32 citations · 183 across the 54 of their papers we have counts for
59 papers
Time-uniform accuracy of ensemble Kalman filters with localization
Xiaoou Cheng, Daniel Sanz-Alonso, Nathan Waniorek
This paper establishes time-uniform accuracy guarantees for deterministic square-root ensemble Kalman filters in linear--Gaussian state-space models under perfect-model dynamics. F…
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…
Concentration Inequalities for Sample Cross-Covariances
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vector…
Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms
Melissa Adrian, Daniel Sanz-Alonso, Rebecca Willett
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tun…
Convergence Rates for Learning Pseudo-Differential Operators
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physic…
Bayesian Optimization on Networks
Wenwen Li, Daniel Sanz-Alonso, Ruiyi Yang
This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black b…
Elliptic Bayesian Inverse Problems on Metric Graphs
David Bolin, Wenwen Li, Daniel Sanz-Alonso
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connect…
On the Estimation of Gaussian Moment Tensors
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso
This paper studies two estimators for Gaussian moment tensors: the standard sample moment estimator and a plug-in estimator based on Isserlis's theorem. We establish dimension-free…
Functional Multi-Reference Alignment via Deconvolution
Omar Al-Ghattas, Anna Little, Daniel Sanz-Alonso +1
This paper studies the multi-reference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection…
Sharp Concentration of Simple Random Tensors II: Asymmetry
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes sharp concentration inequalities for simple random tensors. Our theory unveils a phenomenon that arises only for asymmetric tensors of order when…
Sharp Concentration of Simple Random Tensors
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of…
Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems
Daniel Sanz-Alonso, Nathan Waniorek
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble…
Precision and Cholesky Factor Estimation for Gaussian Processes
Jiaheng Chen, Daniel Sanz-Alonso
This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the prec…
Machine Learning for Inverse Problems and Data Assimilation
Eviatar Bach, Ricardo Baptista, Daniel Sanz-Alonso +1
The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is…
Optimal Estimation of Structured Covariance Operators
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso +1
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly…
A First Course in Monte Carlo Methods
Daniel Sanz-Alonso, Omar Al-Ghattas
This is a concise mathematical introduction to Monte Carlo methods, a rich family of algorithms with far-reaching applications in science and engineering. Monte Carlo methods are a…
Covariance Operator Estimation via Adaptive Thresholding
Omar Al-Ghattas, Daniel Sanz-Alonso
This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covari…
Data Assimilation with Machine Learning Surrogate Models: A Case Study with FourCastNet
Melissa Adrian, Daniel Sanz-Alonso, Rebecca Willett
Modern data-driven surrogate models for weather forecasting provide accurate short-term predictions but inaccurate and nonphysical long-term forecasts. This paper investigates onli…
Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint
Daniel Sanz-Alonso, Nathan Waniorek
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizer…