In this paper, we study the problem of correcting for distribution shift using mixture search.

It is a truth universally acknowledged that an observed association without known mechanism must be in want of a causal estimate. However, Causal estimates from observational data will be biased in the presence of'unobserved confounding'. Nevertheless, we might hope that the influence of unobserved confounders is weak relative to a'large' estimated effect. The purpose of this paper is to develop Austen plots, a sensitivity analysis tool to aid such judgments by making it easier to reason about potential bias induced by unobserved confounding. We formalize confounding strength in terms of how strongly the unobserved confounding influences treatment assignment and outcome. For a target level of bias, an Austen plot shows the minimum values of treatment and outcome influence required to induce that level of bias. Austen plots generalize the classic sensitivity analysis approach of Imbens [Imb03]. Critically, Austen plots allow any approach for modeling the observed data. We illustrate the tool by assessing biases for several real causal inference problems, using a variety of machine learning approaches for the initial data analysis.

We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation.

We thank the reviewers for their comments. We then address reviewer's comments individually (due to space limits please zoom in the tiny figures). For [18] we used Alg. 2 We thank the reviewer for the additional reference, which we will add to the paper. Gradient Descent) applied in parallel to multiple starting points. We thank R2 for the reference "Entropic regularization of continuous optimal transport problems".

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper extends the stochastic gradient langevin dynamics by using the Reimannian structure and applies it into probability simplex. The idea appears to be quite interesting. But there are several confusing parts that I don't quite get. Maybe the authors can elaborate those a bit.

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

We consider the problem of fitting variational posterior approximations using stochastic optimization methods.

We consider the problem of fitting variational posterior approximations using stochastic optimization methods.