**Speaker:**

Mathias Drton

University of Chicago

**Title:**

Algebraic Factor Analysis: Tetrads, Pentads and Beyond

**Abstract:**

Factor analysis refers to a statistical model in which observed variables
are conditionally independent given fewer hidden variables, known as factors,
and all the random variables follow a multivariate normal distribution. The
parameter space of a factor analysis model is a subset of the cone of positive
definite matrices. This parameter space is studied from the perspective of
computational algebraic geometry. Grobner bases and resultants are applied to
compute the ideal of all polynomial functions which vanish on the parameter
space. These polynomials, known as model invariants, arise from rank conditions
on a symmetric matrix under elimination of the diagonal entries of the matrix.
Besides revealing the geometry of the factor analysis model, the model
invariants also furnish useful statistics for testing goodness-of-fit. This talk
is based on the paper with Bernd Sturmfels and Seth Sullivant which is posted at
http://front.math.ucdavis.edu/math.ST/0509390.