Influence diagram

In [1]:

import os

%matplotlib inline
from pylab import *
import matplotlib.pyplot as plt
from IPython.display import display,HTML

import math

In [2]:

import pyAgrum as gum
import pyAgrum.lib.notebook as gnb

Build a Influence Diagram

fast build with string

In [3]:

gum.fastID("A->*B->$C<-D<-*E->*G->H->*I<-D")

Out[3]:

bifxml format file

In [4]:

diag=gum.loadID("res/diag.bifxml")
gnb.showInfluenceDiagram(diag)

../_images/notebooks_21-Models_InfluenceDiagram_7_0.svg

In [5]:

diag

Out[5]:

the hard way :-)

In [6]:

F=diag.addChanceNode(gum.LabelizedVariable("F","F",2))
diag.addArc(diag.idFromName("decisionVar1"),F)

U=diag.addUtilityNode(gum.LabelizedVariable("U","U",1))
diag.addArc(diag.idFromName("decisionVar3"),U)
diag.addArc(diag.idFromName("F"),U)
gnb.showInfluenceDiagram(diag)

../_images/notebooks_21-Models_InfluenceDiagram_10_0.svg

In [7]:

diag.cpt(F)[{'decisionVar1':0}]=[0.9,0.1]
diag.cpt(F)[{'decisionVar1':1}]=[0.3,0.7]

diag.utility(U)[{'F':0,'decisionVar3':0}]=2
diag.utility(U)[{'F':0,'decisionVar3':1}]=4
diag.utility(U)[{'F':1}]=[[0],[5]]

Optimization in an influence diagram (actually LIMID)

In [8]:

oil=gum.loadID("res/OilWildcatter.bifxml")
gnb.flow.row(oil,gnb.getInference(oil))

In [9]:

# a function to show results on decision nodes T and D
def show_decisions(ie):
    gnb.flow.row(ie.optimalDecision("Testing"),
                   ie.optimalDecision("Drilling"),
                   f"$${ie.MEU()['mean']:5.3f}\\ (stdev : {math.sqrt(ie.MEU()['variance']):5.3f})$$",
                   captions=["Strategy for T",
                             "Strategy for D",
                             "MEU and its standard deviation"])
    gnb.flow.row(ie.posterior("Testing"),ie.posteriorUtility("Testing"),
                   ie.posterior("Drilling"),ie.posteriorUtility("Drilling"),
                  captions=["Final decision for Testing","Final reward for Testing",
                            "Final decision for Drilling","Final reward for Drilling"])

ie=gum.ShaferShenoyLIMIDInference(oil)

display(HTML("<h2>Inference in the LIMID optimizing the decisions nodes</h2>"))
ie.makeInference()
show_decisions(ie)

Inference in the LIMID optimizing the decisions nodes

Testing
Yes	No
1.0000	0.0000

Strategy for T

	Drilling
TestResult	Yes	No
closed	1.0000	0.0000
open	1.0000	0.0000
diffuse	0.0000	1.0000

Strategy for D

$$22.500\ (stdev : 87.457)$$
MEU and its standard deviation

Testing
Yes	No
1.0000	0.0000

Final decision for Testing

Testing
Yes	No
22.5000	20.0000

Final reward for Testing

Drilling
Yes	No
0.5900	0.4100

Final decision for Drilling

Drilling
Yes	No
45.0847	-10.0000

Final reward for Drilling

Graphical inference with evidence and targets (developped nodes)

In [10]:

gnb.sideBySide(oil,
               gnb.getInference(oil,evs={'TestResult':'closed'}),
               gnb.getInference(oil,evs={'TestResult':'open'}),
               gnb.getInference(oil,evs={'TestResult':'diffuse'}),
               oil,
               gnb.getInference(oil,evs={'OilContents':'Dry'}),
               gnb.getInference(oil,evs={'OilContents':'Wet'}),
               gnb.getInference(oil,evs={'OilContents':'Soaking'}),
               ncols=4)

Soft evidence on chance node

In [11]:

gnb.showInference(oil,evs={'OilContents':[0.7,0.5,0.8]})

../_images/notebooks_21-Models_InfluenceDiagram_18_0.svg

Forced decision

In [12]:

gnb.showInference(oil,evs={'Drilling':'Yes'})

../_images/notebooks_21-Models_InfluenceDiagram_20_0.svg

LIMID versus Influence Diagram

The default inference for influence diagram actually an inference for LIMIDs. In order to use it for classical (and solvable) influence diagram, do not forget to add the sequence of decision nodes using addNoForgettingAssumption.

In [13]:

infdiag=gum.fastID("Chance->*Decision1->Chance2->$Utility<-Chance3<-*Decision2<-Chance->Utility")
infdiag

Out[13]:

In [14]:

ie=gum.ShaferShenoyLIMIDInference(infdiag)
try:
    ie.makeInference()
except gum.GumException as e:
    print(e)

[pyAgrum] Fatal error: This LIMID/Influence Diagram is not solvable.

In [15]:

ie.addNoForgettingAssumption(["Decision1","Decision2"])
gnb.sideBySide(ie.reducedLIMID(),ie.junctionTree(),gnb.getInference(infdiag,engine=ie))

Customizing visualization of the results

Using pyAgrum.config, it is possible to adapt the graphical representations for Influence Diagram (see the notebook 99-Tools_configForPyAgrum.ipynb).

In [16]:

gum.config.reset()
gnb.showInference(infdiag,engine=ie,size="7!")

../_images/notebooks_21-Models_InfluenceDiagram_26_0.svg

Many visual options can be changed when displaing an inference (especially for influence diagrams)

In [17]:

# do not show inference time
gum.config["notebook","show_inference_time"]=False
# more digits for probabilities
gum.config["notebook","histogram_horizontal_visible_digits"]=3

gnb.showInference(infdiag,engine=ie,size="7!")

../_images/notebooks_21-Models_InfluenceDiagram_28_0.svg

In [18]:

# specificic for influence diagram :
# more digits for utilities
gum.config["influenceDiagram","utility_visible_digits"]=5
# disabling stdev for utility and MEU
gum.config["influenceDiagram","utility_show_stdev"]=False
# showing loss (=-utility) and mEL (minimum Expected Loss) instead of MEU
gum.config["influenceDiagram","utility_show_loss"]=True

gnb.showInference(infdiag,engine=ie,size="7!")

../_images/notebooks_21-Models_InfluenceDiagram_29_0.svg

In [19]:

# more visual changes for influence diagram and inference
gum.config.reset()

#shape (https://graphviz.org/doc/info/shapes.html)
gum.config["influenceDiagram","chance_shape"] = "cylinder"
gum.config["influenceDiagram","utility_shape"] = "star"
gum.config["influenceDiagram","decision_shape"] = "box3d"

#colors
gum.config["influenceDiagram","default_chance_bgcolor"] = "green"
gum.config["influenceDiagram","default_utility_bgcolor"] = "MediumVioletRed"
gum.config["influenceDiagram","default_decision_bgcolor"] = "DarkSalmon"

gum.config["influenceDiagram","utility_show_stdev"]=False

gnb.sideBySide(infdiag,gnb.getInference(infdiag,engine=ie,targets=["Decision1","Chance3"]))