**A**t ICML last year, Ciwan Ceylan and Michael Gutmann presented a new version of noise constrative estimation to deal with intractable constants. While noise contrastive estimation relies upon a second independent sample to contrast with the observed sample, this approach uses instead a perturbed or noisy version of the original sample, for instance a Normal generation centred at the original datapoint. And eliminates the annoying constant by breaking the (original and noisy) samples into two groups. The probability to belong to one group or the other then does not depend on the constant, which is a very effective trick. And can be optimised with respect to the parameters of the model of interest. Recovering the score matching function of Hyvärinen (2005). While this is in line with earlier papers by Gutmann and Hyvärinen, this line of reasoning (starting with Charlie Geyer’s logistic regression) never ceases to amaze me!

## Archive for ICML 2018

## conditional noise contrastive estimation

Posted in Books, pictures, University life with tags Charlie Geyer, conference, ICML 2018, intractable constant, logistic regression, machine learning, noise contrasting estimation, Stockholm, Sweden on August 13, 2019 by xi'an## did variational Bayes work?

Posted in Books, Statistics with tags approximate Bayesian inference, asymptotic Bayesian methods, ICML 2018, importance sampling, misspecified model, Pareto distribution, Pareto smoothed importance sampling, posterior predictive, variational Bayes methods, what you get is what you see on May 2, 2019 by xi'an**A**n interesting ICML 2018 paper by Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman I missed last summer on [the fairly important issue of] assessing the quality or lack thereof of a variational Bayes approximation. In the sense of being near enough from the true posterior. The criterion that they propose in this paper relates to the Pareto smoothed importance sampling technique discussed in an earlier post and which I remember discussing with Andrew when he visited CREST a few years ago. The truncation of the importance weights of prior x likelihood / VB approximation avoids infinite variance issues but induces an unknown amount of bias. The resulting diagnostic is based on the estimation of the Pareto order k. If the true value of k is less than ½, the variance of the associated Pareto distribution is finite. The paper suggests to conclude at the worth of the variational approximation when the estimate of k is less than 0.7, based on the empirical assessment of the earlier paper. The paper also contains a remark on the poor performances of the generalisation of this method to marginal settings, that is, when the importance weight is the ratio of the true and variational marginals for a sub-vector of interest. I find the counter-performances somewhat worrying in that Rao-Blackwellisation arguments make me prefer marginal ratios to joint ratios. It may however be due to a poor approximation of the marginal ratio that reflects on the approximation and not on the ratio itself. A second proposal in the paper focus on solely the point estimate returned by the variational Bayes approximation. Testing that the posterior predictive is well-calibrated. This is less appealing, especially when the authors point out the “dissadvantage is that this diagnostic does not cover the case where the observed data is not well represented by the model.” In other words, misspecified situations. This potential misspecification could presumably be tested by comparing the Pareto fit based on the actual data with a Pareto fit based on simulated data. Among other deficiencies, they point that this is “a local diagnostic that will not detect unseen modes”. In other words, *what you get is what you see*.