What is Laplace prior?
The Laplace prior (equivalently regularization or shrinkage with the norm, also known as the lasso) enforces a preference for parameters that are zero, but otherwise is more dispersed than a Gaussian prior (equivalently regularization or shrinkage with the. norm, also known as ridge regression).
Where is Laplace distribution used?
The Laplace distribution is used for modeling in signal processing, various biological processes, finance, and economics. Examples of events that may be modeled by Laplace distribution include: Credit risk and exotic options in financial engineering.
Is Laplace a distribution?
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.
Is Laplace distribution Leptokurtic?
The Laplace distribution, one of the earliest known probability distributions, is a continuous probability distribution named after the French mathematician Pierre-Simon Laplace. Like the normal distribution, this distribution is unimodal (one peak) and it is also a symmetrical distribution.
How is the Laplacian prior used in regression?
In regression, the use of the Laplacian prior is known as the LASSO (Tibshirani, 1996; Efron et al., 2004). t of the Gaussian are hidden variables and Ga() is the gamma distribution (in the present instan- tiation, an exponential (Bernardo and Smith, 1994)). t recovers the Laplacian marginal prior density.
How are Laplace priors used in classification?
Laplace priors have been previously used extensively as a sparsity-inducing mechanism to perform feature selection simultaneously with classi- fication or regression.
How is Laplace prior related to the median?
The relation of Laplace distribution prior with median (or L1 norm) was found by Laplace himself, who found that using such prior you estimate median rather than mean as with Normal distribution (see Stingler, 1986 or Wikipedia ).
Which is equivalent to Laplace prior in Bayesian setting?
The robust priors you asked about were described also by Tibshirani (1996) who noticed that robust Lasso regression in Bayesian setting is equivalent to using Laplace prior.
