Related papers: Expected $L_2-$discrepancy bound for a class of ne…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
The aim of this paper is to obtain convergence in mean in the uniform topology of piecewise linear approximations of Stochastic Differential Equations (SDEs) with $C^1$ drift and $C^2$ diffusion coefficients with uniformly bounded…
We introduce an alternative to the notion of `fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot…
We consider stochastic gradient descent and its averaging variant for binary classification problems in a reproducing kernel Hilbert space. In the traditional analysis using a consistency property of loss functions, it is known that the…
An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…
We prove a priori estimates in $L_\infty$ for a class of quasilinear stochastic partial differential equations. The estimates are obtained independently of the ellipticity constant $\varepsilon$ and thus imply analogous estimates for…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…
Deterministically generating near-uniform point samplings of the motion groups like SO(3), SE(3) and their n-wise products SO(3)^n, SE(3)^n is fundamental to numerous applications in computational and data sciences. The natural measure of…
Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured…
Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
We analyze the convergence rates of two popular variants of coordinate descent (CD): random CD (RCD), in which the coordinates are sampled uniformly at random, and random-permutation CD (RPCD), in which random permutations are used to…
We give an improved lower bound for the $L_2$-discrepancy of finite point sets in the unit square.
Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected…
A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…
We establish two-sided bounds for expectations of order statistics ($k$-th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants…