ML EPS REG

ML_EPS_REG = [real]
Default: ML_EPS_REG = 1E-14 

Description: Initial value for the threshold of the eigenvalues of the covariance matrix in the evidence approximation.

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This threshold is used to determine which eigenvalues $\lambda _{k}$ of the covariance matrix $\mathbf {\Phi } ^{\mathrm {T} }\mathbf {\Phi } /\sigma _{\mathrm {v} }^{2}$ are used in the optimization of the regularization parameters $\sigma _{\mathrm {w} }^{2}$ and $\sigma _{\mathrm {v} }^{2}$ determined by the following equations

$\sigma _{\mathrm {w} }^{2}={\frac {|\mathbf {\bar {w}} |^{2}}{\gamma }},$

$\sigma _{\mathrm {v} }^{2}={\frac {|\mathbf {T} -\mathbf {\phi } \mathbf {\bar {w}} |^{2}}{M-\gamma }},$

$\gamma =\sum \limits _{k=1}^{N_{\mathrm {B} }}{\frac {\lambda _{k}}{\lambda _{k}+1/\sigma _{\mathrm {w} }^{2}}}$.

All eigenvalues satisfying $\lambda _{i}/\lambda _{\mathrm {max} }$ > ML_EPS_REG are contributing by the above equations.

The smaller the value of ML_EPS_REG the smaller the error of the fit. But at the same time the effects of over fitting increase. We determined empirically that the default of ML_EPS_REG=1E-14 is safe in most cases. If a user desires higher accuracy of the force field, the user can try to set ML_EPS_REG=1E-15 or lower, but the user should very carefully monitor the convergence of the calculations as described below.

If at any point in the iterations of the Evidence Approximation of the square of the quadratic norm of errors (eigth column of REGR/REGRF in ML_LOGFILE) gets too big (more than 1.2 times larger than before) then ML_EPS_REG is doubled. Whenever the regression doesn't converge within 10 steps ML_EPS_REG is increased by a factor of 4. The counter for the 10 strucures is reset whenever ML_EPS_REG is changed. The maximum allowed iteration steps are 50 (the number of each step is the second entry of REGR/REGRF in ML_LOGFILE), but when this value is reached no force field is created and there is most likely something seriously wrong in the calculation.

The seventh entry of REGR/REGRF in the ML_LOGFILE shows the ratio of the regularization ($\sigma _{v}^{2}/\sigma _{w}^{2}$) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), it is an indication that the cap for the current ML_EPS_REG is reached. That means that regularization becomes crucial.

Related Tags and Sections

ML_LMLFF, ML_IALGO_LINREG, ML_IREG, ML_SIGV0, ML_SIGW0

Examples that use this tag

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