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.

This threshold is used to determine which eigenvalues $\lambda_{k}$ of the covariance matrix $\mathbf{\Phi}^{\mathrm{T}}\mathbf{\Phi}/\sigma^{2}_{\mathrm{v}}$ are used in the optimization of the regularization parameters $\sigma^{2}_{\mathrm{w}}$ and Failed to parse (Conversion error. Server ("cli") reported: "[INVALID]"): {\displaystyle \sigma^{2}_{\mathrm{v}} determined by the following equations

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

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

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

All eigenvalues satisfying $\lambda_{i} / lambda_{\mathrm{max}}$ > ML_EPS_REG are contributing by the above equations. All eigenvalues not satisfying that relation are contributing as ${\displaystyle \frac{\lambda_{k}}{+1/\sigma^{2}_{\mathrm{w}}} }$