Thresholds of descending algorithms in inference problems

We review recent works [1, 2, 3] on analyzing the dynamics of gradient-based algorithms in a prototypical statistical inference problem. Using methods and insights from the physics of glassy systems, these works showed how to understand quantitatively and qualitatively the performance of gradient-based algorithms. Here we review the key results and their interpretation in nontechnical terms accessible to a wide audience of physicists in the context of related works. PACS numbers: 00.00, 20.00, 42.10 Keywords: analysis of algorithms, statistical inference, spin glasses, machine learning.