In the previous section, we computed the maximum unnormalized probability value, but for MAP, we need to compute the states of the variables corresponding to the one in which this value occurs. Taking our earlier example of the network A
→
B, we first computed 
, but the state of the variable B for which P(b|a) gives the maximum value also depends on the state of the variable A. So, we will first need to compute and then compute the state of B accordingly. So, from the CPDs of the network, we can see that 
. Now we will look for 
, which gives us 
. Hence, we get the maximum values corresponding to 
and 
.
Also, the computational cost of this operation is not high, as we are simply doing another pass over the factors that have already been computed. Hence, the cost would be linear in the number of variables in the network.
Now, let's continue the previous code example and do some map queries over the networks using pgmpy:
In [20]: model_inference.map_query(variables=['late_for_school'])
Out[20]: {'late_for_school': 0}
In [21]: model_inference.map_query(variables=['late_for_school',
'accident'])
Out[21]: {'accident': 1, 'late_for_school': 0}
# Again we can pass the evidence to the query using the evidence
# argument in the form of {variable: state}.
In [22]: model_inference.map_query(variables=['late_for_school'],
evidence={'accident': 1})
Out[22]: {'late_for_school': 0}
In [23]: model_inference.map_query(variables=['late_for_school'],
evidence={'accident': 1,
'rain': 1})
Out[23]: {'late_for_school': 0}
# Also in the case of MAP queries we can specify the elimination
# order of the variables. But if the elimination order is not
# specified pgmpy automatically computes the best elimination
# order for the query.
In [24]: model_inference.map_query(
variables=['late_for_school'],
elimination_order=['accident', 'rain',
'traffic_jam',
'getting_up_late',
'long_queues'])
Out[24]: {'late_for_school': 0}
In [25]: model_inference.map_query(
variables=['late_for_school'],
evidence={'accident': 1},
elimination_order=['rain',
'traffic_jam',
'getting_up_late',
'long_queues'])
Out[25]: {'late_for_school': 0}
# Similarly MAP queries can be done for belief propagation as well.
In [26]: belief_propagation.map_query(['late_for_school'],
evidence={'accident': 1})
Out[26]: {'late_for_school': 0}