The introduction of machine learning (ML) techniques to the field of survival analysis has increased the flexibility of modeling approaches, and ML based models have become state-of-the-art. These models optimize their own cost functions, and their performance is often evaluated using the concordance index (C-index). From a statistical learning perspective, it is therefore an important problem to analyze the relationship between the optimizers of the C-index and those of the ML cost functions. We address this issue by providing C-index Fisher-consistency results and excess risk bounds for several of the commonly used cost functions in survival analysis. We identify conditions under which they are consistent, under the form of three nested families of survival models. We also study the general case where no model assumption is made and present a new, off-the-shelf method that is shown to be consistent with the C-index, although computationally expensive at inference. Finally, we perform limited numerical experiments with simulated data to illustrate our theoretical findings.

The Expectation Maximization (EM) algorithm is the default algorithm for inference in latent variable models. As in any other field of machine learning, applications of latent variable models to very large datasets make the use of advanced parallel and distributed architecture mandatory. This paper introduces FedEM, which is the first extension of the EM algorithm to the federated learning context. FedEM is a new communication efficient method, which handles partial participation of local devices, and is robust to heterogeneous distribution of the datasets. To alleviate the communication bottleneck, FedEM compresses appropriately defined complete data sufficient statistics. We also develop and analyze an extension of FedEM to further incorporate a variance reduction scheme. In all cases, we derive finite-time complexity bounds for smooth non-convex problems. Numerical results are presented to support our theoretical findings, as well as an application to federated missing values imputation for biodiversity monitoring.

Many applications of machine learning involve the analysis of large data frames -- matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples -- with missing values. Low-rank models, as studied by Udell et al. (2016), are popular in this framework for tasks such as visualization, clustering and missing value imputation. Yet, available methods with statistical guarantees and efficient optimization do not allow explicit modeling of main additive effects such as row and column, or covariate effects. In this paper, we introduce a low-rank interaction and sparse additive effects (LORIS) model which combines matrix regression on a dictionary and low-rank design, to estimate main effects and interactions simultaneously. We provide statistical guarantees in the form of upper bounds on the estimation error of both components. Then, we introduce a mixed coordinate gradient descent (MCGD) method which provably converges sub-linearly to an optimal solution and is computationally efficient for large scale data sets. We show on simulated and survey data that the method has a clear advantage over current practices.