# Sparse Coding

### From Ufldl

(→Probabilistic Interpretation) |
(→Probabilistic Interpretation [Based on Olshausen and Field 1996]) |
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\end{align}</math> | \end{align}</math> | ||

- | Using a probabilistic approach, it can also be seen that the choices of the <math>L_1</math> penalty <math>\left|a_i\right|_1 </math> and the log penalty <math>\log(1+a_i^2)</math> for <math>S(.)</math> correspond to the use of the Laplacian | + | Using a probabilistic approach, it can also be seen that the choices of the <math>L_1</math> penalty <math>\left|a_i\right|_1 </math> and the log penalty <math>\log(1+a_i^2)</math> for <math>S(.)</math> correspond to the use of the Laplacian <math>P(a_i) \propto \exp\left(-\beta|a_i|\right)</math> and the Cauchy prior <math>P(a_i) \propto \frac{\beta}{1+a_i^2}</math> respectively. |

== Learning == | == Learning == |