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

The generalized linear model (GLM) plays a key role in regression analyses.In high-dimensional data, the sparse GLM has been used but it is not robustagainst outliers. Recently, the robust methods have been proposed for thespecific example of the sparse GLM. Among them, we focus on the robust andsparse linear regression based on the $\gamma$-divergence. The estimator of the$\gamma$-divergence has strong robustness under heavy contamination. In thispaper, we extend the robust and sparse linear regression based on the$\gamma$-divergence to the robust and sparse GLM based on the$\gamma$-divergence with a stochastic optimization approach in order to obtainthe estimate. We adopt the randomized stochastic projected gradient descent asa stochastic optimization approach and extend the established convergenceproperty to the classical first-order necessary condition. By virtue of thestochastic optimization approach, we can efficiently estimate parameters forvery large problems. Particularly, we show the linear regression, logisticregression and Poisson regression with $L_1$ regularization in detail asspecific examples of robust and sparse GLM. In numerical experiments and realdata analysis, the proposed method outperformed comparative methods.

Robust and Sparse Regression in GLM by Stochastic Optimization