We present a novel methodology for causal inference based on an invariance principle. It exploits the advantage of heterogeneity in larger datasets, arising from different experimental conditions (i.e. an aspect of "Big Data"). Despite fundamental identifiability issues, the method comes with statistical confidence statements leading to more reliable results than alternative procedures based on graphical modeling. We also discuss applications in biology, in particular for large-scale gene knock-down experiments in yeast where computational and statistical methods have an interesting potential for prediction and prioritization of new experimental interventions.[-]

Inferring causal effects of a treatment or policy from observational data is central to many applications. However, state-of-the-art methods for causal inference suffer when covariates have missing values, which is ubiquitous in application.
Missing data greatly complicate causal analyses as they either require strong assumptions about the missing data generating mechanism or an adapted unconfoundedness hypothesis. In this talk, I will first provide a classification of existing methods according to the main underlying assumptions, which are based either on variants of the classical unconfoundedness assumption or relying on assumptions about the mechanism that generates the missing values. Then, I will present two recent contributions on this topic: (1) an extension of doubly robust estimators that allows handling of missing attributes, and (2) an approach to causal inference based on variational autoencoders adapted to incomplete data.
I will illustrate the topic an an observational medical database which has heterogeneous data and a multilevel structure to assess the impact of the administration of a treatment on survival.[-]

We consider the problem of estimating the mean vector of the multivariate complex normaldistribution with unknown covariance matrix under an invariant loss function when the samplesize is smaller than the dimension of the mean vector. Following the approach of Chételat and Wells (2012, Ann.Statist, p. 3137–3160), we show that a modification of Baranchik-tpye estimatorsbeats the MLE if it satisfies certain conditions. Based on this result, we propose the James-Stein-like shrinkage and its positive-part estimators.[-]

This work presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part, we calculate multivariate transformed tail dependence coefficients when the generator of the considered transformed copula exhibits some regular variation properties, and we investigate the behavior of these coefficients in cases that are close to tail independence. We obtain new results under specific conditions involving regularly varying hazard rates of components of the transformation. These results are also valid for non-transformed Archimedean copulas. In the second part we deal with a class of particular hyperbolic transformations. We show the utility of using transformed Archimedean copulas, as they permit to build Archimedean generators exhibiting any chosen couple of lower and upper tail dependence coefficients.[-]

In recent years rank aggregation has received significant attention from the machine learning community. The goal of such a problem is to combine the (partially revealed) preferences over objects of a large population into a single, relatively consistent ordering of those objects. However, in many cases, we might not want a single ranking and instead opt for individual rankings. We study a version of the problem known as collaborative ranking. In this problem we assume that individual users provide us with pairwise preferences (for example purchasing one item over another). From those preferences we wish to obtain rankings on items that the users have not had an opportunity to explore. The results here have a very interesting connection to the standard matrix completion problem. We provide a theoretical justification for a nuclear norm regularized optimization procedure, and provide high-dimensional scaling results that show how the error in estimating user preferences behaves as the number of observations increase.

rank aggregation - nuclear norm - rank centrality - convex optimization - regularized $M$-estimation - matrix completion - collaborative filtering[-]