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 $\lambda_{k}$ 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

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

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

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

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

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

Related Tags and Sections

ML_LMLFF, ML_IALGO_LINREG, ML_IREG, ML_SIGV0, ML_SIGW0

Examples that use this tag

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