Black Box Variational Inference

By Rajesh Ranganath, Sean Gerrish, David M. Blei. 2013

1,251 citations recorded by the source corpus.

Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these efforts can hinder and deter us from quickly developing and exploring a variety of models for a problem at hand. In this paper, we present a "black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational distribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid difficult model-based derivations. We evaluate our method against the corresponding black box sampling based methods. We find that our method reaches better predictive likelihoods much faster than sampling methods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data.

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

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Citations in the corpus

Auto-Encoding Variational Bayes (2013, positive): “In [RGB13] some general methods, i.e. a control variate scheme, were introduced for reducing the variance of the original gradient estimator.”
Neural Variational Inference and Learning in Belief Networks (2014, methodology): “Like NVIL, Black Box Variational Inference (BBVI, Ranganath et al., 2013) learns the variational parameters of the posterior by optimizing the variational bound using sampling-based gradient estimates, which makes it applicable to a large range of models.”
VQ-DRAW: A Sequential Discrete VAE (2020, background): “Other works do away with the reparameterization trick entirely, opting for other strategies for reducing variance in the variational lower bound [5] [6] [7].”
A-NICE-MC: Adversarial Training for MCMC (2017, background): “Our hope is that these ideas will allow us to bridge the gap between MCMC and neural network function approximators, similarly to what “black-box techniques” did in the context of variational inference [1].”
Variational Inference with Normalizing Flows (2015, background): “An important advantage of stochastic backpropagation is that, for models with continuous latent variables, it has the lowest variance among competing estimators.”
Gradient Estimation Using Stochastic Computation Graphs (2015, background): “[20]; both papers mostly focus on mean-field approximations without amortized inference.”
Foundation Posteriors for Approximate Probabilistic Inference (2022, positive): “In this case, we propose to ﬁnetune our pretrained inference model using stochastic variational inference, or SVI [35, 50, 39].”
An Introduction to Probabilistic Programming (2018, methodology): “This can be interpreted as a form of Rao-Blackwellization (Ranganath et al., 2014), which reduces the variance by ignoring the components of the weight that are not directly associated with the sampled value Xv.”
The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables (2016, methodology): “For models with discrete latent variables, the discontinuous nature of which makes reparameterization not useful, a number of score function estimators have been developed [31, 17, 33, 28, 42, 18], which differ primarily in the variance reduction techniques used.”
The price of debiasing automatic metrics in natural language evalaution (2018, methodology): “The technique has also been used in machine learning and reinforcement learning to lower variance estimates of gradients (Greensmith et al., 2004; Paisley et al., 2012; Ranganath et al., 2014).”
One-Shot Generalization in Deep Generative Models (2016, methodology): “, 2015) and when they are discrete, score function estimators are used (Mnih & Gregor, 2014; Ranganath et al., 2014; Mansimov et al., 2015).”
SNAS: Stochastic Neural Architecture Search (2018, methodology): “ subsection how SNAS calculates gradients w.r.t and . 2.2 PARAMETER LEARNING FOR OPERATIONS AND ARCHITECTURES Though the objective (4) could be optimized with black-box gradient descent method as in Ranganath et al. (2014), it would suffer from the high variance of likelihood ratio trick (Williams, ”
Variational Inference: A Review for Statisticians (2016, methodology): “As examples, see Kingma and Welling (2014); Rezende, Mohamed, and Wierstra (2014); Ranganath, Gerrish, and Blei (2014); Ranganath, Tran, and Blei (2016); Salimans and Knowles (2014); Titsias and Lázaro-Gredilla (2014); and Tran, Ranganath, and Blei (2016).”
MuProp: Unbiased Backpropagation for Stochastic Neural Networks (2015, methodology): “rgence guarantees. Recently, several new scalable methods have been proposed for training such models. A number of these algorithms use likelihood ratio estimators with variance reduction techniques (Ranganath et al., 2014; Mnih & Gregor, 2014; Gregor et al., 2014), inspired by methods from rein”
Towards a Neural Statistician (2016, methodology): “gure 1 on the left is equivalent to that of a standard topic model. In contrast to traditional topic models we do not use discrete latent variables, or restrict to discrete data. Work such as that by Ranganath et al. (2014) has extended topic models in various directions, but importantly we use ﬂexi”
The Variational Gaussian Process (2015, methodology): “, 2013), deriving generic strategies for easily fitting many models (Ranganath et al., 2014), and applying neural networks as a flexible parametric family of approximations (Kingma & Welling, 2014; Rezende et al.”
Variational Inference for Monte Carlo Objectives (2016, methodology): “Black Box Variational Inference (BBVI Ranganath et al., 2014) and NVIL (Mnih & Gregor, 2014)”
Stochastic Gradient Descent as Approximate Bayesian Inference (2017, methodology): “For non-conjugate models, Black-Box variational inference (Ranganath et al., 2014) has enabled SVI for a large class of models, but this approach may suffer from high-variance gradients.”
Hierarchical Variational Models (2015, background): “One term of the gradient involves the product of the score function with all of r , Localizing (Rao-Blackwellizing) the inner expectation as in Ranganath et al. (2014); Mnih and Gregor (2014) can drastically reduce the variance.”