ML IALGO LINREG: Difference between revisions

Revision as of 18:43, 12 October 2021

ML_IALGO_LINREG = [integer]
Default: ML_IALGO_LINREG = 1

Description: This tag determines with which algorithm to solve the system of linear equations in the ridge regression method for machine learning.

In the ridge regression method for machine learning one needs to solve for the unknown weights $\mathbf{w}$ within the following equations

${\displaystyle \mathbf{Y} = \mathbf{\Phi} \mathbf{w}. }$

For more details please see here.

The following options are available to solve for $\mathbf{w}$ :

ML_IALGO_LINREG=1: Bayesian linear regression (see here). Recoomended for NSW $\ge$ 1. Usable with on-the-fly learning.
ML_IALGO_LINREG=2: QR factorization. Usable with NSW=0,1.
ML_IALGO_LINREG=3: Singular value decomposition. Usable with NSW=0,1.
ML_IALGO_LINREG=4: Singular value decomposition with Tikhonov regularization. Usable with NSW=0,1.

In the current implementation the on-the-fly learning algorithm requires to have a probability model included within the regression. So only the Bayesian linear regression method (ML_IALGO_LINREG=1) is usable with this option. All other methods should be used only a single step calculation (NSW=0) to refine the force-field after the force field was trained with {TAG|ML_IALGO_LINREG}}=1. ML_IALGO_LINREG=3 is the most tested for this purpose up to now. It should be also noted that this method is also computationally more demanding that the Bayesian linear regression.

Related Tags and Sections

ML_LMLFF, ML_W1, ML_WTOTEN, ML_WTIFOR, ML_WTSIF, ML_ISTART

Examples that use this tag

@@ Line 13: / Line 13: @@
 The following options are available to solve for <math>\mathbf{w}</math>:
-*{{TAG|ML_IALGO_LINREG}}=1: Bayesian linear regression (see [[Machine learning force field: Theory#Bayesian error estimation|here]]). Usable with {{TAG|NSW}}<math>\ge</math>1.
+*{{TAG|ML_IALGO_LINREG}}=1: Bayesian linear regression (see [[Machine learning force field: Theory#Bayesian error estimation|here]]). Recoomended for {{TAG|NSW}}<math>\ge</math>1. Usable with on-the-fly learning.
 *{{TAG|ML_IALGO_LINREG}}=2: QR factorization. Usable with {{TAG|NSW}}=0,1.
 *{{TAG|ML_IALGO_LINREG}}=3: Singular value decomposition. Usable with {{TAG|NSW}}=0,1.
 *{{TAG|ML_IALGO_LINREG}}=4: Singular value decomposition with Tikhonov regularization. Usable with {{TAG|NSW}}=0,1.
+In the current implementation the on-the-fly learning algorithm requires to have a probability model included within the regression. So only the Bayesian linear regression method ({{TAG|ML_IALGO_LINREG}}=1) is usable with this option. All other methods should be used only a single step calculation ({{TAG|NSW}}=0) to refine the force-field after the force field was trained with {TAG|ML_IALGO_LINREG}}=1. {{TAG|ML_IALGO_LINREG}}=3  is the most tested for this purpose up to now. It should be also noted that this method is also computationally more demanding that the Bayesian linear regression.
 == Related Tags and Sections ==