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

We consider the problem of streaming kernel regression, when the observationsarrive sequentially and the goal is to recover the underlying mean function,assumed to belong to an RKHS. The variance of the noise is not assumed to beknown. In this context, we tackle the problem of tuning the regularizationparameter adaptively at each time step, while maintaining tight confidencebounds estimates on the value of the mean function at each point. To this end,we first generalize existing results for finite-dimensional linear regressionwith fixed regularization and known variance to the kernel setup with aregularization parameter allowed to be a measurable function of pastobservations. Then, using appropriate self-normalized inequalities we buildupper and lower bound estimates for the variance, leading to Bersntein-likeconcentration bounds. The later is used in order to define the adaptiveregularization. The bounds resulting from our technique are valid uniformlyover all observation points and all time steps, and are compared against theliterature with numerical experiments. Finally, the potential of these tools isillustrated by an application to kernelized bandits, where we revisit theKernel UCB and Kernel Thompson Sampling procedures, and show the benefits ofthe novel adaptive kernel tuning strategy.

Streaming kernel regression with provably adaptive mean, variance, and regularization