English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This note examines the behavior of generalization capabilities - as definedby out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixeddesign matrix) and Linear Least Squares regression. Particularly, we consider awell-specified model setting, i.e. we assume that there exists a `true'combination of model parameters within the chosen model form. While thestatistical properties of Least Squares regression have been extensivelystudied over the past few decades - particularly with {\bf less restrictiveproblem statements} compared to the present work - this note targets boundsthat are {\bf non-asymptotic and more quantitative} compared to the literature.Further, the analytical formulae for distributions and bounds (on the MSE) aredirectly compared to numerical experiments. Derivations are presented in aself-contained and pedagogical manner, in a way that a reader with a basicknowledge of probability and statistics can follow.

`Basic' Generalization Error Bounds for Least Squares Regression with Well-specified Models