Burkholder inequality by Bregman divergence

Bregman-Wasserstein散度：几何与应用

Bregman-Wasserstein divergence: geometry and applications

本文研究以Bregman散度为代价函数的最优传输问题，建立其基本性质与广义传输几何，提出广义位移插值、对偶几何及JKO格式，并给出神经估计、重心适定性与贝叶斯学习的联系。

最优Bregman量化：重探最优量化器的存在性与唯一性

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited

本文重探了Bregman散度下$L^r$-最优量化的存在性与唯一性定理，在更轻假设下证明了最优量化器的存在性，并在一维强单峰分布等条件下证明了唯一性定理。

关于Bregman散度的最优量化Zador定理

Zador Theorem for optimal quantization with respect to Bregman divergences

本文基于Bregman散度建立Zador定理，研究L^r最优向量量化问题，并证明了在正定矩阵集上的类似结果，克服了特定框架下的挑战。

传输信息Bregman散度

Transport information Bregman divergences

本文研究了$L^2$-Wasserstein空间中的Bregman散度，推导了传输KL散度及其对偶性，并给出一维概率密度与高斯族的解析公式。

Understanding the bias-variance tradeoff of Bregman divergences

This paper builds upon the work of Pfau (2013), which generalized the bias variance tradeoff to any Bregman divergence loss function. Pfau (2013) showed that for Bregman divergences, the bias and variances are defined with respect to a central label, defined as the mean of the label variable, and a central prediction, of a more complex form. We show that, similarly to the label, the central prediction can be interpreted as the mean of a random variable, where the mean operates in a dual space defined by the loss function itself. Viewing the bias-variance tradeoff through operations taken in du…

On Bregman Distances and Divergences of Probability Measures

The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic observations, but also the distances of random processes and signals. It is shown that the scaled Bregman distances extend not only the classical ones studied in the previous literature, but also the information divergence and the related wider class of convex divergences of probability measures. An information processing theorem is established too, but onl…