292 citations · 770 across the 46 of their papers we have counts for
7 papers · 1 filter
Hebbian learning inspired estimation of the linear regression parameters from queries
Johannes Schmidt-Hieber, Wouter M Koolen
Local learning rules in biological neural networks (BNNs) are commonly referred to as Hebbian learning. [26] links a biologically motivated Hebbian learning rule to a specific zero…
Convergence guarantees for forward gradient descent in the linear regression model
Thijs Bos, Johannes Schmidt-Hieber
Renewed interest in the relationship between artificial and biological neural networks motivates the study of gradient-free methods. Considering the linear regression model with ra…
Dropout Regularization Versus -Penalization in the Linear Model
Gabriel Clara, Sophie Langer, Johannes Schmidt-Hieber
We investigate the statistical behavior of gradient descent iterates with dropout in the linear regression model. In particular, non-asymptotic bounds for the convergence of expect…
A supervised deep learning method for nonparametric density estimation
Thijs Bos, Johannes Schmidt-Hieber
Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into…
Lower bounds for the trade-off between bias and mean absolute deviation
Alexis Derumigny, Johannes Schmidt-Hieber
In nonparametric statistics, rate-optimal estimators typically balance bias and stochastic error. The recent work on overparametrization raises the question whether rate-optimal es…
Codivergences and information matrices
Alexis Derumigny, Johannes Schmidt-Hieber
We propose a new concept of codivergence, which quantifies the similarity between two probability measures relative to a reference probability measure . In the neig…
Interpreting learning in biological neural networks as zero-order optimization method
Johannes Schmidt-Hieber
Recently, significant progress has been made regarding the statistical understanding of artificial neural networks (ANNs). ANNs are motivated by the functioning of the brain, but d…