Autocorrelations were analyzed by a multi-tau regularized-fit procedure to obtain the distribution of decay rates.
By comparing the medians of the distributions we see that in almost all cases the non-regularized models overfit the calibration data, i.e. the non-regularized models fit well the calibration data, but do not predict cross-validation data as well as the regularized models.
For discrete ill-conditioned problems, this plot displays an 'L-shape' with a corner point, where a certain balance between the regularized solution and fit to the data is achieved (Hansen et al. 2007).
Inverting this convolution is a numerically ill-posed problem requiring regularized least squares fit or related algorithms (Dembo and Wang, 1999; Merkel et al., 2007; Schwarz et al., 2002).
In our study, a flexible model allowing distinct daily variation patterns for different road types (frc) together with regularized least-squares fitting dominates all its competitors.
It is a convenient graphical tool for displaying the trade-off between the size of a regularized solution and its fit to the given data, as the regularization parameter varies.
LAMs are fitted using regularized estimation, i.e. the regression coefficients in the components are penalized to arrive at a compromise between model fit and smoothness of the fitted curve.
All GLM results shown in the "Results and discussion" section are for L2-regularized logistic regression models fit with the default settings for this R package and an L2-regularization cost parameter C equal to the ratio of negative to positive class labels.
The models are fitted using regularized least-squares.
The hyper-parameter (or regularization parameter) λ is a critical value which measures the trade-off between a good fit and a regularized solution.
Among many regularization methods, Tikhonov regularization is the most commonly used method of regularization which tries to obtain regularized solution to Ax = b by choosing x to fit data b in least-square sense, but penalize solutions of large norm [49, 50].
