Zobrazeno 1 - 10
of 1 369
pro vyhledávání: '"ALONSO, DANIEL"'
Autor:
Chen, Jiaheng, Sanz-Alonso, Daniel
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 precision and the observations, we show that the sample complexity scales
Externí odkaz:
http://arxiv.org/abs/2412.08820
The aim of these notes 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 primarily aimed at researchers from inverse problems and/or data as
Externí odkaz:
http://arxiv.org/abs/2410.10523
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an unordered sparsity
Externí odkaz:
http://arxiv.org/abs/2408.02109
Autor:
Al-Ghattas, Omar, Sanz-Alonso, Daniel
This paper studies sparse covariance operator estimation for nonstationary Gaussian processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the sample
Externí odkaz:
http://arxiv.org/abs/2405.18562
Autor:
Sanz-Alonso, Daniel, Al-Ghattas, Omar
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 an exciting subject for mathematical statisticians and computational an
Externí odkaz:
http://arxiv.org/abs/2405.16359
Modern data-driven surrogate models for weather forecasting provide accurate short-term predictions but inaccurate and nonphysical long-term forecasts. This paper investigates online weather prediction using machine learning surrogates supplemented w
Externí odkaz:
http://arxiv.org/abs/2405.13180
The accurate characterisation of energy exchanges between nanoscale quantum systems and their environments is of paramount importance for quantum technologies, and central to quantum thermodynamics. Here, we show that, in order to accurately approxim
Externí odkaz:
http://arxiv.org/abs/2403.13776
Autor:
Kim, Hwanwoo, Sanz-Alonso, Daniel
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 algorithms retain the ease of implementation of the classical GP-UCB al
Externí odkaz:
http://arxiv.org/abs/2401.17037
Autor:
Sanz-Alonso, Daniel, Waniorek, Nathan
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bo
Externí odkaz:
http://arxiv.org/abs/2401.03074
Autor:
Sanz-Alonso, Daniel, Yang, Ruiyi
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the
Externí odkaz:
http://arxiv.org/abs/2312.09225