Laplace distribution (Double exponential)¶
This distribution is robust to outliers, and puts more weight to values closer to 0 than a Gaussian distribution. This property is useful to encourage sparsity in a model.
\[X \sim Lap(\mu, b)\]
PDF:¶
\[Lap(x| \mu, b) \triangleq \frac{1}{2b}\exp {( - \frac{|x - \mu |}{b} )}\]
Here:
\(\mu\) is a location parameter
\(b\) is a scale parameters