198 citations · 732 across the 46 of their papers we have counts for
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cs.AI2012
Factorization of Discrete Probability Distributions
Dan Geiger, Christopher Meek, Bernd Sturmfels
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or…
math.AG2012★ 4 cited
Maximum Likelihood for Matrices with Rank Constraints
Jonathan Hauenstein, Jose Rodriguez, Bernd Sturmfels
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of dis…
math.ST2012
Geometry of Higher-Order Markov Chains
Bernd Sturmfels
We determine an explicit Gröbner basis, consisting of linear forms and determinantal quadrics, for the prime ideal of Raftery's mixture transition distribution model for Markov cha…