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A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
We explicitly quantify the empirically observed phenomenon that estimation under a stochastic block model (SBM) is hard if the model contains classes that are similar. More precisely, we consider estimation of certain functionals of random…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
We adapt the interactive spline model of Wahba to growth curves with covariates. The smoothing spline formulation permits a non-parametric representation of the growth curves. In the limit when the discretization error is small relative to…
Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total…
Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In…
Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the…
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to…
We prove a quantitative estimate for the homogenization length scale in terms of the ellipticity ratio $\Lambda/\lambda$ of the coefficient field. This upper bound applies to high-contrast elliptic equations exhibiting near-critical…
In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\alpha$ in probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$ in…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…
We reanalyse optical gravitational lens surveys from the literature in order to determine relative probabilities in the $\lambda_{0}$-$\Omega_{0}$ plane, using a softened singular isothermal sphere lens model. In addition, we examine a…
It is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where…
We define regularity scales to study the behavior of the Calabi flow. Based on estimates of the regularity scales, we obtain convergence theorems of the Calabi flow on extremal Kahler surfaces, under the assumption of global existence of…
We present global convergence rates for a line-search method which is based on random first-order models and directions whose quality is ensured only with certain probability. We show that in terms of the order of the accuracy, the…