☰  dynamicBn

# dynamic Bayesian Networks with pyAgrum¶

In :
import pyAgrum as gum
import pyAgrum.lib.notebook as gnb
import pyAgrum.lib.dynamicBN as gdyn
%matplotlib inline


### Building a 2TBN¶

Note the naming convention for a 2TBN : a variable with a name $A$ is present at t=0 with the name $A0$ and at time t as $At$.

In :
twodbn=gum.BayesNet()
for s in ["a0","b0","c0","at","bt","ct"]]
for s in ["d0","dt"]]

twodbn.generateCPTs()

gnb.showBN(twodbn)


## 2TBN¶

The dbn above actually is a 2TBN and is not correctly shown as a BN. Using the naming convention, it can be shown as a 2TBN.

In :
gdyn.showTimeSlices(twodbn)


## unrolling 2TBN¶

A dBN is 'unrolled' using the 2TBN and the time period size. For a couple $a_0$,$a_t$ in the 2TBN, the unrolled dBN will include $a_0, a_1, \cdots, a_{T-1}$

In :
T=5

dbn=gdyn.unroll2TBN(twodbn,T)
gdyn.showTimeSlices(dbn,size="10")


We can infer on bn just as on a normal bn. Following the naming convention in 2TBN, the variables in a dbN are named using the convention $a_i$ where $i$ is the number of their time slice.

In :
for i in range(T):
gnb.showPosterior(dbn,target="d{}".format(i),evs={})


## dynamic inference : following variables¶

gdyn.plotFollow directly ask for the 2TBN, unroll it and add evidence evs. Then it shows the dynamic of variable $a$ for instance by plotting $a_0,a_1,\cdots,a_{T-1}$.

In :
import matplotlib.pyplot as plt

plt.rcParams['figure.figsize'] = (10, 2)
gdyn.plotFollow(["a","b","c","d"],twodbn,T=51,evs={'a9':2,'a30':0,'c14':0,'b40':0,'c50':3})


# nsDBN (Non-Stationnary Dynamic Bayesian Network)¶

In :
T=15

dbn=gdyn.unroll2TBN(twodbn,T)
gdyn.showTimeSlices(dbn,size="14")


Non-stationnaty DBN allows to express that the dBN do not follow the same 2TBN during all steps. A unrolled dbn is a classical BayesNet and then can be changed as you want after unrolling.

In :
# new P(ct|c0)
pot.fillWith([1,0,0,0.1]*9).normalizeAsCPT() # 36 valeurs normalized as CPT

Out:
ct
c0
0
1
2
3
4
5
0
0.47620.00000.00000.04760.47620.0000
1
0.00000.08330.83330.00000.00000.0833
2
0.47620.00000.00000.04760.47620.0000
3
0.00000.08330.83330.00000.00000.0833
4
0.47620.00000.00000.04760.47620.0000
5
0.00000.08330.83330.00000.00000.0833
In :
# from steps 5 to 10, $C_t$ only depends on $C_{t-1}$ and follows this new CPT
for i in range(5,11):
dbn.eraseArc(f"d{i-1}",f"c{i}")
dbn.eraseArc(f"a{i}",f"c{i}")
dbn.cpt(f"c{i}").fillWith(pot,["ct","c0"]) # ct in pot <- first var of cpt, c0 in pot<-second var in cpt

gdyn.showTimeSlices(dbn,size="14")

In :
plt.rcParams['figure.figsize'] = (10, 2)
gdyn.plotFollowUnrolled(["a","b","c","d"],dbn,T=15,evs={'a9':2,'c14':0})

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