AB-SID-iVAR enables Gaussian process active learning for self-induced Boltzmann distributions by closed-form approximation of the target, with high-probability error vanishing guarantees and empirical gains on PES and drug discovery tasks.
arXiv preprint arXiv:2506.17366 , year=
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abstract
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences between them are reviewed for fundamental topics such as regression, interpolation, numerical integration, distributional discrepancies, and statistical dependence, as well as for sample path properties of Gaussian processes. A unifying perspective for these equivalences is established, based on the equivalence between the Gaussian Hilbert space and the RKHS. The monograph serves as a basis to bridge many other methods based on Gaussian processes and reproducing kernels, which are developed in parallel by the two research communities.
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A unified Bayesian framework based on derivative matching shows that diverse Gaussian process methods for differential equations are instances of a common probabilistic structure.
Bayesian optimization on low-dimensional Negishi-weight equilibrium manifolds enables reliable computation and probabilistic certification of optimal carbon taxes in a calibrated heterogeneous-agent climate economy.
Novel non-asymptotic uniform error bounds are derived for kernel regression under broad classes of non-Gaussian noise distributions that include correlated cases.
citing papers explorer
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Active Learning for Gaussian Process Regression Under Self-Induced Boltzmann Weights
AB-SID-iVAR enables Gaussian process active learning for self-induced Boltzmann distributions by closed-form approximation of the target, with high-probability error vanishing guarantees and empirical gains on PES and drug discovery tasks.
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A unified perspective of Gaussian process approximation for differential equations
A unified Bayesian framework based on derivative matching shows that diverse Gaussian process methods for differential equations are instances of a common probabilistic structure.
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Bayesian Optimization on the Equilibrium Manifold
Bayesian optimization on low-dimensional Negishi-weight equilibrium manifolds enables reliable computation and probabilistic certification of optimal carbon taxes in a calibrated heterogeneous-agent climate economy.
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On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise
Novel non-asymptotic uniform error bounds are derived for kernel regression under broad classes of non-Gaussian noise distributions that include correlated cases.
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