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

We study convex empirical risk minimization for high-dimensional inference inbinary models. Our first result sharply predicts the statistical performance ofsuch estimators in the linear asymptotic regime under isotropic Gaussianfeatures. Importantly, the predictions hold for a wide class of convex lossfunctions, which we exploit in order to prove a bound on the best achievableperformance among them. Notably, we show that the proposed bound is tight forpopular binary models (such as Signed, Logistic or Probit), by constructingappropriate loss functions that achieve it. More interestingly, for binarylinear classification under the Logistic and Probit models, we prove that theperformance of least-squares is no worse than 0.997 and 0.98 times the optimalone. Numerical simulations corroborate our theoretical findings and suggestthey are accurate even for relatively small problem dimensions.

Sharp Asymptotics and Optimal Performance for Inference in Binary Models