Variational Inference with Holder Bounds
The recent introduction of thermodynamic integration techniques has provided a new framework for understanding and improving variational inference (VI). In this work, we present a careful analysis of the thermodynamic variational objective (TVO), bridging the gap between existing variational objectives and shedding new insights to advance the field. In particular, we elucidate how the TVO naturally connects the three key variational schemes, namely the importance-weighted VI, Renyi-VI, and MCMC-VI, which subsumes most VI objectives employed in practice. To explain the performance gap between theory and practice, we reveal how the pathological geometry of thermodynamic curves negatively affects TVO. By generalizing the integration path from the geometric mean to the weighted Holder mean, we extend the theory of TVO and identify new opportunities for improving VI. This motivates our new VI objectives, named the Holder bounds, which flatten the thermodynamic curves and promise to achieve a one-step approximation of the exact marginal log-likelihood. A comprehensive discussion on the choices of numerical estimators is provided. We present strong empirical evidence on both synthetic and real-world datasets to support our claims.
Code (0)
등록된 구현이 없습니다.
Tasks
Variational InferenceMethods 이 논문이 사용한 방법론
Similar 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 IntegrationValidated Variational Inference via Practical Posterior Error Bounds
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods …
Bayesian InferenceVariational InferenceLearning with Importance Weighted Variational Inference: Asymptotics for Gradient Estimators of the VR-IWAE Bound
Several popular variational bounds involving importance weighting ideas have been proposed to generalize and improve on the Evidence Lower BOund (ELBO) in the context of maximum likelihood optimization, such as the Impor…
Variational InferenceDebiasing Evidence Approximations: On Importance-weighted Autoencoders and Jackknife Variational Inference
The importance-weighted autoencoder (IWAE) approach of Burda et al. defines a sequence of increasingly tighter bounds on the marginal likelihood of latent variable models. Recently, Cremer et al. reinterpreted the IWAE b…
Computational EfficiencyVariational InferenceFew Shot Activity Recognition Using Variational Inference
There has been a remarkable progress in learning a model which could recognise novel classes with only a few labeled examples in the last few years. Few-shot learning (FSL) for action recognition is a challenging task of…
Action RecognitionActivity RecognitionFew-Shot LearningHuman Activity Recognition+1