Machine Learning based on the Regularized Least Squares (RLS) model requires one to solve a system of linear equations. Direct-solution methods exhibit predictable complexity and storage, but often prove impractical for large-scale problems; iterative methods attain approximate solutions at lower complexities, but heavily depend on learning parameters. The paper shows that applying the properties of Toeplitz matrixes to RLS yields two benefits: first, both the computational cost and the memory space required to train an RLS-based machine reduce dramatically; secondly, timing and storage requirements are defined analytically. The paper proves this result formally for the one-dimensional case, and gives an analytical criterion for an effective approximation in multidimensional domains. The approach validity is demonstrated in several real-world problems involving huge data sets with highly dimensional data
Efficient Approximate Regularized Least Squares by Toeplitz Matrix
GASTALDO, PAOLO;ZUNINO, RODOLFO
2011-01-01
Abstract
Machine Learning based on the Regularized Least Squares (RLS) model requires one to solve a system of linear equations. Direct-solution methods exhibit predictable complexity and storage, but often prove impractical for large-scale problems; iterative methods attain approximate solutions at lower complexities, but heavily depend on learning parameters. The paper shows that applying the properties of Toeplitz matrixes to RLS yields two benefits: first, both the computational cost and the memory space required to train an RLS-based machine reduce dramatically; secondly, timing and storage requirements are defined analytically. The paper proves this result formally for the one-dimensional case, and gives an analytical criterion for an effective approximation in multidimensional domains. The approach validity is demonstrated in several real-world problems involving huge data sets with highly dimensional dataI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.