Communications in Mathematical Sciences

Volume 8 (2010)

Number 1

Special Issue on the Occasion of Andrew Majda’s Sixtieth Birthday: Part I

Density estimation by dual ascent of the log-likelihood

Pages: 217 – 233



Esteban G. Tabak

Eric Vanden-Eijnden


A methodology is developed to assign, from an observed sample, a joint-probability distribution to a set of continuous variables. The algorithm proposed performs this assignment by mapping the original variables onto a jointly-Gaussian set. The map is built iteratively, ascending the log-likelihood of the observations, through a series of steps that move the marginal distributions along a random set of orthogonal directions towards normality.


Density estimation; machine learning; maximum likelihood

2010 Mathematics Subject Classification

60H35, 65C30, 65L20

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