Paper introduces RKHM and KME for richer data analysis.
problem Lack of rich data structures in kernel methods.
method Proposes RKHM and KME for functional data analysis.
result RKHM captures structural properties in functional data.
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5 results for “RKHM”
Paper introduces RKHM for more explicit variable structures analysis.
problem Explicitly analyzing structures among variables.
method Orthonormal systems in Hilbert -modules, RKHM.
result Theoretical and practical procedures for RKHM orthonormalization.
Deep learning framework for kernel methods using RKHM and Perron-Frobenius operators.
problem Kernel methods in deep learning with potential overfitting issues.
method Combining RKHM and Perron-Frobenius operator to derive a new Rademacher bound and analyze deep kernel methods.
result Theoretical interpretation of benign overfitting and milder dependency on output dimension.
New approach to supervised learning in RKHS and vvRKHS using -algebras.
problem Traditional supervised learning in RKHS and vvRKHS.
method Generalizing supervised learning to RKHM using -algebras.
result Constructing RKHMs with enhanced representation power.
Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.
problem Analyzing complex multivariate distributions and quantum mechanics.
method Generalizes kernel mean embedding to von Neumann-algebra-valued measures in reproducing kernel Hilbert modules.
result Injectivity and universality of the generalized KME are confirmed.