Rectified Gaussian distribution
In probability theory, the rectified Gaussian distribution is a modification of the Gaussian distribution when its negative elements are reset to 0 (analogous to an electronic rectifier). It is essentially a mixture of a discrete distribution (constant 0) and a continuous distribution (a truncated Gaussian distribution with interval ).
is the Dirac delta function
and, is the unit step function:
Often, a simpler alternative form is to consider a case, where,
A rectified Gaussian distribution is semi-conjugate to the Gaussian likelihood, and it has been recently applied to factor analysis, or particularly, (non-negative) rectified factor analysis. Harva  proposed a variational learning algorithm for the rectified factor model, where the factors follow a mixture of rectified Gaussian; and later Meng  proposed an infinite rectified factor model coupled with its Gibbs sampling solution, where the factors follow a Dirichlet process mixture of rectified Gaussian distribution, and applied it in computational biology for reconstruction of gene regulatory network.
- Harva, M.; Kaban, A. (2007). "Variational learning for rectified factor analysis☆". Signal Processing 87 (3): 509. doi:10.1016/j.sigpro.2006.06.006.
- Meng, Jia; Zhang, Jianqiu (Michelle), Chen, Yidong, Huang, Yufei (1 January 2011). "Bayesian non-negative factor analysis for reconstructing transcription factor mediated regulatory networks". Proteome Science 9 (Suppl 1): S9. doi:10.1186/1477-5956-9-S1-S9.