Learning the intensity of time events with change-points

International audienceWe consider the problem of learning the inhomogeneous intensity of a counting process, under a sparse segmentation assumption. We introduce a weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We prove that this leads to a sharp tuning of the convex relaxation of the segmentation prior, by stating oracle inequalities with fast rates of convergence, and consistency for change-points detection. This provides first theoretical guarantees for segmentation with a convex proxy beyond the standard i.i.d signal + white noise setting. We introduce a fast algorithm to solve this convex problem. Numerical experiments illustrate our approach on simulated and on a high-frequency genomics dataset

Open Set Domain Adaptation using Optimal Transport

We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of the approach aims at rejecting the samples issued from these new classes using an optimal transport plan. The second step solves the target (class ratio) shift still as an optimal transport problem. We develop a dual approach to solve the optimization problem involved at each step and we prove that our results outperform recent state-of-the-art performances. We further apply the approach to the setting where the source and target distributions present both a label-shift and an increasing covariate (features) shift to show its robustness.Comment: Accepted at ECML-PKDD 2020, Acknowledgements adde

Theoretical Guarantees for Bridging Metric Measure Embedding and Optimal Transport

We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we consider a method allowing to embed the metric measure spaces in a common Euclidean space and compute an optimal transport (OT) on the embedded distributions. This leads to what we call a sub-embedding robust Wasserstein (SERW) distance. Under some conditions, SERW is a distance that considers an OT distance of the (low-distorted) embedded distributions using a common metric. In addition to this novel proposal that generalizes several recent OT works, our contributions stand on several theoretical analyses: (i) we characterize the embedding spaces to define SERW distance for distribution alignment; (ii) we prove that SERW mimics almost the same properties of GW distance, and we give a cost relation between GW and SERW. The paper also provides some numerical illustrations of how SERW behaves on matching problems

Screening Sinkhorn Algorithm for Regularized Optimal Transport

International audienceWe introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering the Sinkhorn problem. This allows us to solve a smaller Sinkhorn problem while ensuring approximation with provable guarantees. More formally, the approach is based on a new formulation of dual of Sinkhorn divergence problem and on the KKT optimality conditions of this problem, which enable identification of dual components to be screened. This new analysis leads to the Screenkhorn algorithm. We illustrate the efficiency of Screenkhorn on complex tasks such as dimensionality reduction and domain adaptation involving regularized optimal transport

Heterogeneous Wasserstein Discrepancy for Incomparable Distributions

Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be supported on the $\textit{same}$ metric space. Because of its high computational complexity, several approximate Wasserstein distances have been proposed based on entropy regularization or on slicing, and one-dimensional Wassserstein computation. In this paper, we propose a novel extension of Wasserstein distance to compare two incomparable distributions, that hinges on the idea of $\textit{distributional slicing}$, embeddings, and on computing the closed-form Wassertein distance between the sliced distributions. We provide a theoretical analysis of this new divergence, called $\textit{heterogeneous Wasserstein discrepancy (HWD)}$, and we show that it preserves several interesting properties including rotation-invariance. We show that the embeddings involved in HWD can be efficiently learned. Finally, we provide a large set of experiments illustrating the behavior of HWD as a divergence in the context of generative modeling and in query framework

Match and Reweight Strategy for Generalized Target Shift

We address the problem of unsupervised domain adaptation under the setting of generalized target shift (both class-conditional and label shifts occur). We show that in that setting, for good generalization, it is necessary to learn with similar source and target label distributions and to match the class-conditional probabilities. For this purpose, we propose an estimation of target label proportion by blending mixture estimation and optimal transport. This estimation comes with theoretical guarantees of correctness. Based on the estimation, we learn a model by minimizing a importance weighted loss and a Wasserstein distance between weighted marginals. We prove that this minimization allows to match class-conditionals given mild assumptions on their geometry. Our experimental results show that our method performs better on average than competitors accross a range domain adaptation problems including digits,VisDA and Office

Improved control strategy of DFIG-based wind turbines using direct torque and direct power control techniques

This paper presents different control strategies for a variable-speed wind energy conversion system (WECS), based on a doubly fed induction generator. Direct Torque Control (DTC) with Space-Vector Modulation is used on the rotor side converter. This control method is known to reduce the fluctuations of the torque and flux at low speeds in contrast to the classical DTC, where the frequency of switching is uncontrollable. The reference for torque is obtained from the maximum power point tracking technique of the wind turbine. For the grid-side converter, a fuzzy direct power control is proposed for the control of the instantaneous active and reactive power. Simulation results of the WECS are presented to compare the performance of the proposed and classical control approaches.Peer reviewedFinal Accepted Versio

History, epidemiology and regional diversities of urolithiasis

Archeological findings give profound evidence that humans have suffered from kidney and bladder stones for centuries. Bladder stones were more prevalent during older ages, but kidney stones became more prevalent during the past 100 years, at least in the more developed countries. Also, treatment options and conservative measures, as well as ‘surgical’ interventions have also been known for a long time. Our current preventive measures are definitively comparable to those of our predecessors. Stone removal, first lithotomy for bladder stones, followed by transurethral methods, was definitively painful and had severe side effects. Then, as now, the incidence of urolithiasis in a given population was dependent on the geographic area, racial distribution, socio-economic status and dietary habits. Changes in the latter factors during the past decades have affected the incidence and also the site and chemical composition of calculi, with calcium oxalate stones being now the most prevalent. Major differences in frequency of other constituents, particularly uric acid and struvite, reflect eating habits and infection risk factors specific to certain populations. Extensive epidemiological observations have emphasized the importance of nutritional factors in the pathogenesis of urolithiasis, and specific dietary advice is, nowadays, often the most appropriate for prevention and treatment of urolithiasis