9,294 research outputs found
Importance Sampled Stochastic Optimization for Variational Inference
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient descent, using Monte Carlo approximation for the gradients. This enables variational inference for arbitrary differentiable probabilistic models, and consequently makes variational inference feasible for probabilistic programming languages. In this work we develop more efficient inference algorithms for the task by considering importance sampling estimates for the gradients. We show how the gradient with respect to the approximation parameters can often be evaluated efficiently without needing to re-compute gradients of the model itself, and then proceed to derive practical algorithms that use importance sampled estimates to speed up computation. We present importance sampled stochastic gradient descent that outperforms standard stochastic gradient descent by a clear margin for a range of models, and provide a justifiable variant of stochastic average gradients for variational inference.Peer reviewe
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
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