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# Kernel Ridge Regression

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  1. Journal of Chemical Theory and Computation

    A minimal auxiliary basis fills in the Hartree–Fock CBS limit: one minimal-basis calculation plus kernel ridge regression cuts error to 7.03 mHa

    Approaching the complete basis set (CBS) limit in quantum chemistry usually means several mid-quality calculations plus extrapolation. Here a single Hartree–Fock calculation in the minimal pcseg-0 basis is augmented with an optimized, minimal complementary auxiliary basis set (CABS) singles correction, and kernel ridge regression learns the residual. On GDB-BSIE, CABSmin/pcseg-0 with atomic detrending gives an RMSE of 7.03 mHa against RHF/cc-pV5Z, at about 16% of the cost of a cc-pVDZ single point.

    University of Kassel
    Nicolas Grimblat（First author）Guido Falk von Rudorff（Corresponding author）
    Minimal CABS Complete Basis Set EstimationKernel Ridge RegressionDelta Machine LearningAutoKRRChebyshev Polynomial Approximation of Local Kernels
  2. arXiv

    Discount-curve fits must survive no-arbitrage drift: only the Segal–Bargmann kernel family keeps kernel ridge regression states drift-invariant

    Discount curves are usually estimated day by day with kernel ridge regression, but a good daily fit does not guarantee that the estimated curves can serve as states of a continuous-time arbitrage-free model. This work asks whether the finite-dimensional hypothesis space of kernel ridge regression is invariant under the risk-neutral drift of the discount curve for every grid of cash flow dates. Apart from kernels whose Hilbert space has dimension at most two, only the family built from the Segal–Bargmann kernel qualifies; for that kernel the estimate is an affine combination of flat discount curves, and the drift-invariant subspaces that allow dimension reduction correspond to sub-grids of the cash flow dates.

    Andreas Celary（First author）
    Kernel Ridge RegressionDiscount CurveDrift-Invariance of Hypothesis SpacesTerm Structure ModelsSegal–Bargmann Kernel
  3. arXiv

    Kernel solvers stop choking on preconditioner memory: sketched blocks push model size to ten million parameters with better accuracy

    The preconditioner memory of kernel ridge regression no longer grows with model size, letting Bloks scale to ten million parameters and match or beat state-of-the-art accuracy on large-scale benchmarks such as Higgs.

    University of GenoaUniversité Côte d'AzurUniversity of Milano-BicoccaCentre National de la Recherche ScientifiqueInstitut national de recherche en sciences et technologies du numérique
    Giordano Vitale（First author）
    BloksSketched Block Jacobi PreconditionerKernel Ridge RegressionPreconditioned Conjugate GradientNyström Approximation

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