Results 31 to 40 of about 3,323 (160)

Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences

Entropy, 2015
This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties.
Andrzej Cichocki, Sergio Cruces, Shun-ichi Amari   +2 more
doaj   +1 more source

Preconditioner Design via the Bregman Divergence

CoRR, 2023
We study a preconditioner for a Hermitian positive definite linear system, which is obtained as the solution of a matrix nearness problem based on the Bregman log determinant divergence. The preconditioner is of the form of a Hermitian positive definite matrix plus a low-rank matrix.
Andreas A. Bock, Martin S. Andersen 0001
openaire   +2 more sources

Minimax quantum state estimation under Bregman divergence [PDF]

Quantum, 2019
We investigate minimax estimators for quantum state tomography under general Bregman divergences. First, generalizing the work of Koyama et al. [Entropy 19, 618 (2017)] for relative entropy, we find that given any estimator for a quantum state, there ...
Maria Quadeer, Marco Tomamichel, Christopher Ferrie   +2 more
doaj   +1 more source

Information Geometry of Positive Measures and Positive-Definite Matrices: Decomposable Dually Flat Structure

Entropy, 2014
Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ,τ)-divergence.
Shun-ichi Amari
doaj   +1 more source

Neural Bregman Divergences for Distance Learning

CoRR, 2022
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis), and the algorithm must learn to embed points into the pre-chosen space.
Fred Lu, Edward Raff, Francis Ferraro
openaire   +3 more sources

Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities

Entropy, 2010
In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered.
Andrzej Cichocki, Shun-ichi Amari
doaj   +1 more source

Bregman–Hausdorff Divergence: Strengthening the Connections Between Computational Geometry and Machine Learning

Machine Learning and Knowledge Extraction
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures.
Tuyen Pham, Hana Dal Poz Kouřimská, Hubert Wagner   +2 more
doaj   +1 more source

Sum decomposition of divergence into three divergences

, 2018
Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the f-divergences. In
Nishiyama, Tomohiro
core   +1 more source

Probabilistic Forecasts: Scoring Rules and Their Decomposition and Diagrammatic Representation via Bregman Divergences

Entropy, 2015
A scoring rule is a device for evaluation of forecasts that are given in terms of the probability of an event. In this article we will restrict our attention to binary forecasts.
Gareth Hughes, Cairistiona F.E. Topp
doaj   +1 more source

Discounted dynamic optimization and Bregman divergence

Journal of Mathematical Economics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source