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Tag: generalized

  • Characterizing Online and Private Learnability under Distributional Constraints via Generalized Smoothness

    Characterizing Online and Private Learnability under Distributional Constraints via Generalized Smoothness arXiv:2602.20585v1 Announce Type: new Abstract: Understanding minimal assumptions that enable learning and generalization is perhaps the central question of learning theory. Several celebrated results in statistical learning theory, such as the VC theorem and Littlestone’s characterization of online learnability, establish conditions on the hypothesis…

  • Generalized infinite dimensional Alpha-Procrustes based geometries

    Generalized infinite dimensional Alpha-Procrustes based geometries arXiv:2511.09801v1 Announce Type: new Abstract: This work extends the recently introduced Alpha-Procrustes family of Riemannian metrics for symmetric positive definite (SPD) matrices by incorporating generalized versions of the Bures-Wasserstein (GBW), Log-Euclidean, and Wasserstein distances. While the Alpha-Procrustes framework has unified many classical metrics in both finite- and infinite- dimensional…

  • Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling

    Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling arXiv:2508.10782v1 Announce Type: new Abstract: We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms — including gradient-based optimization methods and approximate message passing (AMP) — with Gaussian data matrices and full-memory, non-separable nonlinearities. The central result constructs an explicit coupling between the…

  • Mirror Descent Using the Tempesta Generalized Multi-parametric Logarithms

    Mirror Descent Using the Tempesta Generalized Multi-parametric Logarithms arXiv:2506.13984v1 Announce Type: new Abstract: In this paper, we develop a wide class Mirror Descent (MD) algorithms, which play a key role in machine learning. For this purpose we formulated the constrained optimization problem, in which we exploits the Bregman divergence with the Tempesta multi-parametric deformation logarithm…

  • Majorization-Minimization Dual Stagewise Algorithm for Generalized Lasso

    Majorization-Minimization Dual Stagewise Algorithm for Generalized Lasso arXiv:2501.02197v1 Announce Type: new Abstract: The generalized lasso is a natural generalization of the celebrated lasso approach to handle structural regularization problems. Many important methods and applications fall into this framework, including fused lasso, clustered lasso, and constrained lasso. To elevate its effectiveness in large-scale problems, extensive research…