Algebraic statistics advocates the use of algebraic geometry, commutative algebra, and geometric combinatorics as tools for making statistical inferences. The starting point for this connection is the observation that most statistical models for discrete random variables are, in fact, algebraic varieties. While some of the varieties that appear are classical varieties (like Segre varieties and toric varieties), most are new, and there are many challenging open problems about the algebraic structure of these varieties.

Now there is a great program holding at the  Mittag-Leffler Institute.

Algebraic Geometry with a view towards applications

which including a Ph.D course “Algebraic Geometry, computations and applications” co-taught by Alicia Dickenstein from Buenos Aires and Bernd Sturmfels from UC Berkeley.

There are several famous professors in this field:

Alicia Dickenstein from Buenos Aires

Bernd Sturmfels from UC Berkeley

Seth Sullivant from North Carolina State University     

Risi Kondor from Center for the Mathematics of Information, Caltech

Sumio Watanabe, Ph.D.  from Tokyo Institute of Technology

Caroline Uhler from Berkeley

Here is a short course on Algebraic statistics by Professor Seth Sullivant:

Algebraic Statistics Short Course

Here is the video lecture by Risi Kondor:

Group Theory and Machine Learning

And you can find his thesis on this topic in his homepage.