#
Parameter identification in graphical models

October 4 to October 8, 2010
at the

American Institute of Mathematics,
Palo Alto, 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: