The Spectral Condition Number Plot for Regularization Parameter Determination
Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample covariance matrix. These estimators depend on a penalty parameter and choosing its value can be hard, in terms of being computationally unfeasible or tenable only for a restricted set of ridge-type estimators. Here we introduce a simple graphical tool, the spectral condition number plot, for informed heuristic penalty parameter selection. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators.
Code (1)
Tasks
Vocal Bursts Type PredictionSimilar Papers 제목 키워드 기반
Residuum-Condition Diagram and Reduction of Over-Complete Endmember-Sets
Extracting reference spectra, or endmembers (EMs) from a given multi- or hyperspectral image, as well as estimating the size of the EM set, plays an important role in multispectral image processing. In this paper, we pre…
Chebyshev Moment Regularization (CMR): Condition-Number Control with Moment Shaping
We introduce \textbf{Chebyshev Moment Regularization (CMR)}, a simple, architecture-agnostic loss that directly optimizes layer spectra. CMR jointly controls spectral edges via a log-condition proxy and shapes the interi…
Bayesian Matrix Completion via Adaptive Relaxed Spectral Regularization
Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral …
Bayesian InferenceCollaborative FilteringMatrix CompletionNumerical Approximation of Andrews Plots with Optimal Spatial-Spectral Smoothing
Andrews plots provide aesthetically pleasant visualizations of high-dimensional datasets. This work proves that Andrews plots (when defined in terms of the principal component scores of a dataset) are optimally ``smooth'…
An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration
We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dim…
Computational EfficiencyConstrained Diffeomorphic Image RegistrationImage Registration