Faïcel Chamroukhi

Abdelmouaiz Tebjou, Goran Frehse, Faïcel Chamroukhi

An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems even if the system dynamics are known and given by a system of ordinary differential equations with known coefficients. In practice, parameters are often unknown and mathematical models difficult to obtain. Data-based approaches are promised to avoid these difficulties by estimating the reach set based on a sample of states. If a model is available, this training set can be obtained through numerical simulation. In the absence of a model, real-life observations can be used instead. A recently proposed approach for data-based reach set approximation uses Christoffel functions to approximate the reach set. Under certain assumptions, the approximation is guaranteed to converge to the true solution. In this paper, we improve upon these results by notably improving the sample efficiency and relaxing some of the assumptions by exploiting statistical guarantees from conformal prediction with training and calibration sets. In addition, we exploit an incremental way to compute the Christoffel function to avoid the calibration set while maintaining the statistical convergence guarantees. Furthermore, our approach is robust to outliers in the training and calibration set.

Thien Pham, Angelo Furno, Faïcel Chamroukhi et al.

This paper presents an advanced Federated Learning (FL) framework for forecasting complex spatiotemporal data, improving upon recent state-of-the-art models. In the proposed approach, the original Gated Recurrent Unit (GRU) module within previous Dynamic Spatial--Temporal Graph Convolutional Recurrent Network (DSTGCRN) modeling is first replaced with a Long Short-Term Memory (LSTM) network, enabling the resulting model to more effectively capture long-term dependencies inherent to time series data. The resulting architecture significantly improves the model's capacity to handle complex temporal patterns in diverse forecasting applications. Furthermore, the proposed FL framework integrates a novel Client-Side Validation (CSV) mechanism, introducing a critical validation step at the client level before incorporating aggregated parameters from the central server into local models, ensuring only the most effective updates are retained and improving both the robustness and accuracy of the forecasting model across clients. The efficiency of our approach is demonstrated through extensive experiments on real-world applications, including public datasets for multimodal transport demand forecasting and private datasets for Origin-Destination (OD) matrix forecasting in urban areas. The results demonstrate substantial improvements over conventional methods, highlighting the framework's ability to capture complex spatiotemporal dependencies while preserving data privacy. This work not only provides a scalable and privacy-preserving solution for real-time, region-specific forecasting and management but also underscores the potential of leveraging distributed data sources in a FL context. We provide our algorithms as open-source on GitHub

Faïcel Chamroukhi, Nhat Thien Pham

In modern machine learning problems we deal with datasets that are either distributed by nature or potentially large for which distributing the computations is usually a standard way to proceed, since centralized algorithms are in general ineffective. We propose a distributed learning approach for mixtures of experts (MoE) models with an aggregation strategy to construct a reduction estimator from local estimators fitted parallelly to distributed subsets of the data. The aggregation is based on an optimal minimization of an expected transportation divergence between the large MoE composed of local estimators and the unknown desired MoE model. We show that the provided reduction estimator is consistent as soon as the local estimators to be aggregated are consistent, and its construction is performed by a proposed majorization-minimization (MM) algorithm that is computationally effective. We study the statistical and numerical properties for the proposed reduction estimator on experiments that demonstrate its performance compared to namely the global estimator constructed in a centralized way from the full dataset. For some situations, the computation time is more than ten times faster, for a comparable performance. Our source codes are publicly available on Github.

Faïcel Chamroukhi, Nhat Thien Pham, Van Hà Hoang et al.

We consider the statistical analysis of heterogeneous data for prediction in situations where the observations include functions, typically time series. We extend the modeling with Mixtures-of-Experts (ME), as a framework of choice in modeling heterogeneity in data for prediction with vectorial observations, to this functional data analysis context. We first present a new family of ME models, named functional ME (FME) in which the predictors are potentially noisy observations, from entire functions. Furthermore, the data generating process of the predictor and the real response, is governed by a hidden discrete variable representing an unknown partition. Second, by imposing sparsity on derivatives of the underlying functional parameters via Lasso-like regularizations, we provide sparse and interpretable functional representations of the FME models called iFME. We develop dedicated expectation--maximization algorithms for Lasso-like (EM-Lasso) regularized maximum-likelihood parameter estimation strategies to fit the models. The proposed models and algorithms are studied in simulated scenarios and in applications to two real data sets, and the obtained results demonstrate their performance in accurately capturing complex nonlinear relationships and in clustering the heterogeneous regression data.