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

In the pooled data problem, the goal is to identify the categories associatedwith a large collection of items via a sequence of pooled tests. Each pooledtest reveals the number of items of each category within the pool. We study anapproximate message passing (AMP) algorithm for estimating the categories andrigorously characterize its performance, in both the noiseless and noisysettings. For the noiseless setting, we show that the AMP algorithm isequivalent to one recently proposed by El Alaoui et al. Our results provide arigorous version of their performance guarantees, previously obtained vianon-rigorous techniques. For the case of pooled data with two categories, knownas quantitative group testing (QGT), we use the AMP guarantees to computeprecise limiting values of the false positive rate and the false negative rate.Though the pooled data problem and QGT are both instances of estimation in alinear model, existing AMP theory cannot be directly applied since the designmatrices are binary valued. The key technical ingredient in our result is arigorous analysis of AMP for generalized linear models defined via generalizedwhite noise design matrices. This result, established using a recentuniversality result of Wang et al., is of independent interest. Our theoreticalresults are validated by numerical simulations. For comparison, we proposeestimators based on convex relaxation and iterative thresholding, withoutproviding theoretical guarantees. Our simulations indicate that AMP outperformsthe convex programming estimator for a range of QGT scenarios, but the convexprogram performs better for pooled data with three categories.

Approximate Message Passing with Rigorous Guarantees for Pooled Data and Quantitative Group Testing