Lectures on Algebraic Statistics

By Mathias Drton, Bernd Sturmfels, Seth Sullivant. 2008

397 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c89f3852e017f1c8107ddc7cd67a33df88695b1f

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In Computational Mathematics

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Citations in the corpus

Symmetric rank covariances: a generalized framework for nonparametric measures of dependence (2017, background): “It then holds that BX(x)⊥⊥BY (y) if and only if M(x, y) has rank 1 (Drton et al., 2009, Chapter 3).”
Geometry of the Restricted Boltzmann Machine (2009, background): “This class of algebraic statistical models includes graphical models for both Gaussian and discrete random variables [11, 13].”
Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry (2009, methodology): “ss of algebraic statistical models is to characterize those models which have ML degree one. These are the models whose maximum likelihood estimator is a rational function in the suﬃcient statistics (Drton et al. 2009, §2.1). In the context here, we have the following characterization of matroids wh”
FIXED POINTS OF THE EM ALGORITHM AND NONNEGATIVE RANK BOUNDARIES (2013, methodology): “In that case, P is generally not a critical point for the likelihood function in the manifold of rank r matrices, and none of the results on ML degrees in [14, 19, 23, 24, 25] are applicable.”
A Bayesian information criterion for singular models (2013, background): “Indeed, theorem 6.7 in Watanabe (2009) shows that a wide variety of singular models have the property that, for Yn drawn from π0 ∈Mi, log{L.Mi/}= log{P.Yn|π0, Mi/}−λi.π0/ log.n/+{mi.π0/−1} log{log.n/}+Op.1/; .2:6/ see also the introduction to the topic in Drton et al. (2009), chapter 5.1.”
Decompositions of binomial ideals (2009, background): “Starting with Eisenbud and Sturmfels (1996), the combinatorial theory of binomial ideals has developed into a branch of combinatorial commutative algebra which has many connections to different areas of mathematics (Miller and Sturmfels 2005). The interest in binomial ideals is motivated by the freq”
Maximum Likelihood Estimation in Log-Linear Models: Theory and Algorithms (2011, background): “ling scheme is a toric variety, an object with remarkable algebraic and geometric properties extensively studied in algebraic geometry and algebraic statistics (see, e.g. Pachter and Sturmfels, 2005; Drton et al., 2008). Section 4 describes algorithms for extended maximum likelihood estimation under”
Finite Groebner bases in infinite dimensional polynomial rings and applications (2009, methodology): “Markov bases of the matrices AΓ are useful for performing statistical hypothesis tests by running random walks over contingency tables (see [4] or Chapter 1 in [8]).”