2016/10/13 by Quang, Minh Ha · 1 citation
Mathematics · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Machine Learning (stat.ML) #Mathematical Inequalities and Applications #Quantum Mechanics and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1610.08087
openalex publication_date 2016/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infinite-dimensional setting. The family of Alpha-Beta Log-Det divergences is highly general and contains many divergences as special cases, including the recently formulated infinite dimensional affine-invariant Riemannian distance and the infinite-dimensional Alpha Log-Det divergences between positive definite unitized trace class operators. In particular, it includes a parametrized family of metrics between positive definite trace class operators, with the affine-invariant Riemannian distance and the square root of the symmetric Stein divergence being special cases. For the Alpha-Beta Log-Det divergences between covariance operators on a Reproducing Kernel Hilbert Space (RKHS), we obtain closed form formulas via the corresponding Gram matrices.