PARABOLA_FIT

Warning

Deprecated since version 0.11.0.

This functionality was experimental. Parabola fits don’t appear to be very realiable at the moment and may be removed or significantly reworked in the future. Use at your own risk. Perform an error calculation for more reliable 1D \(R\)-factor data.

PARABOLA_FIT allows fitting the \(R\)-factor data over the N-dimensional space of fit parameter values with a paraboloid.

Default: PARABOLA_FIT = off

Syntax:

PARABOLA_FIT = type linearregression       ! set the regression method to linear regression
PARABOLA_FIT = type lasso, alpha 1e-5      ! set the regression method to Lasso, with weight 1e-5 for the penalty function
PARABOLA_FIT = type linear, localize 0.25  ! set the regression method to linear regression, use only the data points within in 1/4 of the displacement ranges, near the best known configuration.
PARABOLA_FIT = off                         ! turn the parabola fit off entirely (may improve search performance)

Acceptable values: see below for each flag.

Generally, input is expected in the form flag value, where the different flags and allowed values are described below. Values for the different flags can be set in one line with comma separation, as in the examples above. Alternatively, you can set different flags by having multiple lines PARABOLA_FIT = flag value.

The paraboloid model fits weights for all the independent parameters x, the x^2, and the mixed terms x_i*x_j, as well as one bias term.

type

The regression method to be used.

Acceptable values (not case sensitive): linear / linearregression, ridge, lasso, elasticnet

Regression methods are imported from the sklearn.linear_model module. A brief description is given here, but you can find more detailed information on the documentation pages: LinearRegression, Ridge, ElasticNet, Lasso, as well as this overview page

  • Linear regression: Unbiased least-squares fit.

  • Ridge: Least-squares fit with a penalty term on the sum over the squares of weights w1_i and w2_i. This helps prevent overfitting, but does not artificially sparsen the number of used parameters.

  • Lasso: Least-squares fit with a penalty term on the sum over the absolute values of the weights w1_i and w2_i. This tends to select a solution with as few non-zero weights as possible.

  • Elastic Net: Linear combination of the Lasso and Ridge methods.

Note that for all methods except ordinary linear regression, the penalty term affects not only the curvature of the parabola, but also the position of the minimum, as this is given by the w1_i * x_i term. Fitting is performed with the parameter values centered around the current best configuration (i.e., the combination yielding the lowest \(R\)-factor value in the search so far), so Ridge, Lasso and Elastic Net will all favour solutions close to the best known configuration.

alpha

Acceptable values: positive float.

The prefactor for the penalty term of the ridge, lasso, and elastic net methods (see above). If linear regression is used, alpha will remain unused. Note that all methods listed above become ordinary linear regression for alpha = 0.