Emmanuel Bacry

Emmanuel Bacry, Martin Bompaire, Stéphane Gaïffas et al.

Tick is a statistical learning library for Python~3, with a particular emphasis on time-dependent models, such as point processes, and tools for generalized linear models and survival analysis. The core of the library is an optimization module providing model computational classes, solvers and proximal operators for regularization. tick relies on a C++ implementation and state-of-the-art optimization algorithms to provide very fast computations in a single node multi-core setting. Source code and documentation can be downloaded from https://github.com/X-DataInitiative/tick

Ruihua Ruan, Emmanuel Bacry, Jean-François Muzy

Thanks to the access to the labeled orders on the CAC40 data from Euronext, we are able to analyze agents' behaviors in the market based on their placed orders. In this study, we construct a self-supervised learning model using triplet loss to effectively learn the representation of agent market orders. By acquiring this learned representation, various downstream tasks become feasible. In this work, we utilize the K-means clustering algorithm on the learned representation vectors of agent orders to identify distinct behavior types within each cluster.

Daniel de Barros Soares, François Andrieux, Bastien Hell et al.

Estimating the amount of electricity that can be produced by rooftop photovoltaic systems is a time-consuming process that requires on-site measurements, a difficult task to achieve on a large scale. In this paper, we present an approach to estimate the solar potential of rooftops based on their location and architectural characteristics, as well as the amount of solar radiation they receive annually. Our technique uses computer vision to achieve semantic segmentation of roof sections and roof objects on the one hand, and a machine learning model based on structured building features to predict roof pitch on the other hand. We then compute the azimuth and maximum number of solar panels that can be installed on a rooftop with geometric approaches. Finally, we compute precise shading masks and combine them with solar irradiation data that enables us to estimate the yearly solar potential of a rooftop.

Ibrahim Merad, Yiyang Yu, Emmanuel Bacry et al.

Contrastive representation learning has been recently proved to be very efficient for self-supervised training. These methods have been successfully used to train encoders which perform comparably to supervised training on downstream classification tasks. A few works have started to build a theoretical framework around contrastive learning in which guarantees for its performance can be proven. We provide extensions of these results to training with multiple negative samples and for multiway classification. Furthermore, we provide convergence guarantees for the minimization of the contrastive training error with gradient descent of an overparametrized deep neural encoder, and provide some numerical experiments that complement our theoretical findings

Anastasiia Kabeshova, Yiyang Yu, Bertrand Lukacs et al.

This paper considers the problems of modeling and predicting a long-term and ``blurry'' relapse that occurs after a medical act, such as a surgery. The relapse is observed only indirectly, in a ``blurry'' fashion, through longitudinal prescriptions of drugs over a long period of time after the medical act. We introduce a new model, called ZiMM (Zero-inflated Mixture of Multinomial distributions) in order to capture long-term and blurry relapses. On top of it, we build an end-to-end deep-learning architecture called ZiMM Encoder-Decoder (ZiMM ED) that can learn from the complex, irregular, highly heterogeneous and sparse patterns of health events that are observed through a claims-only database. ZiMM ED is applied on a ``non-clinical'' claims database, that contains only timestamped reimbursement codes for drug purchases, medical procedures and hospital diagnoses, the only available clinical feature being the age of the patient. This setting is more challenging than a setting where bedside clinical signals are available. Our motivation for using such a non-clinical claims database is its exhaustivity population-wise, compared to clinical electronic health records coming from a single or a small set of hospitals. Indeed, we consider a dataset containing the claims of almost \emph{all French citizens} who had surgery for prostatic problems, with a history between 1.5 and 5 years. We consider a long-term (18 months) relapse (urination problems still occur despite surgery), which is blurry since it is observed only through the reimbursement of a specific set of drugs for urination problems. Our experiments show that ZiMM ED improves several baselines, including non-deep learning and deep-learning approaches, and that it allows working on such a dataset with minimal preprocessing work.

Martin Bompaire, Emmanuel Bacry, Stéphane Gaïffas

The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic first-order solvers based on the idea of variance reduction are available and combine both computational efficiency and sound theoretical guarantees (linear convergence rates). Such rates are obtained under both gradient-Lipschitz and strong convexity assumptions. Motivated by learning problems that do not meet the gradient-Lipschitz assumption, such as linear Poisson regression, we work under another smoothness assumption, and obtain a linear convergence rate for a shifted version of Stochastic Dual Coordinate Ascent (SDCA) that improves the current state-of-the-art. Our motivation for considering a solver working on the Fenchel-dual problem comes from the fact that such objectives include many linear constraints, that are easier to deal with in the dual. Our approach and theoretical findings are validated on several datasets, for Poisson regression and another objective coming from the negative log-likelihood of the Hawkes process, which is a family of models which proves extremely useful for the modeling of information propagation in social networks and causality inference.

Maryan Morel, Emmanuel Bacry, Stéphane Gaïffas et al.

With the increased availability of large databases of electronic health records (EHRs) comes the chance of enhancing health risks screening. Most post-marketing detections of adverse drug reaction (ADR) rely on physicians' spontaneous reports, leading to under reporting. To take up this challenge, we develop a scalable model to estimate the effect of multiple longitudinal features (drug exposures) on a rare longitudinal outcome. Our procedure is based on a conditional Poisson model also known as self-controlled case series (SCCS). We model the intensity of outcomes using a convolution between exposures and step functions, that are penalized using a combination of group-Lasso and total-variation. This approach does not require the specification of precise risk periods, and allows to study in the same model several exposures at the same time. We illustrate the fact that this approach improves the state-of-the-art for the estimation of the relative risks both on simulations and on a cohort of diabetic patients, extracted from the large French national health insurance database (SNIIRAM), a SQL database built around medical reimbursements of more than 65 million people. This work has been done in the context of a research partnership between Ecole Polytechnique and CNAMTS (in charge of SNIIRAM).

Massil Achab, Emmanuel Bacry, Stéphane Gaïffas et al.

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the third-order integrated cumulants of the process. We show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database.

Massil Achab, Agathe Guilloux, Stéphane Gaïffas et al.

We introduce a doubly stochastic proximal gradient algorithm for optimizing a finite average of smooth convex functions, whose gradients depend on numerically expensive expectations. Our main motivation is the acceleration of the optimization of the regularized Cox partial-likelihood (the core model used in survival analysis), but our algorithm can be used in different settings as well. The proposed algorithm is doubly stochastic in the sense that gradient steps are done using stochastic gradient descent (SGD) with variance reduction, where the inner expectations are approximated by a Monte-Carlo Markov-Chain (MCMC) algorithm. We derive conditions on the MCMC number of iterations guaranteeing convergence, and obtain a linear rate of convergence under strong convexity and a sublinear rate without this assumption. We illustrate the fact that our algorithm improves the state-of-the-art solver for regularized Cox partial-likelihood on several datasets from survival analysis.

Emmanuel Bacry, Stéphane Gaïffas, Jean-François Muzy

This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to the class of continuous time processes. Our analysis relies on a new supermartingale property of the trace exponential proved within the framework of stochastic calculus. We provide also several examples that illustrate the fact that our results allow us to recover easily several formerly obtained sharp bounds for discrete time matrix martingales.