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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In many high-dimensional estimation problems the main task consists inminimizing a cost function, which is often strongly non-convex when scanned inthe space of parameters to be estimated. A standard solution to flatten thecorresponding rough landscape consists in summing the losses associated todifferent data points and obtain a smoother empirical risk. Here we propose acomplementary method that works for a single data point. The main idea is thata large amount of the roughness is uncorrelated in different parts of thelandscape. One can then substantially reduce the noise by evaluating anempirical average of the gradient obtained as a sum over many randomindependent positions in the space of parameters to be optimized. We present analgorithm, called Averaged Gradient Descent, based on this idea and we apply itto tensor PCA, which is a very hard estimation problem. We show that AveragedGradient Descent over-performs physical algorithms such as gradient descent andapproximate message passing and matches the best algorithmic thresholds knownso far, obtained by tensor unfolding and methods based on sum-of-squares.

How to iron out rough landscapes and get optimal performances: Averaged Gradient Descent and its application to tensor PCA