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solverMLE(...,ConcentrationMatrix=>...) -- output MLE for concentration matrix instead of MLE for covariance matrix

Description

By default, solverMLE outputs the MLE for the covariance matrix. By providing true as the value for the option solverMLE(...,ConcentrationMatrix=>...), solverMLE provides the MLE for the concentration matrix.

Note that both the maximum value attained in the log-likelihood function and the ML-degree remain the same.

i1 : G= mixedGraph(graph{{a,b},{b,c}},digraph {{a,d},{c,e},{f,g}},bigraph {{d,e}})

o1 = MixedGraph{Bigraph => Bigraph{d => {e}}}
                                   e => {d}
                Digraph => Digraph{a => {d}}
                                   c => {e}
                                   d => {}
                                   e => {}
                                   f => {g}
                                   g => {}
                Graph => Graph{a => {b}   }
                               b => {a, c}
                               c => {b}

o1 : MixedGraph
 
i2 : solverMLE (G, random(QQ^7,QQ^7))

o2 = (-12.0989, | 1.69516  .604848  .25133   .142162  .0281614 0      
                | .604848  6.60263  2.74357  .0507245 .307415  0      
                | .25133   2.74357  10.9686  .0210774 1.22903  0      
                | .142162  .0507245 .0210774 2.62373  -.179884 0      
                | .0281614 .307415  1.22903  -.179884 .267176  0      
                | 0        0        0        0        0        3.56723
                | 0        0        0        0        0        -1.2919
     ------------------------------------------------------------------------
     0       |, 5)
     0       |
     0       |
     0       |
     0       |
     -1.2919 |
     1.8834  |

o2 : Sequence
 
i3 : solverMLE (G, random(QQ^7,QQ^7), ConcentrationMatrix=>true)

o3 = (-5.21063, | .679783  -.315658 .319631  .259967 .379545 0       
                | -.315658 5.34198  -.307143 0       0       0       
                | .319631  -.307143 11.0115  .344706 1.21718 0       
                | .259967  0        .344706  .280361 .40932  0       
                | .379545  0        1.21718  .40932  1.44533 0       
                | 0        0        0        0       0       .848729 
                | 0        0        0        0       0       .0539863
     ------------------------------------------------------------------------
     0        |, 5)
     0        |
     0        |
     0        |
     0        |
     .0539863 |
     1.33     |

o3 : Sequence

See also

Functions with optional argument named ConcentrationMatrix:

Further information

  • Default value: false
  • Function: solverMLE -- Maximum likelihood estimate of a loopless mixed graph
  • Option key: ConcentrationMatrix -- optional input to output MLE for concentration matrix instead of MLE for covariance matrix

The source of this document is in GraphicalModelsMLE.m2:1592:0.