hiddenMap -- Creates a linear map from a ring of probability distributions among observed discrete random variables into a ring of probability distributions among observed variables and one hidden variable specified by the integer input.

Synopsis

Usage:
phi = hiddenMap(i,R)
Inputs:
- i, an integer, the index corresponding to the hidden random variable
- R, a ring, a Markov ring
Outputs:
- phi, a ring map

Description

A linear map from a ring of probability distributions among observed discrete random variables into a ring of probability distributions among observed variables and one hidden variable specified by the integer input. This method is used to work with Bayesian networks with hidden variables. For more details see the paper "Algebraic Geometry of Bayesian Networks" by Garcia, Stillman, and Sturmfels.

i1 : hiddenMap(1,markovRing(2,3,2))

o1 = map(QQ[p     , p     , p     , p     , p     , p     , p     , p     , p     , p     , p     , p     ],QQ[p   , p   , p   , p   , p   , p   ],{p      + p     , p      + p     , p      + p     , p      + p     , p      + p     , p      + p     })
             1,1,1   1,1,2   1,2,1   1,2,2   1,3,1   1,3,2   2,1,1   2,1,2   2,2,1   2,2,2   2,3,1   2,3,2      1,1   1,2   2,1   2,2   3,1   3,2    1,1,1    2,1,1   1,1,2    2,1,2   1,2,1    2,2,1   1,2,2    2,2,2   1,3,1    2,3,1   1,3,2    2,3,2

o1 : RingMap QQ[p     , p     , p     , p     , p     , p     , p     , p     , p     , p     , p     , p     ] <--- QQ[p   , p   , p   , p   , p   , p   ]
                 1,1,1   1,1,2   1,2,1   1,2,2   1,3,1   1,3,2   2,1,1   2,1,2   2,2,1   2,2,2   2,3,1   2,3,2           1,1   1,2   2,1   2,2   3,1   3,2

Ways to use `hiddenMap` :

hiddenMap(ZZ,Ring)

hiddenMap -- Creates a linear map from a ring of probability distributions among observed discrete random variables into a ring of probability distributions among observed variables and one hidden variable specified by the integer input.

Synopsis

Description

See also

Ways to use hiddenMap :

Ways to use `hiddenMap` :