ML EPS REG: Difference between revisions

Revision as of 17:54, 4 January 2022

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 $\sigma^{2}_{\mathrm{v}}$ 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

${\displaystyle \frac{\lambda_{k}}{+1/\sigma^{2}_{\mathrm{w}}} }$

Related Tags and Sections

ML_LMLFF, ML_IALGO_LINREG, ML_IREG, ML_SIGV0, ML_SIGW0

Examples that use this tag

@@ Line 3: / Line 3: @@
 Description: Threshold for the eigenvalues of the covariance matrix in the evidence approximation.
 ----
-This threshold is used to determine which eigenvalues <math>\lambda_{k}</math> of the covariance matrix <math>\mathbf{\Phi}^{\mathrm{T}}\mathbf{\Phi}/\sigma^{2}_{\mathrm{v}}</math> are used in the optimization of the regularization parameters <math>\sigma^{2}_{\mathrm{w}}</math> and <math>\sigma^{2}_{\mathrm{v}</math> determined by the following equations
+This threshold is used to determine which eigenvalues <math>\lambda_{k}</math> of the covariance matrix <math>\mathbf{\Phi}^{\mathrm{T}}\mathbf{\Phi}/\sigma^{2}_{\mathrm{v}}</math> are used in the optimization of the regularization parameters <math>\sigma^{2}_{\mathrm{w}}</math> and <math>\sigma^{2}_{\mathrm{v}}</math> determined by the following equations
 <math>
@@ Line 18: / Line 18: @@
 All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are contributing by the above equations. All eigenvalues not satisfying that relation are contributing as
 <math>
 \frac{\lambda_{k}}{+1/\sigma^{2}_{\mathrm{w}}}