Parameter identification in graphical models

October 4 to October 8, 2010

at the

American Institute of Mathematics, San Jose, California

organized by

Mathias Drton and Seth Sullivant

Original Announcement

This workshop is devoted to identifiability problems in graphical statistical models. The connection between graph and statistical models is made by identifying the graph's nodes with random variables and translating the graph's edges into a parametrization map that returns a covariance matrix or a probability vector (depending on whether the random variables are jointly normal or discrete). These combinatorially defined parametrizations are polynomial maps, and identifiability problems concern their injectivity properties giving rise to questions such as: For which graphs is the associated parametrization injective? or generically injective? or finite-to-one?

Due to its importance to many applied fields there exists a considerable literature on the problem. For instance, in statistics and computer science, an active community working in an area referred to as 'causal inference' publishes formulas identifying a parameter as a function of a possibly only partially given covariance matrix/probability vector. However, despite its algebraic and combinatorial nature, it is only recently that the problem has attracted the attention of mathematicians.

The goal of this workshop is to bring together key researchers working in statistics, computer science, and discrete mathematics to formulate precise open problems and discuss approaches to their resolution using the machinery of algebraic geometry, commutative algebra, combinatorics, and symbolic computation.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Half-trek criterion for generic identifiability of linear structural equation models
by  Rina Foygel, Jan Draisma, and Mathias Drton,  Ann. Statist. 40 (2012), no. 3, 1682-171  MR3015040