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[4:00pm]Mathematics Colloquium
 Description:
 Mathematics Colloquium
Date & Time: 4th April, 2018 at 4pm
Venue: Ramanujan Hall
Speaker: Manoj Gopalkrishnan
Title: Imagining how a cell thinks: The design of reaction network schemes
that do machine learning
Abstract: A living cell responds in sophisticated ways to its environment.
Such behavior is all the more remarkable when one considers that a cell is
a bag of molecules. A detailed algorithmic explanation is required for how
a network of chemical reactions can produce sophisticated behavior. Several
previous works have shown that reaction networks are computationally
universal and can, in principle, implement any algorithm. The problem is
that these constructions have not mapped well onto biological reality, have
made wasteful use of the computational potential of the native dynamics of
reaction networks, and have not made any contact with statistical
mechanics. We seek to address these problems.
We find that the mathematical structure of reaction networks is
particularly well suited to implementing modern machine learning
algorithms. We describe a new reaction network scheme for solving a large
class of statistical problems including the problem of how a cell would
infer its environment from receptorligand bindings. Specificially we show
how reaction networks can implement information projection, and
consequently a generalized ExpectationMaximization algorithm, to solve
maximum likelihood estimation problems in partiallyobserved exponential
families on categorical data. Our scheme can be thought of as an
algorithmic interpretation of E. T. Jaynes's vision of statistical
mechanics as statistical inference.

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