ML EPS REG: Difference between revisions

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{{TAGDEF|ML_EPS_REG|[real]|1E-14}}
{{TAGDEF|ML_EPS_REG|[real]|1E-14}}
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
<math>
\sigma^{2}_{\mathrm{w}}=\frac{|\mathbf{\bar{w}}|^{2}}{\gamma},
</math>
<math>
\sigma^{2}_{\mathrm{v}}=\frac{|\mathbf{T}-\mathbf{\phi}\mathbf{\bar{w}}|^{2}}{M-\gamma},
</math>
<math>
\gamma=\sum\limits_{k=1}^{N_{\mathrm{B}}} \frac{\lambda_{k}}{\lambda_{k}+1/\sigma^{2}_{\mathrm{w}}}
</math>.
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}}}
</math>


== Related Tags and Sections ==
== Related Tags and Sections ==

Revision as of 17:53, 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 of the covariance matrix are used in the optimization of the regularization parameters and Failed to parse (Conversion error. Server ("cli") reported: "[INVALID]"): {\displaystyle \sigma^{2}_{\mathrm{v}} determined by the following equations

.

All eigenvalues satisfying > ML_EPS_REG are contributing by the above equations. All eigenvalues not satisfying that relation are contributing as



Related Tags and Sections

ML_LMLFF, ML_IALGO_LINREG, ML_IREG, ML_SIGV0, ML_SIGW0

Examples that use this tag