Erwan Le Pennec
Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the…
Many classic Reinforcement Learning (RL) algorithms rely on a Bellman operator, which involves an expectation over the next states, leading to the concept of bootstrapping. To introduce a form of pessimism, we propose to replace this…
We study the sample complexity of obtaining an $\epsilon$-optimal policy in \emph{Robust} discounted Markov Decision Processes (RMDPs), given only access to a generative model of the nominal kernel. This problem is widely studied in the…
Robust Reinforcement Learning tries to make predictions more robust to changes in the dynamics or rewards of the system. This problem is particularly important when the dynamics and rewards of the environment are estimated from the data. In…
Patients with diabetes who are self-monitoring have to decide right before each meal how much insulin they should take. A standard bolus advisor exists, but has never actually been proven to be optimal in any sense. We challenged this rule…
In this work we study the problem of inferring a discrete probability distribution using both expert knowledge and empirical data. This is an important issue for many applications where the scarcity of data prevents a purely empirical…
Decades of studies have suggested several criteria to detect Interplanetary coronal mass ejections (ICME) in time series from in-situ spacecraft measurements. Among them the most common are an enhanced and smoothly rotating magnetic field,…
In this work, we present our various contributions to the objective of building a decision support tool for the diagnosis of rare diseases. Our goal is to achieve a state of knowledge where the uncertainty about the patient's disease is…
Aggregating estimators using exponential weights depending on their risk appears optimal in expectation but not in probability. We use here a slight overpenalization to obtain oracle inequality in probability for such an explicit…
In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\top\beta$ is positive.The vectors $X$ and $\beta$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$.We prove lower…
In this study, we consider unsupervised clustering of categorical vectors that can be of different size using mixture. We use likelihood maximization to estimate the parameters of the underlying mixture model and a penalization technique to…
We wish to estimate conditional density using Gaussian Mixture Regression model with logistic weights and means depending on the covariate. We aim at selecting the number of components of this model as well as the other parameters by a…
In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a Kullback-Leibler type loss for a single model maximum likelihood estimate.…
We provide a new algorithm for the treatment of the noisy inversion of the Radon transform using an appropriate thresholding technique adapted to a well-chosen new localized basis. We establish minimax results and prove their optimality. In…
A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the…
This paper deals with the problem of the multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which the knowledge of the regularity of the copula density to be…
To estimate geometrically regular images in the white noise model and obtain an adaptive near asymptotic minimaxity result, we consider a model selection based bandlet estimator. This bandlet estimator combines the best basis selection…
This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…
We address the statistical issue of determining the maximal spaces (maxisets) where model selection procedures attain a given rate of convergence. By considering first general dictionaries, then orthonormal bases, we characterize these…