SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models
The standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. If parameterized by an encoder-decoder architecture, the parameters of the encoder can be optimized to minimize its variance of this estimator. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost. This estimator also allows use of latent variable models for tasks where unbiased estimators, rather than marginal likelihood lower bounds, are preferred, such as minimizing reverse KL divergences and estimating score functions.
The authors consider the unbiased estimation of log marginal likelihood (evidence) after integration of latent variable. On top of the importance-weighted autoencoder (IWAE), which is only guaranteed to be asymptotically unbiased, the authors propose to use Russian Roulette estimator (RRE) to compensate the bias caused by the finite summation. The proposed method is interesting and can be applied in many other estimators with similar properties as Eq. (6). Bias compensation using RRE is interesting, but it seems there must be many literatures that took advantage of using RRE to improve estimators. The authors have to be thorough in presenting previous research and explaining the authors’ contribution that is distinguished from those. The authors showed synthetic and real application of the estimator, but one concern is the variance. Unbiasedness with finite samples often fails because of the variance, and regularization is often useful rather than correcting bias---If unbiasedness in important, regularization definitely breaks the unbiasedness---. The only discussion about variance is a few lines in page 3 after Eq. (7), but it is unclear how the variance problem is mitigated or why the problem does not suffer high variance. In general, this paper is well-written and dealing with important problem with interesting method. Several analysis for understanding the advantages of using the proposed method is insufficient.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models
The standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. If parameterized by an encoder-decoder architecture, the parameters of the encoder can be optimized to minimize its variance of this estimator. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost. This estimator also allows use of latent variable models for tasks where unbiased estimators, rather than marginal likelihood lower bounds, are preferred, such as minimizing reverse KL divergences and estimating score functions.
user
<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>



The authors consider the unbiased estimation of log marginal likelihood (evidence) after integration of latent variable. On top of the importance-weighted autoencoder (IWAE), which is only guaranteed to be asymptotically unbiased, the authors propose to use Russian Roulette estimator (RRE) to compensate the bias caused by the finite summation. The proposed method is interesting and can be applied in many other estimators with similar properties as Eq. (6). Bias compensation using RRE is interesting, but it seems there must be many literatures that took advantage of using RRE to improve estimators. The authors have to be thorough in presenting previous research and explaining the authors’ contribution that is distinguished from those. The authors showed synthetic and real application of the estimator, but one concern is the variance. Unbiasedness with finite samples often fails because of the variance, and regularization is often useful rather than correcting bias---If unbiasedness in important, regularization definitely breaks the unbiasedness---. The only discussion about variance is a few lines in page 3 after Eq. (7), but it is unclear how the variance problem is mitigated or why the problem does not suffer high variance. In general, this paper is well-written and dealing with important problem with interesting method. Several analysis for understanding the advantages of using the proposed method is insufficient.
assistant
The authors consider the unbiased estimation of log marginal likelihood (evidence) after integration of latent variable. On top of the importance-weighted autoencoder (IWAE), which is only guaranteed to be asymptotically unbiased, the authors propose to use Russian Roulette estimator (RRE) to compensate the bias caused by the finite summation. The proposed method is interesting and can be applied in many other estimators with similar properties as Eq. (6). Bias compensation using RRE is interesting, but it seems there must be many literatures that took advantage of using RRE to improve estimators. The authors have to be thorough in presenting previous research and explaining the authors’ contribution that is distinguished from those. The authors showed synthetic and real application of the estimator, but one concern is the variance. Unbiasedness with finite samples often fails because of the variance, and regularization is often useful rather than correcting bias---If unbiasedness in important, regularization definitely breaks the unbiasedness---. The only discussion about variance is a few lines in page 3 after Eq. (7), but it is unclear how the variance problem is mitigated or why the problem does not suffer high variance. In general, this paper is well-written and dealing with important problem with interesting method. Several analysis for understanding the advantages of using the proposed method is insufficient.