Researchers have analyzed kernel ridge regression under anisotropic Gaussian data, specifically examining how a power-law decay in the input covariance affects learning curves. The study reveals that weak anisotropy retains some characteristics of isotropic cases while introducing new dynamics, such as damped variance peaks and bias transitions decoupled from interpolation peaks. For strong anisotropy, the problem's effective dimension becomes constant, and the bias exhibits a sharp transition dependent on the target's decay rate, with results specializing for single-index targets. AI
IMPACT Provides theoretical insights into how input data geometry influences the generalization properties of kernel methods.
RANK_REASON Academic paper detailing theoretical analysis of a machine learning algorithm. [lever_c_demoted from research: ic=1 ai=1.0]
- anisotropy
- arXiv
- Gaussian data
- generalization error
- interpolation peaks
- Kernel Ridge Regression
- kernel spectrum
- polynomial inner-product kernels
- power law
- ridgeless interpolation
- ridge penalty
- single-index targets
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