Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

Adaptive density estimation for stationary processes

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework

General regularization schemes for signal detection in inverse problems

The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can attain the minimax separation rates when the regularization parameter is chosen appropriately. It is also shown how to modify these tests in order to obtain (up to a $\log\log$ factor) a test which adapts to the unknown smoothness in the alternative. Moreover, the authors discuss how the so-called \emph{direct} and \emph{indirect} tests are related via interpolation properties

Learning near-optimal policies with Bellman-residual minimization based fitted policy iteration and a single sample path

We consider the problem of finding a near-optimal policy in continuous space, discounted Markovian Decision Problems given the trajectory of some behaviour policy. We study the policy iteration algorithm where in successive iterations the action-value functions of the intermediate policies are obtained by picking a function from some fixed function set (chosen by the user) that minimizes an unbiased finite-sample approximation to a novel loss function that upper-bounds the unmodified Bellman-residual criterion. The main result is a finite-sample, high-probability bound on the performance of the resulting policy that depends on the mixing rate of the trajectory, the capacity of the function set as measured by a novel capacity concept that we call the VC-crossing dimension, the approximation power of the function set and the discounted-average concentrability of the future-state distribution. To the best of our knowledge this is the first theoretical reinforcement learning result for off-policy control learning over continuous state-spaces using a single trajectory

Effect of Cadmium and Humic Acids on Metal Accumulation in Plants

International audienceThe natural ability of plants to accumulate, exclude or stabilize elements could be exploited to remediate soils contaminated with metals. To implement this alternative technology termed phytoremediation, it is crucial to better understand the various processes controlling metal mobilization or immobilization, uptake, and sequestration by the plants. Metal chelation is recognized as a vital biological process that regulates metal solubility, bioavailability, and internal storage in plants. Natural ligands, e.g. soil humates, root exudates components, or synthetic chelators, i.e. ethylene-diaminetretraacetic acid or EDTA, can interact in a yet-to-be-defined way to influence metal uptake and sequestration by plants. Here, we investigated the interactive effect of Cd and soil humates on metal acquisition and translocation in wheat plants. Metal contents in tissues and root exudates composition were determined, using X-ray fluorescence for metals and gas chromatography-mass spectrometry (GC-MS) and nuclear magnetic resonance (NMR) for organic exudates. Cd inhibited biomass production, from-55% to-65% on tissue dry weight basis, and greatly reduced root exu-dation, of about-84% by dry weight. Cd treatment also resulted in a substantial co-accumulation of transition metals (Fe, Ni, Cu, Zn) and Cd in wheat roots. Moreover, co-treatment with humates alleviated some of the Cd effect showing biomass inhibition reduced by about 10% for the tissues and 17% for the exudates, while accumulation of some metals (Zn, Cu, Ni, Cd) in the root was enhanced. Thus, under Cd treatment, with or without humate, the enhanced accumulation of metals was not mediated via root exudation. This is contrary to the exudate-mediated Fe acquisition under Fe deficiency. The mechanism for this phenomenon is being sought

Efficiency of five scale inhibitors on calcium carbonate precipitation from hard water: Effect of temperature and concentration

International audienc