Seminar Report

In 17 June, professor Tasuku Soma (The university of Tokyo) gave a seminar on scaling problem and information geometry at the math seminar.

In the first part he gave an introductory talk on scaling problem. Assume matrix A is given and each entry of A is positive. Matrix scaling problem is to find good matrix L,R with which LAR and (LAR)* has nice property. He then introduced Sinkhorn algorithm. This is an algorithm to calculate "LAR" in the above problem. He then explained operator scaling, which is quantum analogue of matrix scaling.

He explained his recent result on the operator scaling and information geometry. It is known by Csizar that Sinkhorn algorithm for matrix scaling is actually an alternating e-projection, which appears in the information geometry. He then introduced his recent work with Takeru Matsuda. In that work, they proved that operator scaling is also an alternating e-projection.