# Sparse Coding

 Revision as of 13:31, 21 March 2011 (view source)Zhenghao (Talk | contribs) (→Probabilistic Interpretation)← Older edit Revision as of 13:33, 21 March 2011 (view source)Zhenghao (Talk | contribs) (→Probabilistic Interpretation [Based on Olshausen and Field 1996])Newer edit → Line 93: Line 93: \end{align}[/itex] \end{align}[/itex] - Using a probabilistic approach, it can also be seen that the choices of the $L_1$ penalty $\left|a_i\right|_1$ and the log penalty $\log(1+a_i^2)$ for $S(.)$ correspond to the use of the Laplacian ($P(a_i) \propto \exp\left(-\beta|a_i|\right)$) and the Cauchy prior ($P(a_i) \propto \frac{\beta}{1+a_i^2}$) respectively. + Using a probabilistic approach, it can also be seen that the choices of the $L_1$ penalty $\left|a_i\right|_1$ and the log penalty $\log(1+a_i^2)$ for $S(.)$ correspond to the use of the Laplacian $P(a_i) \propto \exp\left(-\beta|a_i|\right)$ and the Cauchy prior $P(a_i) \propto \frac{\beta}{1+a_i^2}$ respectively. == Learning == == Learning ==