3IA PhD/Postdoc Seminar #43

Abstract: In the domain of computer science, how to optimally allocate cache space is a challenging problem. This study focuses on the Follow the Perturbed Leader (FTPL) algorithm, an online learning approach, considering batched requests and switching costs. We prove that  FTPL has sub-linear regret bounds across various scenarios. We consider a FTPL variant---called Optimistic FTPL (OFTPL)---which has access to future requests' predictions and shows that it enjoys better theoretical regret bound than the classic FTPL when predictions are accurate and switching costs are small. We also show how to optimally set OFTPL batch size.

Differentiable Soft Morphological Filters for Improving Arterial Segmentation in Peripheral Artery Disease

Abstract: Segmenting arteries is essential for automatically diagnosing and monitoring Peripheral Artery Disease (PAD). Traditional morphological operations, such as erosion, dilation, and skeletonization, provide powerful tools for refining segmentation masks but are not inherently differentiable, limiting their integration into deep learning frameworks. We propose a novel approach that formulates soft morphological filters by translating Boolean morphological operations into differentiable multilinear polynomials. This method enables the seamless incorporation of morphological operations into neural networks, either as loss functions or as post-processing layers. Additionally, we explore a new class of regional Hausdorff Distance losses, designed to improve boundary accuracy in segmentation tasks.

Deconvolution with unknown noise distribution for structured signals

Abstract: Deconvolution is the problem of recovering the distribution of a signal X based on noisy observations Y = X + epsilon. Most existing results require stringent assumptions on the noise distribution, for example that it is known, or that an auxiliary sample from the noise distribution is available.
In this talk, I will show that it is possible to recover the distribution of the hidden signal with almost no assumption on the noise and no auxiliary sample, provided the signal is multidimensional with some dependency between its components. I will also show how to use this result to construct estimators of the distribution of the signal and of its support, with rates of convergence that are minimax optimal.
This talk is based on joint works with Elisabeth Gassiat, Sylvain Le Corff and Jérémie Capitao-Miniconi.

Open discussion about the two contributions