The Cold Posterior Effect (CPE) is a phenomenon in Bayesian Deep Learning (BDL), where tempering the posterior to a cold temperature often improves the predictive performance of the posterior predictive distribution (PPD). Although the term `CPE' suggests colder temperatures are inherently better, the BDL community increasingly recognizes that this is not always the case. Despite this, there remains no systematic method for finding the optimal temperature beyond grid search. In this work, we propose a data-driven approach to select the temperature that maximizes test log-predictive density, treating the temperature as a model parameter and estimating it directly from the data. We empirically demonstrate that our method performs comparably to grid search, at a fraction of the cost, across both regression and classification tasks. Finally, we highlight the differing perspectives on CPE between the BDL and Generalized Bayes communities: while the former primarily focuses on predictive performance of the PPD, the latter emphasizes calibrated uncertainty and robustness to model misspecification; these distinct objectives lead to different temperature preferences.

I am happy with all of your responses, though slightly confused over Q2 (rev2). One can't draw samples from improper priors in the first place, and other techniques (such as Rodrigues et al) won't save you there. You simply need to draw your samples from a distribution that is not the prior. I am still positively inclined towards this paper, and following the response and comparison to EP-ABC I will increase my score to 7 (from 6). Of course when the prior is improper or merely diffuse with respect to the posterior this will be impossible or at best highly inefficient.

The presented method learns a structure of a deep ANN by first learning a BN and then constructing the ANN from this BN. The authors state that they "propose a new interpretation for depth and inter-layer connectivity in deep neural networks". Neurons in deep layers represent low-order conditional independencies (ie small conditioning set) and those in'early' (non-deep) layers represent high-order CI relationships. These are all CI relations in the "X" ie the input vector of (observed) random variables. Perhaps I am missing something here but I could not find an argument as to why this is a principled way to build deep ANNs with good performance.

It seems that this could perhaps be expressed more concisely using the output of the discriminator (and the true label) as functions, rather than introducing new random variables. Further, it seems the algorithm is described in sufficient detail to be re-implemented. The experiments are missing some detail to be reproduced or interpreted (e.g.

This paper studies the problem of computing probability bounds, more specifically bounds over probability of atoms of the joint space and conditional probabilities of the class, under the assumption that only some pairwise marginal as well as some univariate marginal values are known. The idea is that such marginals may be easier to obtain than fully specified probabilities, and that cautious inferences can then be used to produce predictions. It is shown that when the marginals follow a tree structure (results are extended to a few other structures), then the problem can actually be solved in closed, analytical form, relating it to cover set and maximum flow problems. Some experiments performed on neural networks show that this simple method is actually competitive with other more complex approaches (Ladder, VAE), while outperforming methods of comparable complexity. The paper is elegantly written, with quite understandable and significant results.

Update: I downgrade my review to 5. The main concern is 1) Some more extensive simulations will make the results more convincing, as the numerical experiment is the only way to assess the performance of the proposed priors. It might take a major revision to reflect such comprehensive comparisons. With that being said, I believe the paper does contain interesting results that are novel and useful to the community. In particular, the theoretical results seem sound, and the paper is fairly readable. But I think there is also room for improvement.

This paper proposes a Bayesian model for adversarial learning problem. Empirical studies on Fashion-MINST and traffic sign recognition show that the proposed methods is slightly better than other adversarial learning baselines. Below I list my concerns about the paper: For modeling, 1. This paper ignore a highly relevant work'Bayesian GAN' [1]. The non-cooperative game between'data generator' and'learner' established in this paper is almost the same as the vanilla GAN.

The manuscript "Learning Concave Conditional Likelihood Models for Improved Analysis of Tandem Mass Spectra" extends a dynamic Bayesian network approach called DIDEA by introducing a new class of emission distributions. The conditional log-likelihood of those functions remains concave leading to an efficient global optimization method for parameter estimation. This is in stark contrast to the previous variant, for which the best parameter had to be found by grid search. In comparison to other state-of-the-art methods, the new approach outperforms the other methods, while being faster at the same time. Quality Overall the quality of the manuscript is good.

I preface this by saying that I have reviewed this paper once for NIPS 2016, and re-read it. It seems the paper has no essential changes, so my opinion is largely the same. The paper considers the problem of learning the parameters of a Bayes net with known structure, given samples from it with potentially adversarial noise. The main goal is to get bounds on the samples that are independent of dimension. The main requirements on the Bayes net parameters are reasonable: the probability of any configuration of the parents is reasonable and the conditional probabilities on any edge are bounded away from 0 and 1.

This paper puts forward the idea that we should in certain cases regularize the generative model in VAEs in order to improve generalization properties. Since VAEs perform maximum likelihood estimation, they can in principle exhibit the same overfitting problems as any other maximum likelihood model. This paper argues that we can regularize the generative model by increasing the smoothness of the inference model. The authors consider the Denoising VAE (DVAE) as a means of achieving such regularization. In the special case where the encoder is an exponential family, they show that the optimum natural parameters for any input data can be expressed as a weighted average over the optimum parameters for the data in the training set.