Online Machine Learning in Montpellier, Theory & Practice Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures such as multivariate data, functional data, and random graphs. Despite their versatility, integrating depth measures into regression modeling for establishing prediction regions remains a largely underexplored area. To address this gap, we propose novel model-free uncertainty quantification algorithms based on conditional depth measures and the notion of conditional kernel mean embeddings. The new algorithms can be used to define prediction and tolerance regions when the predictors and responses are defined in separable Hilbert spaces. To enhance the practical utility of the algorithms, we also introduce a conformal prediction version, providing non-asymptotic guarantees for the derived prediction regions. Additionally, we establish both conditional and unconditional consistency results and fast convergence rates in some special homoscedastic cases. We evaluate the model's finite-sample performance in extensive simulation studies involving different functional data objects and probability distributions. Finally, we apply the approach to a digital health application related to physical activity, aiming to offer personalized recommendations to the U.S. population based on individuals' characteristics. Machine Learning in Montpellier, Theory & Practice

Room 02.022, Building 5, St Priest campus Machine Learning in Montpellier, Theory & Practice In federated learning, multiple agents collaboratively train a machine learning model without exchanging local data. To achieve this, each agent locally updates a global model, and the updated models are periodically aggregated by a central server. In this talk, I will first focus on federated linear stochastic approximation (FedLSA), with an emphasis on agent heterogeneity. I will derive upper bounds on the sample and communication complexity of FedLSA and present a method to reduce communication costs using control variates. Special attention will be given to the "linear speed-up" phenomenon, demonstrating that the sample complexity scales inversely with the number of agents in both methods. Finally, I will discuss possible extensions of these results to non-linear federated learning and provide first-order expansions of the bias in federated averaging. Machine Learning in Montpellier, Theory & Practice

Amphi JJ Moreau, Building 2, St Priest campus Machine Learning in Montpellier, Theory & Practice Given within the framework of the AI and Data Science Axis, LIRMM.,, Machine Learning in Montpellier, Theory & Practice

Room 02.022, Building 5, St Priest campus Machine Learning in Montpellier, Theory & Practice Personal data is being collected at an unprecedented scale by businesses and public organizations, driven by the progress of data science and machine learning. While such data can be turned into useful knowledge about the global population by computing aggregate statistics or training machine learning models, this can also lead to undesirable disclosure of personal information. We must therefore deal with two conflicting objectives: maximizing the utility of data while protecting the privacy of individuals whose data is used in the analysis. In this talk, I will present differential privacy (DP), a statistical definition of privacy which comes with rigorous guarantees as well as an algorithmic framework that allows the design of practical privacy-preserving algorithms. I will then discuss the application of DP to machine learning, and some related open questions. Machine Learning in Montpellier, Theory & Practice

Online Machine Learning in Montpellier, Theory & Practice I will mainly present the paper "Evaluating Probabilistic Classifiers: The Triptych" [ https://isdm.umontpellier.fr/doi.org/10.1016/j.ijforecast.2023.09.007 | https://isdm.umontpellier.fr/doi.org/10.1016/j.ijforecast.2023.09.007 ] that provides a trinity of evaluating plots for probability forecasts for binary events: Reliability diagrams, ROC curves and Murphy diagrams, which focus on the individual aspects of calibration, discrimination and overall predictive performance, respectively. Summary statistics for these properties are given by an associated score decomposition. I will furthermore present extensions of the underlying ideas such as statistical inference methods and extensions to point (e.g., mean or quantile) forecasts. Machine Learning in Montpellier, Theory & Practice