Bayesian inference is desirable but extremely challenging.

Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Near-optimal density estimation in near-linear time using variable-width histograms Given a univariate distribution with support on the unit interval, this paper develops a method for estimating the density of the distribution via a histogram. The histogram has the following features: the bins are data-dependent, the bins are determined efficiently (near linear time), the number of bins k is specified by the user, and the estimator satisfies a probably approximately correct type performance guarantee. The paper is entirely theoretical. Pros: The writing is clear.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

The EBP method is indeed capable of learning binary NNs in a fairly effective way. The catch is though that using binary models directly (i.e. the MAP solution) at test time directly does not seem to lead to competitive results (see column "Binary EBP-D" in Table 1: the error rate is >= doubled for 4 datasets out of 7). What seems to work well is Bayesian model averaging with the binary model ("Binary EBP-P") but this is again a'continuous' computation which is at least as expensive as the computation with a normal NN. At the very least the authors need to clarify this point, currently, as the binary version is the key motivation of this research (see the first paragraph of the paper).

However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change.