ML EPS REG

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

Description: Threshold for the eigenvalues of the covariance matrix in the evidence approximation.

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

[math]\displaystyle{ \sigma^{2}_{\mathrm{w}}=\frac{|\mathbf{\bar{w}}|^{2}}{\gamma}, }[/math]

[math]\displaystyle{ \sigma^{2}_{\mathrm{v}}=\frac{|\mathbf{T}-\mathbf{\phi}\mathbf{\bar{w}}|^{2}}{M-\gamma}, }[/math]

[math]\displaystyle{ \gamma=\sum\limits_{k=1}^{N_{\mathrm{B}}} \frac{\lambda_{k}}{\lambda_{k}+1/\sigma^{2}_{\mathrm{w}}} }[/math].

All eigenvalues satisfying [math]\displaystyle{ \lambda_{i} / \lambda_{\mathrm{max}} }[/math] > ML_EPS_REG are contributing by the above equations.

The seventh entry of REGR/REGRF in the ML_LOGFILE shows the ratio of the regularization ([math]\displaystyle{ \sigma_{v}^{2}/ \sigma_{w}^{2} }[/math]) 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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