RMSE Time (seconds) ours (20%) ours (80%) MICE (20%) MICE (80%) MC (20%) MC (80%) ours (learning) ours (prediction) MICE MC Abalone(1e 0) 2.72. 04 2.99. 02 2.71. 07 4.50. 09 2.80

We thank the reviewers for their valuable feedback. We appreciate they recognize that the paper is " well-written " and " clear " (R#2, R#3, R#4, R#5), whose technical contribution " quality is solid " (R#2), " very good " (R#1, R#5) and " non-trivial " (R#3) while it considers " an important problem in ML " (R#3, R#4) which can " be of interest to many We hope to address all questions and concerns raised in the following. We disagree with the reviewer. We are actively working on applying it to the other application scenarios. E.g., sums (marginals) require only decomposability and smoothness, with the addition of determinism We agree that computations are simple, i.e., elegant, once the Note that our contribution is more theoretical than empirical.