Related papers: Approximation of Smooth Numbers for Harmonic Sampl…
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
Consider an It\^{o} process $X$ satisfying the stochastic differential equation $dX=a(X)\,dt+b(X)\,dW$ where $a,b$ are smooth and $W$ is a multidimensional Brownian motion. Suppose that $W_n$ has smooth sample paths and that $W_n$ converges…
We study the problem of minimizing a relatively-smooth convex function using stochastic Bregman gradient methods. We first prove the convergence of Bregman Stochastic Gradient Descent (BSGD) to a region that depends on the noise (magnitude…
We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…
We present a static analysis for discovering differentiable or more generally smooth parts of a given probabilistic program, and show how the analysis can be used to improve the pathwise gradient estimator, one of the most popular methods…
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance for a large class of geometric functionals of marked Poisson and binomial point processes on general metric spaces. The rates are valid…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations combines Stein's method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. In the last decade,…
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…
This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances…
The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone…
This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior…
We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…
In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm --- the stochastic…
Stein's method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation the functional equation is a first order differential equation. Malliavin calculus is an…