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Tag: norm

  • $L_1$-norm Regularized Indefinite Kernel Logistic Regression

    $L_1$-norm Regularized Indefinite Kernel Logistic Regression arXiv:2510.26043v1 Announce Type: new Abstract: Kernel logistic regression (KLR) is a powerful classification method widely applied across diverse domains. In many real-world scenarios, indefinite kernels capture more domain-specific structural information than positive definite kernels. This paper proposes a novel $L_1$-norm regularized indefinite kernel logistic regression (RIKLR) model, which extends…

  • Transformed $ell_1$ Regularizations for Robust Principal Component Analysis: Toward a Fine-Grained Understanding

    Transformed $ell_1$ Regularizations for Robust Principal Component Analysis: Toward a Fine-Grained Understanding arXiv:2510.03624v1 Announce Type: new Abstract: Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations, such as nuclear norm and $ell_1$…

  • Sobolev norm inconsistency of kernel interpolation

    Sobolev norm inconsistency of kernel interpolation arXiv:2504.20617v1 Announce Type: new Abstract: We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis…

  • Local Polynomial Lp-norm Regression

    Local Polynomial Lp-norm Regression arXiv:2504.18695v1 Announce Type: new Abstract: The local least squares estimator for a regression curve cannot provide optimal results when non-Gaussian noise is present. Both theoretical and empirical evidence suggests that residuals often exhibit distributional properties different from those of a normal distribution, making it worthwhile to consider estimation based on other…

  • Empirical Bound Information-Directed Sampling for Norm-Agnostic Bandits

    Empirical Bound Information-Directed Sampling for Norm-Agnostic Bandits arXiv:2503.05098v1 Announce Type: new Abstract: Information-directed sampling (IDS) is a powerful framework for solving bandit problems which has shown strong results in both Bayesian and frequentist settings. However, frequentist IDS, like many other bandit algorithms, requires that one have prior knowledge of a (relatively) tight upper bound on…