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Found 6 papers, 2 papers with code
Rigorous dynamical mean field theory for stochastic gradient descent methods
We prove closed-form equations for the exact high-dimensional asymptotics of a family of first order gradient-based methods, learning an estimator (e. g. M-estimator, shallow neural network, ...) from observations on Gaussian data with empirical risk minimization.
Thresholds of descending algorithms in inference problems
We review recent works on analyzing the dynamics of gradient-based algorithms in a prototypical statistical inference problem.
Precise asymptotics for phase retrieval and compressed sensing with random generative priors
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix.
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
We also show that for a large set of parameters, an iterative algorithm called approximate message-passing is Bayes optimal.
Phase Transitions in Sparse PCA
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data.
Model Selection for Degree-corrected Block Models
We present the first principled and tractable approach to model selection between standard and degree-corrected block models, based on new large-graph asymptotics for the distribution of log-likelihood ratios under the stochastic block model, finding substantial departures from classical results for sparse graphs.
