Algebraic geometric comparison of probability distributions

  • Authors:

  • Franz J. Király;Paul Von Bünau;Frank C. Meinecke;Duncan A. J. Blythe;Klaus-Robert Müller

  • Affiliations:

  • Machine Learning Group, Computer Science, Berlin Institute of Technology, TU Berlin, Berlin, Germany and Institute of Mathematics, FU Berlin;Machine Learning Group, Computer Science, Berlin Institute of Technology, TU Berlin, Berlin, Germany;Machine Learning Group, Computer Science, Berlin Institute of Technology, TU Berlin, Berlin, Germany;Machine Learning Group, Computer Science, Berlin Institute of Technology, TU Berlin, Berlin, Germany and Bernstein Center for Computational Neuroscience, Berlin;Machine Learning Group, Computer Science, Berlin Institute of Technology, TU Berlin, Berlin, Germany and Department of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Se ...

  • Venue:
  • The Journal of Machine Learning Research
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

We propose a novel algebraic algorithmic framework for dealing with probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem, at a lower computational cost and with higher accuracy. Moreover, the algebraic viewpoint on probability distributions allows us to invoke the theory of algebraic geometry, which we demonstrate in a compact proof for an identifiability criterion.