4 papers · 1 filter
On the estimation rate of Bayesian PINN for inverse problems
Yi Sun, Debarghya Mukherjee, Yves Atchade
Solving partial differential equations (PDEs) and their inverse problems using Physics-informed neural networks (PINNs) is a rapidly growing approach in the physics and machine lea…
Minimax Optimal rates of convergence in the shuffled regression, unlinked regression, and deconvolution under vanishing noise
Cecile Durot, Debarghya Mukherjee
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regres…
Trade-off Between Dependence and Complexity for Nonparametric Learning -- an Empirical Process Approach
Nabarun Deb, Debarghya Mukherjee
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many…
Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension
Sohom Bhattacharya, Jianqing Fan, Debarghya Mukherjee
Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regr…