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 [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. All eigenvalues not satisfying that relation are contributing as
[math]\displaystyle{ \frac{\lambda_{k}}{+1/\sigma^{2}_{\mathrm{w}}} }[/math]
Related Tags and Sections
ML_LMLFF, ML_IALGO_LINREG, ML_IREG, ML_SIGV0, ML_SIGW0