Related papers: Maximizing the Bregman divergence from a Bregman f…
The links between the mean families of Lehmer and H\"older and the weighted maximum likelihood estimator have recently been established in the case of a regular univariate exponential family. In this article, we will extend the outcomes…
In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…
Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…
Consider the all-time maximum of a Brownian motion with negative drift. Assume that this process is sampled at certain points in time, where the time between two consecutive points is rendered by an Erlang distribution with mean $1/\omega$.…
We provide a method that enables the simple calculation of the maximal correlation coefficient of a bivariate distribution, under suitable conditions. In particular, the method readily applies to known results on order statistics and…
We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational…
Analysis of the convergence rates of modern convex optimization algorithms can be achived through binary means: analysis of emperical convergence, or analysis of theoretical convergence. These two pathways of capturing information diverge…
We prove Burkholder inequality using Bregman divergence.
We re-visit the classical problem of optimal payment of dividends and determine the degree to which the diffusion approximation serves as a valid approximation of the classical risk model for this problem. Our results parallel some of those…
We study information projections with respect to statistical $f$-divergences between any two location-scale families. We consider a multivariate generalization of the location-scale families which includes the elliptical and the spherical…
Dynamic processes on networks are fundamental to understanding modern-day phenomena such as information diffusion and opinion polarization on the internet or epidemics spreading through society. However, such processes are notoriously…
The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly…
A family of information theoretic models of communication was introduced more than a decade ago to explain the origins of Zipf's law for word frequencies. The family is a based on a combination of two information theoretic principles:…
We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After…
A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior,…
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…