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In this paper, we develop a new elegant framework relying on the Kullback-Leibler Information Criterion to address the design of one-stage adaptive detection architectures for multiple hypothesis testing problems. Specifically, at the…
Recent works have demonstrated that the convergence rate of a nonparametric density estimator can be greatly improved by using a low-rank estimator when the target density is a convex combination of separable probability densities with…
A novel type of a multiscale approach, called Relative Resolution (RelRes), can correctly retrieve the behavior of various nonpolar liquids, whilst speeding up molecular simulations by almost an order of magnitude. In this approach in a…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
Based on $X \sim N_d(\theta, \sigma^2_X I_d)$, we study the efficiency of predictive densities under $\alpha-$divergence loss $L_{\alpha}$ for estimating the density of $Y \sim N_d(\theta, \sigma^2_Y I_d)$. We identify a large number of…
Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985)…
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…
A Wishart kernel density estimator (KDE) is introduced for density estimation in the cone of positive definite matrices. The estimator is boundary-aware and mitigates the boundary bias suffered by conventional KDEs, while remaining simple…
This is the eighth and final paper in a series giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is…
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…
We study density thresholds that force a measurable set $E\subseteq\mathbb{R}^d$ to contain all sufficiently large similar copies of every $n$-point configuration. We prove a lower bound of the form $1-O((\log n)/n)$, which matches the…
In this paper, we extend the correspondence between Bayesian estimation and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) adding a convexe constraints on the solution. Through a sequence of approximating Hilbertian spaces…
In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…
Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the {generalised Pareto…
Motivated by modern applications like image processing and wireless sensor networks, we consider a variation of the famous Kepler Conjecture. Given any infinite set of unit balls covering the whole space, we want to know the optimal (lim…
Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
Existing rotated object detectors are mostly inherited from the horizontal detection paradigm, as the latter has evolved into a well-developed area. However, these detectors are difficult to perform prominently in high-precision detection…