Bridging the Gap Between Variational Inference and Wasserstein Gradient Flows
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of probability measures where they do not necessarily admit a parametric density function. In this paper, we bridge the gap between these two methods. We demonstrate that, under certain conditions, the Bures-Wasserstein gradient flow can be recast as the Euclidean gradient flow where its forward Euler scheme is the standard black-box variational inference algorithm. Specifically, the vector field of the gradient flow is generated via the path-derivative gradient estimator. We also offer an alternative perspective on the path-derivative gradient, framing it as a distillation procedure to the Wasserstein gradient flow. Distillations can be extended to encompass $f$-divergences and non-Gaussian variational families. This extension yields a new gradient estimator for $f$-divergences, readily implementable using contemporary machine learning libraries like PyTorch or TensorFlow.
Code (1)
Tasks
Variational InferenceMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Wasserstein Variational Inference
This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes bo…
Bayesian InferenceVariational InferenceWasserstein Gradient Flow over Variational Parameter Space for Variational Inference
Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached…
Variational InferenceParticle-based Variational Inference with Generalized Wasserstein Gradient Flow
Particle-based variational inference methods (ParVIs) such as Stein variational gradient descent (SVGD) update the particles based on the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. How…
Stochastic variance-reduced Gaussian variational inference on the Bures-Wasserstein manifold
Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference…
Variational InferenceMarkov Chain Monte Carlo and Variational Inference: Bridging the Gap
Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore…
Bayesian InferenceVariational Inference