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07/21/2023
Sparse Cholesky factorization by greedy conditional selection
Dense kernel matrices resulting from pairwise evaluations of a kernel fu...
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06/01/2023
A Mini-Batch Method for Solving Nonlinear PDEs with Gaussian Processes
Gaussian processes (GPs) based methods for solving partial differential ...
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04/26/2023
Kernel Methods are Competitive for Operator Learning
We present a general kernel-based framework for learning operators betwe...
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12/14/2022
Multiclass classification utilising an estimated algorithmic probability prior
Methods of pattern recognition and machine learning are applied extensiv...
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09/24/2022
One-Shot Learning of Stochastic Differential Equations with Computational Graph Completion
We consider the problem of learning Stochastic Differential Equations of...
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09/21/2022
Gaussian Process Hydrodynamics
We present a Gaussian Process (GP) approach (Gaussian Process Hydrodynam...
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06/03/2022
Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics
This paper introduces algorithms to select/design kernels in Gaussian pr...
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12/08/2021
Aggregation of Pareto optimal models
In statistical decision theory, a model is said to be Pareto optimal (or...
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11/25/2021
Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series
A simple and interpretable way to learn a dynamical system from data is ...
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11/23/2021
Aggregation of Models, Choices, Beliefs, and Preferences
A natural notion of rationality/consistency for aggregating models is th...
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10/20/2021
Computational Graph Completion
We introduce a framework for generating, organizing, and reasoning with ...
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10/11/2021
Sparse recovery of elliptic solvers from matrix-vector products
In this work, we show that solvers of elliptic boundary value problems i...
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08/24/2021
Uncertainty Quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball
There are essentially three kinds of approaches to Uncertainty Quantific...
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03/18/2021
Decision Theoretic Bootstrapping
The design and testing of supervised machine learning models combine two...
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08/10/2020
Do ideas have shape? Plato's theory of forms as the continuous limit of artificial neural networks
We show that ResNets converge, in the infinite depth limit, to a general...
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07/09/2020
Learning dynamical systems from data: a simple cross-validation perspective
Regressing the vector field of a dynamical system from a finite number o...
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06/17/2020
Competitive Mirror Descent
Constrained competitive optimization involves multiple agents trying to ...
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04/29/2020
Sparse Cholesky factorization by Kullback-Leibler minimization
We propose to compute a sparse approximate inverse Cholesky factor L of ...
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02/19/2020
Deep regularization and direct training of the inner layers of Neural Networks with Kernel Flows
We introduce a new regularization method for Artificial Neural Networks ...
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07/19/2019
Kernel Mode Decomposition and programmable/interpretable regression networks
Mode decomposition is a prototypical pattern recognition problem that ca...
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08/13/2018
Kernel Flows: from learning kernels from data into the abyss
Learning can be seen as approximating an unknown function by interpolati...
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05/28/2018
De-noising by thresholding operator adapted wavelets
Donoho and Johnstone proposed a method from reconstructing an unknown sm...
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03/31/2017
Universal Scalable Robust Solvers from Computational Information Games and fast eigenspace adapted Multiresolution Analysis
We show how the discovery of robust scalable numerical solvers for arbit...
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06/24/2016
Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients
Implicit schemes are popular methods for the integration of time depende...
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03/11/2015