4 papers · 1 filter
Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes
Zhou Fan, Justin Ko, Bruno Loureiro +2
In many applications of statistical estimation via sampling, one may wish to sample from a high-dimensional target distribution that is adaptively evolving to the samples already s…
Dynamical mean-field analysis of adaptive Langevin diffusions: Propagation-of-chaos and convergence of the linear response
Zhou Fan, Justin Ko, Bruno Loureiro +2
Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift co…
Learning single index model with gradient descent: spectral initialization and precise asymptotics
Yuchen Chen, Yandi Shen
Non-convex optimization plays a central role in many statistics and machine learning problems. Despite the landscape irregularities for general non-convex functions, some recent wo…
Besting Good--Turing: Optimality of Non-Parametric Maximum Likelihood for Distribution Estimation
Yanjun Han, Jonathan Niles-Weed, Yandi Shen +1
When faced with a small sample from a large universe of possible outcomes, scientists often turn to the venerable Good--Turing estimator. Despite its pedigree, however, this estima…