Tractable Fully Bayesian Inference via Convex Optimization and Optimal Transport Theory
We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from and the target distribution is log-concave, this can be tractably solved with convex optimization. We show that a special case of this, when the source is the prior and the target is the posterior, is Bayesian inference. Here, we can tractably calculate the normalization constant and draw posterior i.i.d. samples. Remarkably, our Bayesian tractability criterion is simply log concavity of the prior and likelihood: the same criterion for tractable calculation of the maximum a posteriori point estimate. With simulated data, we demonstrate how we can attain the Bayes risk in simulations. With physiologic data, we demonstrate improvements over point estimation in intensive care unit outcome prediction and electroencephalography-based sleep staging.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceSleep StagingSimilar Papers 제목 키워드 기반
Approximate Inference with the Variational Holder Bound
We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to t…
Bayesian InferenceNumerical IntegrationThe computational asymptotics of Gaussian variational inference and the Laplace approximation
Gaussian variational inference and the Laplace approximation are popular alternatives to Markov chain Monte Carlo that formulate Bayesian posterior inference as an optimization problem, enabling the use of simple and sca…
Bayesian InferenceStochastic OptimizationVariational InferenceEnhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementat…
Bayesian InferenceBayesian OptimizationMaximizing acquisition functions for Bayesian optimization
Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functi…
Bayesian Optimizationglobal-optimizationFast Dual Variational Inference for Non-Conjugate LGMs
Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likeliho…
Bayesian InferenceVariational Inference