Related papers: Functional Bregman Divergence and Bayesian Estimat…
To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed…
Bregman proximal-type algorithms (BPs), such as mirror descent, have become popular tools in machine learning and data science for exploiting problem structures through non-Euclidean geometries. In this paper, we show that BPs can get…
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…
Blasiok (SODA'18) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions $f:\{0,1\}^m \to \mathbb{R}$ such that $f(U_m)$ has subgaussian tails, and asked for explicit…
Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss…
In this paper, we propose the Fourier Discrepancy Function, a new discrepancy to compare discrete probability measures. We show that this discrepancy takes into account the geometry of the underlying space. We prove that the Fourier…
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…
We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $\varphi$-divergences like the Kullback-Leibler…
Divergences, also known as contrast functions, are distance-like quantities defined on manifolds of non-negative or probability measures. Using the duality in optimal transport, we introduce and study the one-parameter family of $L^{(\pm…
This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to $U$-statistics satisfying the weak assumption of decomposability in the Hoeffding…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…
The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…
We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform…
We propose an extension of a special form of gradient descent -- in the literature known as linearised Bregman iteration -- to a larger class of non-convex functions. We replace the classical (squared) two norm metric in the gradient…
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…