Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman
and Duo Jensen Divergences, Entropy 2022, 24(3)
Duo FenchelYoung divergence , arXiv:2202.10726.
We define duo Bregman divergences, duo FenchelYoung divergences, duo Jensen divergences.
We show how those divergences occur naturally when calculating the KullbackLeibler divergence and
skew Bhattacharyya distances between densities belonging to nested exponential families.
We report the KLD between truncated normal distributions as a duo Bregman divergence.
Demo code:
Jensen divergences and some generalizations
Conformal divergences
Projective divergences
Optimal transport/Wasserstein distances/Sinkhorn distances
Earth mover distances (EMD), Wasserstein distances
 Optimal Transport
with Tempered Exponential Measures, arxiv:2309.04015

Sinkhorn AutoEncoders, UAI 2019

On The Chain Rule Optimal Transport Distance, Progress in Information Geometry, 2021

Tsallis Regularized Optimal Transport and Ecological Inference, AAAI 2017

Clustering Patterns Connecting COVID19 Dynamics and Human Mobility Using Optimal Transport,
March 2021, Sankhya B 83(S1)

Optimal copula transport for clustering multivariate time series, IEEE ICASSP 2016

Exploring and measuring nonlinear correlations: Copulas, Lightspeed Transportation and Clustering,
Time Series Workshop at NeurIPS 2016

Earth Mover Distance on superpixels, IEEE ICIP 2010
Shannon, Rényi, Tsallis, SharmalMittal entropies, crossentropies and divergences
Chernoff information
Other dissimilarities
Loss functions and proper scoring rules
Divergences between statistical mixtures

Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures
via Mixture Conversions to ExponentialPolynomial Distributions,
Entropy 2021, 23(11), 1417

The Statistical Minkowski Distances: ClosedForm Formula for Gaussian Mixture Models, GSI 2019

Guaranteed Deterministic Bounds on the total variation Distance between univariate mixtures, IEEE MLSP 2018

Comix: Joint estimation and lightspeed comparison of mixture models
, IEEE ICASSP 2016

BagofComponents: An Online Algorithm for Batch Learning of Mixture Models,
GSI 2015

Guaranteed Bounds on InformationTheoretic Measures of Univariate Mixtures Using Piecewise LogSumExp Inequalities
, Entropy 2016, 18(12), 442

Combinatorial bounds on the αdivergence of univariate mixture models, ICASSP 2017

Closedform informationtheoretic divergences for statistical mixtures, ICPR 2012