Filtering Variational Objectives

By Chris J. Maddison, Dieterich Lawson, George Tucker, Nicolas Manfred Otto Heess, Mohammad Norouzi, Andriy Mnih, Arnaud Doucet, Yee Whye Teh. 2017

231 citations recorded by the source corpus.

When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, methodology): “Our second contribution is to show that EIMs provide a unifying conceptual framework to explain many advances in constructing tighter variational lower bounds for latent variable models ( e.g. , [9, 48, 51, 41, 68, 50, 63]).”
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).”
Sequential Attend, Infer, Repeat: Generative Modelling of Moving Objects (2018, methodology): “…on propagated latent variables (Line 4 in Algorithm 3), we encode the latter by using a two-layer MLP similarly to Zaheer et al., 2017, l Training was done by optimising the FIVO bound, which is known to be tighter than the IWAE bound for sequential latent variable models (Maddison et al., 2017).”
Deep Variational Reinforcement Learning for POMDPs (2018, methodology): “− This improves model learning (Le et al., 2018; Maddison et al., 2017) and allows us to train the model jointly with the n -step loss (see Section 3.4).”
Importance Weighting and Variational Inference (2018, neutral): “For large M , the looseness of the IW-ELBO is given by the variance of R. Formally, if there exists some α > 0 such that Maddison et al. [13] give a related result.”
Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation (2019, background): “Recent work has investigated tighter objectives [6, 20, 18, 17, 23, 25], based on the following principle: Let R be an estimator of the likelihood—i.”
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.”
Variational Sequential Monte Carlo (2017, methodology): “Finally, the log-marginal likelihood lower bound (6) was developed concurrently and independently by Maddison et al. [2017] and Le et al. [2017]. The difference with our work lies in how we derive the bound and the implications we explore. Maddison et al. [2017], Le et al.”
Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives (2018, background): “Variational Sequential Monte Carlo (Maddison et al., 2017; Naesseth et al., 2018; Le et al., 2018) and Neural Adapative Sequential Monte Carlo (Gu et al., 2015) extend IWAE and RWS to sequential latent variable models, respectively.”
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).”
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].”
Pushing the bounds of dropout (2018, background): “Indeed, Maddison et al. (2017) show that if the ﬁrst inverse moment of L is ﬁnite, then Here we go a bit further and show that if there is a positive lower and upper bound on L , then there are non-trivial lower and upper bounds on its Jensen gap and these are bounds are multiplicative in var( L ) .”
Sequential Latent Knowledge Selection for Knowledge-Grounded Dialogue (2020, methodology): “First, we can explore other inference models such as sequential Monte Carlo methods using ﬁltering variational objectives (Maddison et al., 2017a).”
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).”
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).”
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, methodology): “…2017; Naesseth et al., 2017; Figurnov 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…”
Tighter Variational Bounds are Not Necessarily Better (2018, background): “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 & Turner, 2016; Bamler et al., 2017).”