25 papers
Non-asymptotic Analysis of Matérn Regression: The Roles of Target and Kernel Lengthscales
Daniel Sanz-Alonso
Theoretical guarantees for kernel regression are typically formulated in terms of smoothness, but practical accuracy depends critically on how the design resolution compares with t…
Sharp Frobenius-Norm Concentration for Sample Moment Tensors
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes sharp dimension-free Frobenius-norm concentration inequalities for sample moment tensors. Our bounds are optimal over the sub-Gaussian class, while for Gauss…
From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan Waniorek
We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time- solution operators of dissipative evolution equations. The analysis build…
Optimal Multiscale Learning of Linear Operators
Jiaheng Chen, Daniel Sanz-Alonso
We study the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy input-output data. In wavelet coordinates, the problem is r…
Continuous Data Assimilation with Learned Surrogate Dynamics
Wenwen Li, Daniel Sanz-Alonso
Continuous data assimilation seeks to estimate the state of a dynamical system from partial observations. In many applications, however, the state dynamics are unknown or prohibiti…
Functional Multi-Target Detection via Bispectrum Inversion
Anna Little, Daniel Sanz-Alonso, Mikhail Sweeney +1
This paper develops a functional theory for multi-target detection, where a compactly supported signal is recovered from a single noisy observation containing many unknown translat…