Black box variational inference for state space models

Abstract

Latent variable time-series models are among the most heavily used tools from machine learning and applied statistics. These models have the advantage of learning latent structure both from noisy observations and from the temporal ordering in the data, where it is assumed that meaningful correlation structure exists across time. A few highly-structured models, such as the linear dynamical system with linear-Gaussian observations, have closed-form inference procedures (e.g. the Kalman Filter), but this case is an exception to the general rule that exact posterior inference in more complex generative models is intractable. Consequently, much work in time-series modeling focuses on approximate inference procedures for one particular class of models. Here, we extend recent developments in stochastic variational inference to develop a `black-box' approximate inference technique for latent variable models with latent dynamical structure. We propose a structured Gaussian variational approximate posterior that carries the same intuition as the standard Kalman filter-smoother but, importantly, permits us to use the same inference approach to approximate the posterior of much more general, nonlinear latent variable generative models. We show that our approach recovers accurate estimates in the case of basic models with closed-form posteriors, and more interestingly performs well in comparison to variational approaches that were designed in a bespoke fashion for specific non-conjugate models.

References in corpus (8)

• Adam: A Method for Stochastic Optimization
• ADADELTA: An Adaptive Learning Rate Method
• Stochastic Backpropagation and Approximate Inference in Deep Generative Models
• NICE: Non-linear Independent Components Estimation
• Theano: new features and speed improvements
• Deep Kalman Filters
• Variational Bayesian Inference with Stochastic Search
• Deep Temporal Sigmoid Belief Networks for Sequence Modeling

Cited by in corpus (53)

• KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics
• Composing graphical models with neural networks for structured representations and fast inference
• Dynamical Variational Autoencoders: A Comprehensive Review
• A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning
• Modeling emotion in complex stories: the Stanford Emotional Narratives Dataset
• Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI
• Metastable dynamics of neural circuits and networks
• Stochastic Latent Actor-Critic: Deep Reinforcement Learning with a Latent Variable Model
• Learning and Querying Fast Generative Models for Reinforcement Learning
• Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models
• Variational Sequential Monte Carlo
• Linear dynamical neural population models through nonlinear embeddings
• Creativity: Generating Diverse Questions using Variational Autoencoders
• State Space LSTM Models with Particle MCMC Inference
• Black-box Variational Inference for Stochastic Differential Equations
• Gaussian variational approximation for high-dimensional state space models
• Neural Dynamics Discovery via Gaussian Process Recurrent Neural Networks
• Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems
• Temporal Difference Variational Auto-Encoder
• Differentiable Particle Filtering via Entropy-Regularized Optimal Transport
• Learning Awareness Models
• Forecasting Individualized Disease Trajectories using Interpretable Deep Learning
• The Neural Moving Average Model for Scalable Variational Inference of State Space Models
• Information Maximizing Visual Question Generation
• Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data
• Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning
• Interpretable VAEs for nonlinear group factor analysis
• Reinforcement Learning for Portfolio Management
• Efficient non-conjugate Gaussian process factor models for spike count data using polynomial approximations
• Scaling Factorial Hidden Markov Models: Stochastic Variational Inference without Messages
• Particle Smoothing Variational Objectives
• Anomaly Detection on Graph Time Series
• Variational online learning of neural dynamics
• A Dynamic Edge Exchangeable Model for Sparse Temporal Networks
• Structured Variational Inference in Unstable Gaussian Process State Space Models
• Stochastic Sequential Neural Networks with Structured Inference
• Unifying and generalizing models of neural dynamics during decision-making
• Variational Tracking and Prediction with Generative Disentangled State-Space Models
• Physics-aware, probabilistic model order reduction with guaranteed stability
• Black-Box Autoregressive Density Estimation for State-Space Models
• A Goal-Based Movement Model for Continuous Multi-Agent Tasks
• Bidirectional Inference Networks: A Class of Deep Bayesian Networks for Health Profiling
• Estimating Nonlinear Dynamics with the ConvNet Smoother
• Optimized Auxiliary Particle Filters: adapting mixture proposals via convex optimization
• Learning Insulin-Glucose Dynamics in the Wild
• Gaussian variational approximation with a factor covariance structure
• Ensemble Kalman Variational Objectives: Nonlinear Latent Trajectory Inference with A Hybrid of Variational Inference and Ensemble Kalman Filter
• Online Variational Filtering and Parameter Learning
• Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Models
• Stanza: A Nonlinear State Space Model for Probabilistic Inference in Non-Stationary Time Series
• Learning Unstable Dynamical Systems with Time-Weighted Logarithmic Loss
• Self-Supervised Inference in State-Space Models
• Neuron's Eye View: Inferring Features of Complex Stimuli from Neural Responses