Structured Inference Networks for Nonlinear State Space Models

By Rahul G. Krishnan, Uri Shalit, David A. Sontag. 2016

537 citations recorded by the source corpus.

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Probabilistic & Bayesian Methods, Signal Processing

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Citations in the corpus

Learning Latent Dynamics for Planning from Pixels (2018, background): “Estimating the outer expectations using a single reparameterized sample yields an efficient objective for inference and learning in non-linear latent variable models that can be optimized using gradient ascent (Kingma & Welling, 2013; Rezende et al., 2014; Krishnan et al., 2017).”
Deconfounding Reinforcement Learning in Observational Settings (2018, methodology): “Inspired by Krishnan et al. (2015, 2017), we similarly choose a bi-directional LSTM (Zaremba and Sutskever, 2014) to parameterize f 11 and f 12 in Equation (15).”
Deep Factors for Forecasting (2019, methodology): “…via a multi-layer perceptron (MLP) or interlacing SSM with transition matrices temporally speciﬁed by RNNs. Deep Markov Models (DMMs), proposed by (Krishnan et al., 2017; 2015), keep the Gaussian transition dynamics with mean and co-variance matrix parameterized by MLPs. Stochastic RNNs (SRNNs)…”
Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction (2019, methodology): “Deep Kalman ﬁlters (DKFs) (Krishnan et al., 2015; Krishnan et al., 2017) take this a step further by allowing for exogenous inputs in their network and incorporating an additional KL loss term to penalise state transitions be-tween time steps.”
A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning (2017, methodology): “We compare the performaces of the KVAE to DVBFs [14] and deep Markov models 4 (DMM) [17], non-linear SSMs parameterized by deep neural networks whose intractable posterior distribution is approximated with an inference network.”
Stochastic Variational Video Prediction (2017, background): “This would allow time-variant latent distributions which is more aligned with generative neural models for time-series(Johnson et al., 2016; Gao et al., 2016; Krishnan et al., 2017).”
Disentangled Sequential Autoencoder (2018, background): “…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 enhance the quality of the learned representations.”
Variational Sequential Monte Carlo (2017, methodology): “Archer et al. [2015], Johnson et al. [2016] develop variational inference for state space models with conjugate dynamics, while Krishnan et al. [2017] develop variational approximations for models with nonlinear dynamics and additive Gaussian noise.”
GP-VAE: Deep Probabilistic Time Series Imputation (2019, background): “Conversely, there are deep probabilistic models for time series [e.g., 14, 26, 27], but those do not explicitly handle missing data.”
Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling (2018, methodology): “In recent years, this toolkit has been expanded to incorporate increasingly ﬂexible components like Gaussian processes (Frigola et al., 2014) and neural networks (Chung et al., 2015; Johnson et al., 2016; Gao et al., 2016; Krishnan et al., 2017) into probabilistic time series models.”
Contextual Explanation Networks (2017, background): “…networks [8, 9, 10], representing potential functions [11] and energy functions [12] with neural networks, encoding learnable structure into Gaussian process kernels with deep and recurrent networks [13, 14], or learning state-space models on top of nonlinear embeddings of observables [15, 16, 17].”
Attentive State-Space Modeling of Disease Progression (2019, methodology): “We construct the inference network qφ(~zT |~xT ) so that it mimics the structure of the true posterior [19].”
Latent Normalizing Flows for Discrete Sequences (2019, background): “(Gan et al., 2015), STORN from (Bayer & Osendorfer, 2015), NASMC from (Gu et al., 2015), SRNN from (Fraccaro et al., 2016), DMM from (Krishnan et al., 2017).”
Unsupervised Recurrent Neural Network Grammars (2019, unknown): “, 2014) and structured VAEs (Johnson et al., 2016; Krishnan et al., 2017), which have been used previously for unsupervised (Cai et al.”
Multi-period Time Series Modeling with Sparsity via Bayesian Variational Inference (2017, unknown): “, filtering, smoothing and bi-direction [24].”
Generating Multi-Agent Trajectories using Programmatic Weak Supervision (2018, background): “…et al., 2014; Kingma & Welling, 2014; Rezende et al., 2014) and can more readily be extended to incorporate additional structure, such as a hierarchy of random variables (Ranganath et al., 2016) or dynamics (Johnson et al., 2016; Chung et al., 2015; Krishnan et al., 2017; Fraccaro et al., 2016).”
Semi-Amortized Variational Autoencoders (2018, background): “Note that unlike to sequential VAEs that employ different latent variables at each time step (Chung et al., 2015; Fraccaro et al., 2016; Krishnan et al., 2017; Serban et al., 2017; Goyal et al., 2017a), in this work we focus on modeling the entire sequence with a global latent variable.”