  A detailed algorithmic explanation is required for how a network of chemical
reactions can generate the sophisticated behavior displayed by living cells.
Though several previous works have shown that reaction networks are
computationally universal and can in principle implement any algorithm, there
is scope for constructions that map well onto biological reality, make
efficient use of the computational potential of the native dynamics of reaction
networks, and make contact with statistical mechanics. 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
receptor-ligand bindings. Specifically we show how reaction networks can
implement information projection, and consequently a generalized
Expectation-Maximization algorithm, to solve maximum likelihood estimation
problems in partially-observed 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.
