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Séminaire Statistique

organisé par l'équipe Statistique

  • Anne Van Delft

    A statistical framework for analyzing shape in a time series of random geometric objects (joint work with Andrew Blumberg)

    16 février 2024 - 11:00Salle de séminaires IRMA

    We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric space-valued stochastic process, possibly of nonstationary nature, thereby integrating geometric data analysis into the realm of functional time series analysis. We focus on the descriptors coming from topological data analysis. Our framework allows for natural incorporation of spatial-temporal dynamics, heterogeneous sampling, and the study of convergence rates. Further, we derive complete invariants for classes of metric space-valued stochastic processes in the spirit of Gromov, and relate these invariants to so-called ball volume processes. Under mild dependence conditions, a weak invariance principle in $D([0,1]\times [0,\mathscr{R}])$ is established for sequential empirical versions of the latter, assuming the probabilistic structure possibly changes over time. Finally, we use this result to introduce novel test statistics for topological change, which are distribution free in the limit under the hypothesis of stationarity.

  • Alaaeddine Chaoub

    Deep learning representations for prognostics and health management

    23 février 2024 - 11:00Salle de séminaires IRMA

    Deep learning technologies have experienced remarkable growth across various sectors, notably in computer vision and natural language processing, fueled by the confluence of data abundance, algorithmic breakthroughs, and hardware advancements. Yet, despite extensive monitoring of complex industrial assets and the accumulation of vast datasets from condition monitoring signals, the application of deep learning approaches for fault prediction for industrial equipment remains limited. This presentation delves into the existing research, highlighting key challenges, potential and proposed solutions, and avenues for future research. Key challenges include model architectures that under-perform across varied operating conditions, the inherent black-box nature of DL models which complicates interpretability and trustworthiness, and the pronounced issue of data scarcity arising from multiple reasons such as preventive maintenance. To tackle these obstacles, we explore a spectrum of strategies, including modular networks, pre-training and fine-tuning, data augmentation, few-shot learning, auxiliary learning, and meta-learning. By delving into these methodologies and shedding light on promising avenues for future exploration, this presentation aims to bridge the gap between DL's potential and its practical application in industrial fault prognostics.

  • Herold Dehling

    Test for independence of long-range dependent time series using distance covariance

    22 mars 2024 - 11:00Salle de séminaires IRMA

  • Louise Martineau

    Introduction à l'analyse topologique de données en statistique

    19 avril 2024 - 11:00Salle de séminaires IRMA