Related papers: Proper Scoring Rules and Bregman Divergences
Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
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…
Every prediction is ultimately used in a downstream task. Consequently, evaluating prediction quality is more meaningful when considered in the context of its downstream use. Metrics based solely on predictive performance often diverge from…
In this work, we develop a level-set subdifferential error bound condition aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It…
Relative entropy (divergence) of Bregman type recently proposed by T. D. Frank and Jan Naudts is considered and its quantum counterpart is used to calculate purity of the Werner state in nonextensive formalism. It has been observed that two…
In this paper we study upper and lower bounds on the Bregman divergence $\Delta_{\mathcal{F}}^{\xi}(y,x):=\mathcal{F}(y)-\mathcal{F}(x)-\langle \xi, y-x\rangle $ for some convex functional $\mathcal{F}$ on a normed space $\mathcal{X}$, with…
We systematically study the local single-valuedness of the Bregman proximal mapping and local smoothness of the Bregman--Moreau envelope of a nonconvex function under relative prox-regularity - an extension of prox-regularity - which was…
Sparse graphs with bounded average degree form a rich class of discrete structures where local geometry strongly influences global behavior. The Benjamini-Schramm (BS) convergence offers a natural framework to describe their asymptotic…
This study introduces novel superior scoring rules called Penalized Brier Score (PBS) and Penalized Logarithmic Loss (PLL) to improve model evaluation for probabilistic classification. Traditional scoring rules like Brier Score and…
The crowdsourcing scenarios are a good example of having a probability distribution over some categories showing what the people in a global perspective thinks. Learn a predictive model of this probability distribution can be of much more…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…
This document expands upon the relationship between discrete and continuous entropy given in (Phys. Rev. Lett. 110 130407), \Violating Continuous Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements". We provide a detailed…
The theoretical advances on the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to…
Propensity Score Matching (PSM) stands as a widely embraced method in comparative effectiveness research. PSM crafts matched datasets, mimicking some attributes of randomized designs, from observational data. In a valid PSM design where all…
Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for…
We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not…
We investigate convergence of alternating Bregman projections between non-convex sets and prove convergence to a point in the intersection, or to points realizing a gap between the two sets. The speed of convergence is generally sub-linear,…
Proper scoring rules are used to assess the out-of-sample accuracy of probabilistic forecasts, with different scoring rules rewarding distinct aspects of forecast performance. Herein, we re-investigate the practice of using proper scoring…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…