Robust blind source separation by beta divergence
Neural Computation
Divergence function, duality, and convex analysis
Neural Computation
Information geometry of U-Boost and Bregman divergence
Neural Computation
Relative information of type s, Csiszár's f-divergence, and information inequalities
Information Sciences—Informatics and Computer Science: An International Journal
Clustering with Bregman Divergences
The Journal of Machine Learning Research
Integration of Stochastic Models by Minimizing α-Divergence
Neural Computation
Sided and symmetrized Bregman centroids
IEEE Transactions on Information Theory
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
The α-EM algorithm: surrogate likelihood maximization using α-logarithmic information measures
IEEE Transactions on Information Theory
Transactions on Computational Science XIV
Pattern learning and recognition on statistical manifolds: an information-geometric review
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Bayesian model diagnostics using functional Bregman divergence
Journal of Multivariate Analysis
| Hi-index | 754.84 |
A divergence measure between two probability distributions or positive arrays (positive measures) is a useful tool for solving optimization problems in optimization, signal processing, machine learning, and statistical inference. The Csiszár f-divergence is a unique class of divergences having information monotonicity, from which the dual α geometrical structure with the Fisher metric is derived. The Bregman divergence is another class of divergences that gives a dually flat geometrical structure different from the α-structure in general. Csiszár gave an axiomatic characterization of divergences related to inference problems. The Kullback-Leibler divergence is proved to belong to both classes, and this is the only such one in the space of probability distributions. This paper proves that the α-divergences constitute a unique class belonging to both classes when the space of positive measures or positive arrays is considered. They are the canonical divergences derived from the dually flat geometrical structure of the space of positive measures.