32 citations · 183 across the 54 of their papers we have counts for
9 papers · 1 filter
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…
Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration
Hwanwoo Kim, Daniel Sanz-Alonso
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new a…