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Sparse data is data with many zeros. Here the authors seem to be calling the prior as sparse because it favorites the zeros. This is pretty self-explanatory if you look at the shape of Laplace (aka double exponential) distribution, that is peaked around zero.

(image source Tibshirani, 1996)

This effect is true for any value of $\tau$ (the distribution is always peaked at zero), although the smaller the value of the parameter, the more regularizing effect it has.

For this reason Laplace prior is often used as robust prior, having the regularizing effect. Having this said, the Laplace prior is popular choice, but if you want really sparse solutions there may be better choices, as described by Van Erp et al (2019).

Sparse data is data with many zeros. Here the authors seem to be calling the prior as sparse because it favorites the zeros. This is pretty self-explanatory if you look at the shape of Laplace (aka double exponential) distribution, that is peaked around zero.

(image source Tibshirani, 1996)

This effect is true for any value of $\tau$ (the distribution is always peaked at it's location parameter, here equal to zero), although the smaller the value of the parameter, the more regularizing effect it has.

For this reason Laplace prior is often used as robust prior, having the regularizing effect. Having this said, the Laplace prior is popular choice, but if you want really sparse solutions there may be better choices, as described by Van Erp et al (2019).

Sparse data is data with many zeros. Here the authors seem to be calling the prior as sparse because it favorites the zeros. This is pretty self-explanatory if you look at the shape of Laplace (aka double exponential) distribution, that is peaked around zero.

This effect is true for any $\tau$, although the smaller the value of the parameter, the more regularizing effect it has.

(image source Tibshirani, 1996)

For this reason Laplace prior is often used as robust prior, having the regularizing effect. Having this said, the Laplace prior is popular choice, but if you want really sparse solutions there may be better choices, as described by Van Erp et al (2019).

Sparse data is data with many zeros. Here the authors seem to be calling the prior as sparse because it favorites the zeros. This is pretty self-explanatory if you look at the shape of Laplace (aka double exponential) distribution, that is peaked around zero.

(image source Tibshirani, 1996)

This effect is true for any value of $\tau$ (the distribution is always peaked at zero), although the smaller the value of the parameter, the more regularizing effect it has.

For this reason Laplace prior is often used as robust prior, having the regularizing effect. Having this said, the Laplace prior is popular choice, but if you want really sparse solutions there may be better choices, as described by Van Erp et al (2019).

Sparse data is data with many zeros. Here the authors seem to be calling the prior as sparse because it favorites the zeros. This is pretty self-explanatory if you look at the shape of Laplace (aka double exponential) distribution, that is peaked around zero.

(image source Tibshirani, 1996)

For this reason Laplace prior is often used as robust prior, having the regularizing effect.

Sparse data is data with many zeros. Here the authors seem to be calling the prior as sparse because it favorites the zeros. This is pretty self-explanatory if you look at the shape of Laplace (aka double exponential) distribution, that is peaked around zero.

This effect is true for any $\tau$, although the smaller the value of the parameter, the more regularizing effect it has.

(image source Tibshirani, 1996)

For this reason Laplace prior is often used as robust prior, having the regularizing effect. Having this said, the Laplace prior is popular choice, but if you want really sparse solutions there may be better choices, as described by Van Erp et al (2019).