Settings (2018, methodology): “Similar to the Healing MNIST dataset (Krishnan et al., 2015), the actions encode rotations of digit images with each entry in ~a satisfying (−π4 ≤ a ≤ + π 4 ) and the actions being divided into two categories (π8 ≤ |a| ≤ π 4 ) and (0 ◦ ≤ |a| < π8 ) according to the confounder u.”
Deep Factors for Forecasting (2019, methodology): “Similar preference can also be found in (Krishnan et al., 2015), although their model structure differs.”
Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction (2019, methodology): “Deep Variational Bayes Filters (DVBFs) (Karl et al., 2017) enhance the interpretability of DKFs by modelling state transitions with parametric – e.g. linear – models, which take in stochastic samples from the recognition model as inputs.”
Sequential Neural Models with Stochastic Layers (2016, methodology): “This shows that, knowing zt−1, the posterior distribution of zt does not depend on the past outputs and deterministic states, but only on the present and future ones; this was also noted in [20].”
Stochastic Video Generation with a Learned Prior (2018, background): “Several additional works train stochastic recurrent neural networks to model speech, handwriting, natural language (Chung et al., 2015; Fraccaro et al., 2016; Bowman et al., 2016), perform counterfactual inference (Krishnan et al., 2015) and anomaly detection (S ¨ olch et al., 2016).”
Structured Inference Networks for Nonlinear State Space Models (2016, methodology): “The current paper instantiates the inference scheme presented in (Krishnan et al., 2015) [Thm.”
Disentangled Sequential Autoencoder (2018, background): “…that a better design for the stochastic transition dynamics, e.g. by combining deep neural networks with well-studied linear dynamical systems (Krishnan et al., 2015; Fraccaro et al., 2016; Karl et al., 2016; Johnson et al., 2016; Krishnan et al., 2017; Fraccaro et al., 2017), can further…”
Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age (2016, neutral): “[142] have recently proposed Deep Kalman Filters; perhaps it might one day be possible to create an end-to-end SLAM system using a deep architecture, without explicit feature modeling, data association, etc.”
State Representation Learning for Control: An Overview (2018, methodology): “This method is also used in [Karl et al., 2016] and [Krishnan et al., 2015].”
Dream to Control: Learning Behaviors by Latent Imagination (2019, background): “Learning effective latent dynamics models is becoming feasible through advances in deep learning and latent variable models (Krishnan et al., 2015; Karl et al., 2016; Doerr et al., 2018; Buesing et al., 2018).”
Learning Awareness Models (2018, background): “Sequence-to-sequence modelling: There has been a lot of recent interest in sequence-to-sequence modelling (Downey et al., 2017; Venkatraman et al., 2017; Chung et al., 2015; Fraccaro et al., 2016; Bayer & Osendorfer, 2014; Archer et al., 2015; Krishnan et al., 2015), particularly in the context of p”
Deep Amortized Inference for Probabilistic Programs (2016, methodology): “Using neural guides with such a setup would permit amortized inference in models such as Deep Kalman Filters [16].”
Learning Attractor Dynamics for Generative Memory (2018, background): “The DKM can be also contrasted with recently proposed nonlinear generalisations of the KF such as [21] in that we preserve the higher-level linearity for efficient analytic inference over a very large latent state (M).”
Decoupling feature extraction from policy learning: assessing benefits of state representation learning in goal based robotics (2018, methodology): “Some examples include mixing a data-reconstruction objective and a forward model loss (Watter et al., 2015; Krishnan et al., 2015; Ha & Schmidhuber, 2018), coupling a forward model together with an inverse model (Pathak et al.”