We provide new general kernel selection rules thanks to penalized least-squares criteria. We derive optimal oracle inequalities using adequate concentration tools. We also investigate the problem of minimal penalty as described in [BM07].

We construct near-optimal coresets for kernel density estimate for points in Rd when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size O( √ d log(1/ε)/ε), and we show a near-matching lower bound of size Ω( √ d/ε). The upper bound is a polynomial in 1/ε improvement when d ∈ [3, 1/ε2) (for all kernels except the Gaussian kernel which had a ...

In bivariate density representation there is an extensive literature on level set estimation when the level is fixed, but this is not so much the case when choosing which level is (or which levels are) of most interest. This is an important practical question which depends on the kind of problem one has to deal with as well as the kind of feature one wishes to highlight in the density, the answ...

We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to 1. We compare the practical performances of these methods in a short simulation study.

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, in the case of Pauli measurements) with explicit dependence of the bounds on t...

We regard histogram density estimation as a model selection problem. Our approach is based on the information-theoretic minimum description length (MDL) principle. MDLbased model selection is formalized via the normalized maximum likelihood (NML) distribution, which has several desirable optimality properties. We show how this approach can be applied for learning generic, irregular (variable-wi...

In this paper, we present a variational method for exposure fusion. In particular, we combine differently exposed images to a single composite that offers optimal exposedness, saturation, and local contrast. To this end, we formulate the output image as a convex combination of the input, and design an energy functional that implements important perceptually inspired concepts from contrast enhan...