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 model averaging problem is to average multiple models to achieve a prediction accuracy not much worse than that of the best single model in terms of mean-squared error. It is known that if the models are misspecified, model averaging is superior to model selection. Specifically, let <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> be the sample size, then the worst case regret of the former decays at a rate of <inline-formula> <tex-math notation="LaTeX">$O(1/n)$ </tex-math></inline-formula>, whereas the worst case regret of the latter decays at a rate of <inline-formula> <tex-math notation="LaTeX">$O(1/\sqrt {n})$ </tex-math></inline-formula>. The recently proposed <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-aggregation algorithm solves the model averaging problem with the optimal regret of <inline-formula> <tex-math notation="LaTeX">$O(1/n)$ </tex-math></inline-formula> both in expectation and in deviation; however, it suffers from two limitations: 1) for continuous dictionary, the proposed greedy algorithm for solving <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-aggregation is not applicable and 2) the formulation of <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-aggregation appears <italic>ad hoc</italic> without clear intuition. This paper examines a different approach to model averaging by considering a Bayes estimator for deviation optimal model averaging by using exponentiated least squares loss. We establish a primal-dual relationship of this estimator and that of <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-aggregation and propose new algorithms that satisfactorily resolve the above-mentioned limitations of <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-aggregation.

Bayesian Model Averaging With Exponentiated Least Squares Loss