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 consider covariance estimation of any subgaussian distribution fromfinitely many i.i.d. samples that are quantized to one bit of information perentry. Recent work has shown that a reliable estimator can be constructed ifuniformly distributed dithers on $[-\lambda,\lambda]$ are used in the one-bitquantizer. This estimator enjoys near-minimax optimal, non-asymptotic errorestimates in the operator and Frobenius norms if $\lambda$ is chosenproportional to the largest variance of the distribution. However, thisquantity is not known a-priori, and in practice $\lambda$ needs to be carefullytuned to achieve good performance. In this work we resolve this problem byintroducing a tuning-free variant of this estimator, which replaces $\lambda$by a data-driven quantity. We prove that this estimator satisfies the samenon-asymptotic error estimates - up to small (logarithmic) losses and aslightly worse probability estimate. We also show that by using refineddata-driven dithers that vary per entry of each sample, one can construct anestimator satisfying the same estimation error bound as the sample covarianceof the samples before quantization -- again up logarithmic losses. Our proofsrely on a new version of the Burkholder-Rosenthal inequalities for matrixmartingales, which is expected to be of independent interest.

Tuning-free one-bit covariance estimation using data-driven dithering