NeurIPS 2020

Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimization

Review 1

Summary and Contributions: The authors study the empirical advantage from recent improvements in black-box VI on probabilistic models from the Stan model library. They specifically consider the effect of step-size search, the sticking the landing (STL) gradient estimator, using importance weighting in the training objective and/or at test time, and the use of RealNVP flows as a more flexible approximating posterior. Combining these significantly outperforms naive ADVI; most techniques appear to be individually helpful, except for importance-weighted training, which gives inconsistent results.

Strengths: Stipulating that the idea of using (and combining) these techniques was likely 'obvious' to anyone working in the field---there is no novel theoretical ground here---the empirical analysis in this paper is careful, convincing, and quite valuable. It considers the most prominent techniques recently proposed for black-box VI, and gives clear evidence of their value (or lack thereof) on a representative set of real-world inference tasks. This should provide developers of probabilistic programming systems with a clarified roadmap, as well as providing inference researchers with a modern set of baselines.

Weaknesses: Any empirical comparison is going to have the flaw of being insufficiently exhaustive, and this one is no exception. For example: - ADVI as implemented in Stan encompasses both full-covariance and diagonal Gaussian surrogates, but this paper evaluates only one of those, and it wasn't even clear which one until quite far in (line 297). This should be clarified earlier. Ideally it would be nice to see the relative performance of both Gaussian baselines (and perhaps other commonly-suggested schemes like a diagonal + low rank covariance). - I've seen IAF-style flows more commonly than RealNVP the past few years. Was RealNVP chosen because it supports sticking-the-landing? It would be useful to see a side-by-side comparison against a similar-size IAF without sticking-the-landing. - A simple method not included (maybe because it's so simple that no one has published on it for VI recently) is Polyak-Ruppert averaging, i.e., averaging the variational parameters over the final steps of stochastic optimization. One might hypothesize that this could yield some of the same benefits as the sticking the landing estimator (the average of noisy optimization steps is much less noisy than any individual step) while being more general and easier to implement; it'd be interesting to see if that's the case. A lot of care was put into evaluating importance-weighted objectives on a fair computational playing field. One might also expect there to be differences in time needed to train a Gaussian (diagonal or full-covariance) versus a normalizing flow, but I didn't see this discussed at all. How did the flow training times compare? Was there a time<->quality tradeoff in the capacity of the flow? Since a full-covariance Gaussian has O(n^2) parameters, at some problem size you'd expect a flow with constant-size layers to be faster than the Gaussian---was this encountered? It's not obvious that the ELBO makes sense as the sole objective to report; at least in principle a method could succeed in improving the ELBO while actually making predictions worse. Was there any analysis of how the ELBO correlates with other metrics of interest; for example, accuracy of estimated posterior moments, or predictive likelihood of held-out data?

Correctness: Subject to the points above, I thought the techniques chosen and the experiments conducted were reasonable.

Clarity: The paper is well written and easy to follow. nits: abstract line 9-10: "for which there are no clear guidance" should probably be "for which there is no clear guidance" line 333: "performs provides"

Relation to Prior Work: The entire paper is a discussion of previous contributions. (so, yes).

Reproducibility: Yes

Additional Feedback:

Review 2

Summary and Contributions: This work makes the necessary and meticulous exercise of exploring and optimizing for the best set of algorithmic components to use for black-box variational inference. The goal is for the practitioner not to have to tinker with inference details. --- UPDATE: Thank you for the rebuttal. I do not wish to change my evaluation. I recommend this paper for acceptance.

Strengths: The main strength of this work is its careful and thorough study of algorithmic components to improve off-the-shelf black-box VI. The final method combines importance sampling, normalizing flows, a robust step-size scheme and the STL gradient estimator to improve performance by one nat or more on a least 60% of the benchmark models when compared to ADVI. The study proceeds incrementally, adding components one by one, hence making it easy to assess the marginal benefits of each component in combination to the previous others. While this work does not contribute any new algorithmic component by itself, I find it important and critical that some in our community take a step back and evaluate how recent developments ought to be best combined in order to be the most helpful for the scientists using the tools we develop. This exercise is far from being trivial to carry out properly -- yet this study follows a strict methodology and successfully identifies several concrete recommendations that lead to significant improvements on average.

Weaknesses: While visualizing and reporting results across 30 benchmarks and multiple variants of a set of algorithmic components is challenging, I would have appreciated if the analysis had come with an assessment of the variability of the performance improvements.

Correctness: Yes. The methodology appears to be correct, although the supplementary materials are full of additional details which I have not checked.

Clarity: Yes, the paper is clearly written and easy to follow for someone familiar with the components that are evaluated.

Relation to Prior Work: Yes.

Reproducibility: Yes

Additional Feedback:

Review 3

Summary and Contributions: The paper studies the best practice of using ADVI with some recent advances in related fields. Specifically, the paper examines 1) the way to search step size, 2) the choice of gradient estimators, 3) variational parameter initialisations, 4) different lower bounds of log-likelihood and 5) replacing Gaussian by normalising flows (NFs) as the variational posterior. The paper performs well-design experiments on 30 Stan models to study each option and the effect of combing them. The paper then concludes the best-practice: using NFs via a regular ELBO under the STL gradient estimator (training) and using importance sampling during inference.

Strengths: The goal of the paper is simple but useful. It answers a few related questions: what's the best practice of using ADVI with the recent new techniques related, how much gain can we get by applying these techniques (together) and how reliable are they? Those are real questions users would meet and would be genuinely nice to have a guide to pave the way of wider use of all these techniques as well as ADVI. How the paper tackles the reliability part by considering a good collection of models is good and the and visualisations are informative. Although there is no novelty of the methods themselves, I think the paper would be useful for a wide range of practitioners.

Weaknesses: No novelty of the methodology. The paper misses a few related works [1,2] and misses a conclusion/discussion section. [1] Structured Conditional Continuous Normalizing Flows for Efficient Amortized Inference in Graphical Models, AISTATS 2020 ( [2] Bijectors.jl: Flexible transformations for probability distributions, AABI 2019 ( [1] is on how to take use of the structure of NFs for a better variational approximation. [2] has a similar but much simple example on the same idea in the context of ADVI.

Correctness: The methodology of conducting the experiments looks correctly to me and the final conclusion makes sense.

Clarity: The paper is very well-written and easy to follow. Although as I mentioned, there seems no conclusion/discussion section.

Relation to Prior Work: I mentioned a few papers the author(s) fail(s) to link on the topic of applying NFs to ADVI, or automated VI (or amortised inference). There might be some more in the field as I'm not closely following it. Despite of this fact, the focus of the paper is quite difference from those I pointed out.

Reproducibility: Yes

Additional Feedback: The Broader Impact section is too vague. One potential concern of so-called "best practice" is that we would also like to know when they might fail so that we can avoid applying them. As from the results, there are still a small fraction of models which has a degraded performance after applying all the techniques - can we take a careful look on them - are they in a special model family? Ideally, questions like this should be addressed in the main paper, as claiming something "the default" would affect a lot of real users. ######### # Update # ######### The author feedback looks good to me and I keep my original score.