Participants: A. Gégout-Petit, S. Mézières, Y. Petot, P. Vallois

In the framework of the esca-illness of vines, we developed different spatial models and spatio-temporal models for different purposes: (1) study the distribution and the dynamics of esca vines in order to tackle the aggregation and the potential spread of the illness (2) propose a spatio-temporal model in order to capture the dynamics of cases and measure the effects of environmental covariates. For purpose (2), we developed an autologistic model (centered in a new way), estimators of the parameters, and showed their good properties, and proposed a way to choose between several neighborhood models. It is the object of preprint .

In the framework of chalara of ashand, through a collaboration with INRA researchers, we have proposed a mechanistic model of propagation whose parameters are estimated by bayesian estimation. It is the object of the communication .

In a collaboration with physicists from Nancy CHRU, we have worked about the interest to use the whole distribution of telomeres lengths until the mean that is usually used to characterise ageing of a cell. We have shown that the shape of the distribution can be seen as a individuals's signature. It is the object of the accepted paper .

We analyse the probabilistic features of the Choquet integral with respect to a capacity over a finite set where the entries are random variables. Despite the amount of studies, the question of uncertainty remains under-considered. Such a question is of first importance in many applications and uses.

In the multifactorial context of modelling for gliomas, we focused our attention on the acquisition of the tumor diameter from clinical-collected data . 3-D reconstruction via an equivalent sphere from multiple contouring of the tumor leads us to characterize its infiltrating phenotype (infiltration rate, direction of infiltration, evolution of morphology over time), current work. Our aim is to incorporate this new factor in the modeling already started (to appear in JBHI, beginning 2019).

A brain cartography obtained by sensorial simulations during awake surgery with the aid of clustering analysis is in revision.

Participants: R. Azaïs, F. Bouguet, A. Gégout-Petit, F. Greciet, B. Scherrer

Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications. Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. The issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, the book “Statistical Inference for Piecewise-deterministic Markov Processes” edited by Romain Azaïs and Florian Bouguet gather 7 chapters by different authors on the topic. The idea for this book stemmed from a workshop organized in Nancy in the 2016-17 winter. Two chapters have been co-authored by one or more BIGS members.

Multiple-step lookahead policies have demonstrated high empirical competence in Reinforcement Learning, via the use of Monte Carlo Tree Search or Model Predictive Control. In , multiple-step greedy policies and their use in vanilla Policy Iteration algorithms were proposed and analyzed. In , , we study multiple-step greedy algorithms in more practical setups: we describe and analyze a stochastic approximation variation and general sensitivity analyses to approximations. In , we describe a short study on an Anderson acceleration of the fixed point computation involved in Reinforcement Learning. These contributions resulted in one publication in ICML, in NeurIPS, and two in EWRL (the European Workshop on Reinforcement Learning).

Participants: A. Gégout-Petit, A. Gueudin, C. Karmann

In the purpose to deal with inference for network of zero-inflated variables, we have developped a new regression model. We consider the problem of variable selection when the response is ordinal, that is an ordered categorical variable. In particular, we are interested in selecting quantitative explanatory variables linked with the ordinal response variable and we want to determine which predictors are relevant. In this framework, we choose to use the polytomous ordinal logistic regression model using cumulative logits which generalizes the logistic regression. We then introduce the Lasso estimation of the regression coefficients using the Frank-Wolfe algorithm. To deal with the choice of the penalty parameter, we use the stability selection method and we develop a new method based on the knockoffs idea. This knockoffs method is general and suitable to any regression and besides, gives an order of importance of the covariates. Finally, we provide some experimental results to corroborate our method and we present an application of this regression method for zero-inflated network inference. This work is the object of a presentation in a conference and a preprint submitted in a journal .

Participants: E. Albuisson, R. Azaïs (Inria, Lyon), T. Bastogne, L. Batista, K. Duarte, S. Ferrigno, A. Gégout-Petit, P. Guyot, J.-M. Monnez, N. Sahki, S. Mézières

In the purpose to detect change of health state for lung-transplanted patient, we have begun to work on breakdowns in multivariate physiological signals. Based on the CUSUM statistics, we have used dynamical thresholds of detection . A more general talk about statistical learning and connected patient was given in a workshop "Evaluation des objets en santé connectée" .

