Algebraic Statistics for Computational Biology: Preface

By Lior S. Pachter, Bernd Sturmfels. 2005

402 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e4e006ccfbdd3af87d0c8e310f8ce2f3f78a1210

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Citations in the corpus

Likelihood ratio tests and singularities (2007, background): “The parameter spaces of many statistical models are such images; compare [22].”
Bioinformatics for Whole-Genome Shotgun Sequencing of Microbial Communities (2005, background): “However, encouraging new algorithmic results and software in this area [66–68] should spur renewed work on these types of methods.”
Ranks of tensors and a generalization of secant varieties (2009, background): “A central problem in many areas (signal processing, algebraic statistics, complexity theory etc., see e.g., [4, 8, 21 , 16]) is to understand the ranks and border ranks of 3-way tensors.”
Equations for secant varieties of Veronese and other varieties (2011, background): “, [7,11,27,41]) to find tests for the border rank of a given tensor.”
Linear conjugacy of chemical reaction networks (2011, unknown): “[5, 15, 22, 25].”
Tropical Mathematics (2004, background): “The tropical Grassmannian Gr2,n is also known as the space of phylogenetic trees [3, 14, 20].”
Combinatorial secant varieties (2005, background): “In the emerging field of algebraic statistics, the construction of joins and secant varieties corresponds to mixture models [13, 22], and it is of considerable interest to compute the defining prime ideals of X ∗ Y and X{r} from those of X and Y .”
On the ideals and singularities of secant varieties of Segre varieties (2006, background): “More generally, in algebraic statistics (see, e.g, [ 8 ]), one would like as much information as possible about different algebraic statistical models, and secant varieties of Segre varieties are important special classes of such models.”
Identifiability of parameters in latent structure models with many observed variables (2008, background): “Thus statistical models have recently been studied by algebraic geometers [19, 37].”
Geometry of the Restricted Boltzmann Machine (2009, background): “In order for the inference function Iθ to be well-defined, it is necessary (and sufficient) that θ = (b,W, c) lies in an open cone of linearity of the tropical morphism Φ.”