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

In data analysis problems where we are not able to rely on distributionalassumptions, what types of inference guarantees can still be obtained? Manypopular methods, such as holdout methods, cross-validation methods, andconformal prediction, are able to provide distribution-free guarantees forpredictive inference, but the problem of providing inference for the underlyingregression function (for example, inference on the conditional mean$\mathbb{E}[Y|X]$) is more challenging. In the setting where the features $X$are continuously distributed, recent work has established that any confidenceinterval for $\mathbb{E}[Y|X]$ must have non-vanishing width, even as samplesize tends to infinity. At the other extreme, if $X$ takes only a small numberof possible values, then inference on $\mathbb{E}[Y|X]$ is trivial to achieve.In this work, we study the problem in settings in between these two extremes.We find that there are several distinct regimes in between the finite settingand the continuous setting, where vanishing-width confidence intervals areachievable if and only if the effective support size of the distribution of $X$is smaller than the square of the sample size.

Distribution-free inference for regression: discrete, continuous, and in between