# Perturbative Black Box Variational Inference

arXiv: https://arxiv.org/abs/1709.07433 · HTML: https://mlsanity.com/paper/1709.07433/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2017.

## Built on by (most cited first, 8 of 8)

- [Challenges and Opportunities in High-dimensional Variational Inference](https://mlsanity.com/paper/2103.01085/) (2021)
- [Mixture weights optimisation for Alpha-Divergence Variational Inference](https://mlsanity.com/paper/2106.05114/) (2021)
- [Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients](https://mlsanity.com/paper/2206.06295/) (2022)
- [Fast Feature Selection with Fairness Constraints](https://mlsanity.com/paper/2202.13718/) (2022)
- [Deterministic training of generative autoencoders using invertible layers](https://mlsanity.com/paper/2205.09546/) (2022)
- [Variational Inference with Holder Bounds](https://mlsanity.com/paper/2111.02947/) (2021)
- [Balancing Molecular Information and Empirical Data in the Prediction of Physico-Chemical Properties](https://mlsanity.com/paper/2406.08075/) (2024)
- [Differentiable Annealed Importance Sampling Minimizes The Symmetrized Kullback-Leibler Divergence Between Initial and Target Distribution](https://mlsanity.com/paper/2405.14840/) (2024)

## Abstract (arXiv)

Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased importance sampling. The choice of divergence determines a bias-variance trade-off between the tightness of a bound on the marginal likelihood (low bias) and the variance of its gradient estimators. Drawing on variational perturbation theory of statistical physics, we use these insights to construct a family of new variational bounds. Enumerated by an odd integer order K, this family captures the standard KL bound for K=1, and converges to the exact marginal likelihood as K→∞. Compared to alpha-divergences, our reparameterization gradients have a lower variance. We show in experiments on Gaussian Processes and Variational Autoencoders that the new bounds are more mass covering, and that the resulting posterior covariances are closer to the true posterior and lead to higher likelihoods on held-out data.