arXiv research

Efficiently estimates shrinkage coefficient for RTME using LOOCV approximation.

A fast method for LOOCV in k-NN regression reduces computation time.

Paper discusses prediction errors for penalized regressions using GAMP and LOOCV.

Adaptive RBF-KAN improves KANs by dynamically adjusting kernel parameters.

Bayesian EM method improves ridge regression tuning without LOOCV's limitations.

Analysis of cross-validation for early-stopped gradient descent in high-dimensional regression.

Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical properties of such estimates have been extensively studied in the low-dimensional setting…

We consider the parametric learning problem, where the objective of the learner is determined by a parametric loss function. Employing empirical risk minimization with possibly regularization, the inferred parameter vector will be biased toward the training samples. Such bias is measured by the cross validation procedu…

Leave-one-out cross-validation (LOOCV) can be particularly accurate among cross-validation (CV) variants for machine learning assessment tasks -- e.g., assessing methods' error or variability. But it is expensive to re-fit a model $N$ times for a dataset of size $N$. Previous work has shown that approximations to LOOCV…

LOOCV is often useful for analyzing small, structured experimental designs.

This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a variable-wise variance and yields selection of better, more robust regressors. Expe…

Background: Functional magnetic resonance imaging (fMRI) provides non-invasive measures of neuronal activity using an endogenous Blood Oxygenation-Level Dependent (BOLD) contrast. This article introduces a nonlinear dimensionality reduction (Locally Linear Embedding) to extract informative measures of the underlying ne…

Consider the following class of learning schemes: $\hat{\boldsymbolβ} := \arg\min_{\boldsymbolβ}\;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbolβ; y_j) + λR(\boldsymbolβ),\qquad\qquad (1)$ where $\boldsymbol{x}_i \in \mathbb{R}^p$ and $y_i \in \mathbb{R}$ denote the $i^{\text{th}}$ feature and response variable …

Consider the following class of learning schemes: \begin{equation} \label{eq:main-problem1} \hat{\boldsymbolβ} := \underset{\boldsymbolβ \in \mathcal{C}}{\arg\min} \;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbolβ; y_j) + λR(\boldsymbolβ), \qquad \qquad \qquad (1) \end{equation} where $\boldsymbol{x}_i \in \mathbb{…

Non-linear dimensionality reduction techniques such as manifold learning algorithms have become a common way for processing and analyzing high-dimensional patterns that often have attached a target that corresponds to the value of an unknown function. Their application to new points consists in two steps: first, embedd…