New framework links generalized splines and Gaussian Processes

This paper introduces a generalized framework for understanding the relationship between minimum mean square error estimators and regularized least-squares fits in linear inverse problems. The research extends this equivalence to infinite-dimensional settings, where generalized splines act as regressors and generalized Gaussian processes on a nuclear space serve as the Gaussian vector counterparts. The formalism utilizes a whitening/regularization operator to define a Hilbert space crucial for characterizing these relationships, encompassing existing methods and revealing new connections, such as between fractional splines and fractional Brownian motion. AI

IMPACT Extends theoretical understanding of estimation techniques relevant to machine learning models.

RANK_REASON The item is an academic paper detailing theoretical advancements in statistics and machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

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• Bayesian Methods
• distribution
• Fractional Brownian motion
• fractional splines
• Gaussian Processes
• Generalized splines on arbitrary graphs
• Hilbert space
• Kailath
• Mandelbrot
• minimum mean square error
• nuclear space
• Regularized least squares
• whitening/regularization operator

• paper
• other

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