Variational Sequential Monte Carlo

By C. A. Naesseth, Scott W. Linderman, Rajesh Ranganath, David M. Blei. 2017

240 citations recorded by the source corpus.

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the variational sequential Monte Carlo (VSMC) family, and show how to optimize it in variational inference. VSMC melds variational inference (VI) and sequential Monte Carlo (SMC), providing practitioners with flexible, accurate, and powerful Bayesian inference. The VSMC family is a variational family that can approximate the posterior arbitrarily well, while still allowing for efficient optimization of its parameters. We demonstrate its utility on state space models, stochastic volatility models for financial data, and deep Markov models of brain neural circuits.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, methodology): “1 under mild conditions [9]. as Bachman and Precup [3] introduced the idea of viewing IWAE auxiliary variable variational inference and Naesseth et al. [51], Cremer et al. [13], Domke and Sheldon [20] formalized the notion.”
An Introduction to Probabilistic Programming (2018, background): “A more advanced version of this idea that uses sequential Monte Carlo instead of importance sampling has appeared recently in triplicate simultaneously (Le et al., 2017c; Naesseth et al., 2017; Maddison et al., 2017).”
Importance Weighting and Variational Inference (2018, background): “Previous work has connected IWVI and NIS by showing that the importance weighted ELBO is a lower bound of the ELBO applied to the NIS distribution [6, 16, 2].”
Reinterpreting Importance-Weighted Autoencoders (2017, background): “See section 5.3 for the proof, which is a special case of the proof in Naesseth et al. (2017).”
KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics (2021, methodology): “Another approach is to combine RNNs [65], or variational inference [32], [66] with MC based sampling.”
MIWAE: Deep Generative Modelling and Imputation of Incomplete Data Sets (2019, background): “Indeed, as studied by Cremer et al. (2017), Naesseth et al. (2018), and Domke & Sheldon (2018) the variational distribution qγ in (5) is replaced by a more complex distribution qIW which depends both on θ and γ.”
Auto-Encoding Sequential Monte Carlo (2017, methodology): “A ESMC was introduced in an earlier preprint (Le et al., 2017) concurrently with the closely related methods of Maddison et al. (2017); Naesseth et al. (2017).”
The Thermodynamic Variational Objective (2019, background): “…et al., 2018), tightening variational bounds in order to obtain better model learning (Burda et al., 2016; Maddison et al., 2017a; Le et al., 2018a; Naesseth et al., 2018), and alleviation of the associated detrimental effects on the learning of the inference network (Rainforth et al., 2018).”
On Nesting Monte Carlo Estimators (2017, background): “Hence, our results have important implications for relaxing mean-ﬁeld assumptions, or using different bounds, in variational inference (Hoffman & Blei, 2015; Naesseth et al., 2017; Maddison et al., 2017) and deep generative models (Burda et al., 2015; Le et al., 2018).”
Reparameterization Gradient for Non-differentiable Models (2018, background): “One interesting future direction is to investigate the possibility of applying our ideas to recent variational objectives [24, 17, 19, 16, 25], which are based on tighter lower bounds of marginal likelihood than the standard ELBO.”
Importance Weighted Hierarchical Variational Inference (2019, background): “This bound has been shown (Domke and Sheldon, 2018) to be a tractable lower bound on ELBO for a variational distribution that has been obtained by self-normalizing importance sampling, or a special case of Sequential Monte Carlo (Maddison et al., 2017; Naesseth et al., 2017; Le et al., 2017).”
Variational Rejection Sampling (2018, background): “Recently, Naesseth et al. [2018] proposed an importance weighted multi-sample objective for probabilistic models of dynamical systems based on sequential Monte Carlo.”
Tighter Variational Bounds are Not Necessarily Better (2018, background): “ically associated with better models p in terms of marginal likelihood on held out data. Other related approaches extend this to sequential Monte Carlo (SMC) (Maddison et al., 2017; Le et al., 2018; Naesseth et al., 2018) or change the lower bound that is optimized to reduce the bias (Li & Turne”
State Space LSTM Models with Particle MCMC Inference (2017, methodology): “On a related note, sequential Monte Carlo methods have recently received attention in approximating the variational objective (Maddison et al., 2017; Le et al., 2017; Naesseth et al., 2017).”
Filtering Variational Objectives (2017, background): “In [37] the bound we call FIVO is cast as a tractable lower bound on the ELBO defined by the particle filter’s non-parameteric approximation to the posterior.”
Debiasing Evidence Approximations: On Importance-weighted Autoencoders and Jackknife Variational Inference (2018, background): “The bounds LK seem quite different from LE , but recently Cremer et al. (2017) and Naesseth et al. (2017) showed that an exact correspondence exists: any LK can be converted into the standard form LE by defining a modified distribution qIW(z|x) through an importance sampling construction.”
Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation (2019, background): “[20] also show that performing VI with an SMC objective can be seen as minimizing (an upper bound to) a divergence from the SMC sampling distribution qSMC(z) to p(z|x).”
A General Method for Amortizing Variational Filtering (2018, methodology): “Finally, several recent works have used particle filtering in conjunction with amortized inference to provide a tighter lower bound on the log likelihood for sequential data [31, 33, 28].”