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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Traditionally in regression one minimizes the number of fitting parameters oruses smoothing/regularization to trade training (TE) and generalization error(GE). Driving TE to zero by increasing fitting degrees of freedom (dof) isexpected to increase GE. However modern big-data approaches, including deepnets, seem to over-parametrize and send TE to zero (data interpolation) withoutimpacting GE. Overparametrization has the benefit that global minima of theempirical loss function proliferate and become easier to find. These phenomenahave drawn theoretical attention. Regression and classification algorithms havebeen shown that interpolate data but also generalize optimally. An interestingrelated phenomenon has been noted: the existence of non-monotonic risk curves,with a peak in GE with increasing dof. It was suggested that this peakseparates a classical regime from a modern regime where over-parametrizationimproves performance. Similar over-fitting peaks were reported previously(statistical physics approach to learning) and attributed to increased fittingmodel flexibility. We introduce a generative and fitting model pair("Misparametrized Sparse Regression" or MiSpaR) and show that the overfittingpeak can be dissociated from the point at which the fitting function gainsenough dof's to match the data generative model and thus provides goodgeneralization. This complicates the interpretation of overfitting peaks asseparating a "classical" from a "modern" regime. Data interpolation itselfcannot guarantee good generalization: we need to study the interpolation withdifferent penalty terms. We present analytical formulae for GE curves forMiSpaR with $l_2$ and $l_1$ penalties, in the interpolating limit$\lambda\rightarrow 0$.These risk curves exhibit important differences and helpelucidate the underlying phenomena.

Understanding overfitting peaks in generalization error: Analytical risk curves for $l_2$ and $l_1$ penalized interpolation