678 citations · 1.5k across the 30 of their papers we have counts for
36 papers
Resolvable Fourier Degree and Minimax Estimation on theBoolean Hypercube
G{é}rard Biau
We study high-dimensional nonparametric regression on the Boolean hypercube \(\{0,1\}^d\), from a sample of size \(n\), under a Fourier--Sobolev budget, i.e., a bound \(B\) on the…
Nonparametric Regression on Fixed-Cardinality Subsets:Minimax Risk and Random-Design Effects
G{é}rard Biau
We study regression with subsets as covariates. The response is an unknown function of the input subset, and observations consist of noisy evaluations at uniformly sampled subsets,…
Influence as soft sparsity: Estimation of monotone functions on
Gérard Biau
We study the problem of estimating a monotone function from noisy observations at uniformly random vertices of the Boolean hypercube. As a measure of complexi…
A Geometry-Aware Residual Correction of Hagan's SABR Implied Volatility Formula
Adil Reghai, Lama Tarsissi, Gérard Biau +1
This paper proposes a hybrid methodology to improve the approximation of SABR (Stochastic Alpha Beta Rho) implied volatility by combining analytical structure with machine learning…
On the convergence of PINNs
Nathan Doumèche, Gérard Biau, Claire Boyer
Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good p…
The insertion method to invert the signature of a path
Adeline Fermanian, Jiawei Chang, Terry Lyons +1
The signature is a representation of a path as an infinite sequence of its iterated integrals. Under certain assumptions, the signature characterizes the path, up to translation an…