no code implementations • 30 Jan 2024 • Hwanwoo Kim, Daniel Sanz-Alonso
This paper studies Bayesian optimization with noise-free observations.
no code implementations • 14 Dec 2023 • Daniel Sanz-Alonso, Ruiyi Yang
Gaussian process regression is a classical kernel method for function estimation and data interpolation.
1 code implementation • 17 Aug 2023 • Omar Al Ghattas, Jiajun Bao, Daniel Sanz-Alonso
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations.
1 code implementation • 27 Jan 2023 • Yuming Chen, Daniel Sanz-Alonso, Rebecca Willett
This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system.
no code implementations • 20 Oct 2022 • Hwanwoo Kim, Daniel Sanz-Alonso, Ruiyi Yang
We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective.
no code implementations • 5 Aug 2022 • Omar Al Ghattas, Daniel Sanz-Alonso
Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data.
no code implementations • 3 Jul 2022 • Nicolas García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
In recent decades, science and engineering have been revolutionized by a momentous growth in the amount of available data.
no code implementations • 26 Nov 2021 • Shiv Agrawal, Hwanwoo Kim, Daniel Sanz-Alonso, Alexander Strang
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems.
1 code implementation • 16 Jul 2021 • Yuming Chen, Daniel Sanz-Alonso, Rebecca Willett
Data assimilation is concerned with sequentially estimating a temporally-evolving state.
no code implementations • 26 Aug 2020 • Daniel Sanz-Alonso, Ruiyi Yang
In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption.
no code implementations • 6 Apr 2019 • Nicolas Garcia Trillos, Daniel Sanz-Alonso, Ruiyi Yang
Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism.
no code implementations • 29 Jan 2019 • Nicolas Garcia Trillos, Zach Kaplan, Daniel Sanz-Alonso
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization.
no code implementations • 20 Oct 2017 • Nicolas Garcia Trillos, Zachary Kaplan, Thabo Samakhoana, Daniel Sanz-Alonso
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework.
no code implementations • 22 Jun 2017 • Nicolas Garcia Trillos, Daniel Sanz-Alonso
We consider the problem of recovering a function input of a differential equation formulated on an unknown domain $M$.