We consider the analysis of cardiomyocyte signals (cardiac cells) for the cardiotoxicity assessment of new pharmaceutical compounds in preclinical assays. The experimental data are either impedance signals measuring the contractility of cardiomyocytes , , field potential signals measuring their functionality or fluorescence signals measuring the activity of some ion channels such as calcium pumps (Ca2+). At this preclinical level, our main contribution is the estimation of important characteristics such the field potential duration  or the identification of cardiotoxic events such as the early-afterdepolarization.We have also developed new methods for the analysis of electrocardiograms at patient level and more precisely the estimation of parameters such as the RR and QT intervals in long and noisy signals provided by wearable sensors , , , , . We also study the efficacy of a new biomarker in radiotherapy. The objective is to compute a score able to predict risk of radiosensitivity for patients in radiotherapy , .We are also developing a new method to characterize the potential interactions between nanoparticles and biological compounds of complex media such as blood. This new method aims at predicting risks on the biodistribution and toxicity of the nanoparticles , .

In , we present a methodology for constructing a short-term event risk score from an ensemble predictor using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selections of variables into the construction of predictors. We establish a property of linear discriminant analysis for mixed data and define an event risk measure by an odds-ratio. This methodology is applied to heart failure patients on whom biological, clinical and medical history variables were measured and the results obtained from our data are detailed.

The study addresses the problem of sequential least square multidimensional linear regression, particularly in the case of a data stream, using a stochastic approximation process. To avoid the phenomenon of numerical explosion which can be encountered and to reduce the computing time in order to take into account a maximum of arriving data, we propose using a process with online standardized data instead of raw data and the use of several observations per step or all observations until the current step. Herein, we define and study the almost sure convergence of three processes with online standardized data: a classical process with a variable step-size and use of a varying number of observations per step, an averaged process with a constant step-size and use of a varying number of observations per step, and a process with a variable or constant step-size and use of all observations until the current step. Their convergence is obtained under more general assumptions than classical ones. These processes are compared to classical processes on 11 datasets for a fixed total number of observations used and thereafter for a fixed processing time. Analyses indicate that the third-defined process typically yields the best results.

Many articles were devoted to the problem of estimating recursively the eigenvectors and eigenvalues in decreasing order of the expectation of a random matrix using an i.i.d. sample of it. In , we make the following contributions. The convergence of a normed process is proved under more general assumptions: the random matrices are not supposed i.i.d. and a new data mini-batch or all data until the current step are taken into account at each step without storing them; three types of processes are studied; this is applied to online principal component analysis of a data stream, assuming that data are realizations of a random vector $Z$ whose expectation is unknown and must be estimated online, as well as possibly the metrics used when it depends on unknown characteristics of $Z$.

Let $Y=m\left(X\right)+\sigma \left(X\right)\epsilon$ be a regression model, where $m(·)$ is the regression function, ${\sigma }^2(·)$ the variance function and $\epsilon$ the random error term. Methods to assess how well a model fits a set of observations fall under the banner of goodness-of-fit tests. Many tests have been developed to assess the different assumptions for this kind of model. Most of them are “directional” in that they detect departures from mainly a given assumption of the model. Other tests are “global” in that they assess whether a model fits a data set on all its assumptions. We focus on the task of choosing the structural part $m(·)$. It gets most attention because it contains easily interpretable information about the relationship between $X$ and $Y$. To valid the form of the regression function, we consider three nonparametric tests based on a generalization of the Cramér-von Mises statistic. The first two are directional tests, while the third is a global test. To perform these goodness-of-fit tests based on a generalization of the Cramér-von Mises statistic, we have used Wild bootstrap methods and we also proposed a method to choose the bandwidth parameter used in nonparametric estimations. Then, we have developed cvmgof R package (being submitted), an easy-to-use tool for many users. The use of the package is illustrated using simulations to compare the three implemented tests .

In epidemiology, we are working with clinicians to study fetal development in the last two trimesters of pregnancy. We have data from the "Service de foetopathologie et de placentologie" of the "Maternité Régionale Universitaire" (CHU Nancy) and from the EDEN cohort (INSERM). We propose to use non parametric methods of estimation to obtain reference curves of fetus and child growth. In addition, we want to develop a test, based on Z-scores, to detect any slope breaks in the fetal development curves (work in progress).