American Institute of Mathematics, Palo Alto, California
Mathias Drton and Seth Sullivant
This workshop, sponsored by AIM and the NSF, 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.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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