# Singular Ridge Regression with Homoscedastic Residuals: Generalization Error with Estimated Parameters

@article{Grigoryeva2016SingularRR, title={Singular Ridge Regression with Homoscedastic Residuals: Generalization Error with Estimated Parameters}, author={Lyudmila Grigoryeva and Juan-Pablo Ortega}, journal={arXiv: Machine Learning}, year={2016} }

This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the time of parameter estimation. The paper provides explicit formulas for those errors. Unlike other classical references in this setup, our results take place in a fully singular setup that does not assume the existence of a solution for the non-regularized… Expand

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Nonlinear Memory Capacity of Parallel Time-Delay Reservoir Computers in the Processing of Multidimensional Signals

- Medicine, Computer Science
- Neural Computation
- 2016

An approximating reservoir model is presented in frameworks that provides an explicit functional link between the reservoir architecture and its performance in the execution of a specific task, and the inference properties of the ridge regression estimator in the multivariate context are used to assess the impact of finite sample training on the decrease of the reservoir capacity. Expand

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