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 $\mathbf {\Phi } ^{\mathrm {T} }\mathbf {\Phi } /\sigma _{\mathrm {v} }^{2}$ 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. All eigenvalues not satisfying that relation are contributing as

${\frac {\lambda _{k}}{1/\sigma _{\mathrm {w} }^{2}}}$

Related Tags and Sections

ML_LMLFF, ML_IALGO_LINREG, ML_IREG, ML_SIGV0, ML_SIGW0

Examples that use this tag

---