Debiasing 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 bounds as ordinary variational evidence lower bounds (ELBO) applied to increasingly accurate variational distributions. In this work, we provide yet another perspective on the IWAE bounds. We interpret each IWAE bound as a biased estimator of the true marginal likelihood where for the bound defined on samples we show the bias to be of order O(1/K). In our theoretical analysis of the IWAE objective we derive asymptotic bias and variance expressions. Based on this analysis we develop jackknife variational inference (JVI), a family of bias-reduced estimators reducing the bias to for any given m < K while retaining computational efficiency. Finally, we demonstrate that JVI leads to improved evidence estimates in variational autoencoders. We also report first results on applying JVI to learning variational autoencoders. Our implementation is available at https://github.com/Microsoft/jackknife-variational-inference
 This paper provides an interesting analysis of the importance sampled estimate of the LL bound and proposes to use Jackknife to correct for the bias. The experiments show that the proposed method works for model evaluation and that computing the correction is archivable at a reasonable computational cost. It also contains an insightful analysis.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Debiasing 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 bounds as ordinary variational evidence lower bounds (ELBO) applied to increasingly accurate variational distributions. In this work, we provide yet another perspective on the IWAE bounds. We interpret each IWAE bound as a biased estimator of the true marginal likelihood where for the bound defined on samples we show the bias to be of order O(1/K). In our theoretical analysis of the IWAE objective we derive asymptotic bias and variance expressions. Based on this analysis we develop jackknife variational inference (JVI), a family of bias-reduced estimators reducing the bias to for any given m < K while retaining computational efficiency. Finally, we demonstrate that JVI leads to improved evidence estimates in variational autoencoders. We also report first results on applying JVI to learning variational autoencoders. Our implementation is available at https://github.com/Microsoft/jackknife-variational-inference
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<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper provides an interesting analysis of the importance sampled estimate of the LL bound and proposes to use Jackknife to correct for the bias. The experiments show that the proposed method works for model evaluation and that computing the correction is archivable at a reasonable computational cost. It also contains an insightful analysis.
assistant
 This paper provides an interesting analysis of the importance sampled estimate of the LL bound and proposes to use Jackknife to correct for the bias. The experiments show that the proposed method works for model evaluation and that computing the correction is archivable at a reasonable computational cost. It also contains an insightful analysis.