Python Model.inference Examples

Example #1

File: sums.py Project: dkasak/pacal

for i in range(n):
    print "X{}".format(i)
    X[i] = BetaDistr(2, 2, sym = "X{}".format(i))
    if i==0:
        S[i] = X[0]        
    else:
        S[i] = S[i-1] + X[i]
        S[i].setSym("S{}".format(i))

M = Model(X, S[1:])
print M
M.toGraphwiz()
#M = M.inference([S[-1], S[-4]], [S[-3]], [1])
#M = M.inference([X[0], X[1]], [S[-1]], [3.5])
print "===================="
M1 = M.inference(wanted_rvs =[X[0], X[1]], cond_rvs=[S[-1]], cond_X=[1])
print "====================",M1
M2 = M.inference(wanted_rvs =[S[1], S[4]])
print "====================",M2
M3 = M.inference(wanted_rvs =[S[1], S[4]], cond_rvs=[S[3]], cond_X=[2])
print "====================",M3
MC_X0 = M.inference(wanted_rvs =[X[0]], cond_rvs=[S[-1]], cond_X=[1])
print "===================="

print M1
figure()
M1.plot(cont_levels=10)
figure()
M1.plot(have_3d=True)

print M2

Example #2

File: diffeq_noise.py Project: dkasak/pacal

M = Model(P, O)
print M
M.eliminate_other(E + Y + O + [A, Y0] + U)
print M
M.toGraphwiz(f=open('bn.dot', mode="w+"))

#!
#! Joint distribution of initial condition and parameter of equation
#! -----------------------------------------------------------------

i = 0
ay0 = []
ui = [0.0]*n
figure()
for yend in [0.25, 1.25, 2.25]:
    M2 = M.inference(wanted_rvs=[A, Y0], cond_rvs=[O[-1]] + U, cond_X=[yend] + ui)
    subplot(1, 3, i + 1)
    title("O_{0}={1}".format(n, yend))
    M2.plot()
    ay0.append(M2.nddistr.mode())           # "most probable" state
    print "yend=", yend, ",  MAP  est. of A, Y0 =", ay0[i]
    i += 1
show()
#!
#! Trajectory
#! ----------

figure()
styles=['-', '--', '-.', ':']
for j in range(len(ay0)):
    ymean, ystd = [], []

Example #3

File: diffeq.py Project: dkasak/pacal

        pass
    else:
        Y[i] = Y[i-1] * K
        Y[i].setSym("Y" + str(i))  
P = NDProductDistr([Factor1DDistr(A), Factor1DDistr(Y[0])])
M = Model(P, Y[1:])
M.eliminate_other([K] + Y)

#M2 = M.inference2([Y[0], A], [Y[n]], [1])
#M2.plot(); print M2; show()
#M2 = M.inference2([Y[0]], [Y[n]], [0.5])
#figure()
#M2.plot(); print M2; 
figure()
Y[-1].plot(color='r',linewidth=5)
M3 = M.inference([Y[-1]], [], [])

M3.plot(); print M3; 

X0 = BetaDistr(2, 2)
y = X0 * exp(A) 
y.summary()
y.plot(label="Y0*exp(A)")
Y[-1].plot('r')
figure()
err = y.get_piecewise_pdf() - M3.as1DDistr().get_piecewise_pdf()
err.plot()
show()

stop

Example #4

File: kalman.py Project: dkasak/pacal

Udenoised = zeros(nT)
yi = 0.0
ydenoise = 0.0
ynoise = 0.0
y = 0.0
figure()
for i in range(nT):
    t[i] = i
    # Deterministic simultation
    u[i] = 0.1 * sign(sin(4 * pi * i / nT))
    y = y * K + u[i]
    Yorg[i] = y
    Ynoised[i] = y + E[0].rand()  
    # Inference (Y[i] | O[i-n+1], ..., O[i]
    if i > n - 1:
        MY = M.inference(wanted_rvs=[Y[-1]], cond_rvs=O + U , cond_X=concatenate((Ynoised[i - n + 1:i + 1], u[i - n + 1:i + 1])))
        ydenoised = MY.as1DDistr().median()
        Ydenoised[i] = ydenoised
        #MY.as1DDistr().boxplot(i, width=0.2, useci=0.1)
plot(t, u, 'k-', label="U", linewidth=1.0)
plot(t, Ynoised, 'k.--', label="O", linewidth=1.0)
plot(t, Yorg, 'k-.', label="Y original", linewidth=3.0)
plot(t, Ydenoised, 'k-', label="Y denoised", linewidth=2.0)
legend(loc='lower left')

#! Error of estimation using median 
#! --------------------------------
print "mse=", sqrt(mean((Yorg - Ynoised) ** 2)), sqrt(mean((Yorg - Ydenoised) ** 2)) 
print "mae=", mean(abs(Yorg - Ynoised)), mean(abs(Yorg - Ydenoised)) 

Example #5

# MXY.plot()
# plot([0.0, 1.0], [0.7, 0.7+a], "k-", linewidth=2.0)
# plot(Xobs, Yobs, "ko")
# plot()
# show()

#print ar, br
print Xobs, Yobs
print X + Y
print concatenate((Xobs, Yobs))

#print M
#MAB = M.inference([A,B]+E, X + Y,  concatenate((Xobs, Yobs)))
#print MAB
#MAB = MAB.inference([A,B], X + Y,  concatenate((Xobs, Yobs)))
MW = M.inference(W, X + Y, concatenate((Xobs, Yobs)))
print "-------------------"
MW0 = MW.inference([W[0]], [], [])
#MB = MW.inference([B],[],[])

#M = M.inference([A,B], [X[0], Y[0]], [0.2, 0.4])
print MW

print MW0
figure()
subplot(211)
MW0.plot()
#print MB
#subplot(212)
#MB.plot()
#print "mean   est. A=", MA.as1DDistr().mean(),   "est. B=", MB.as1DDistr().mean()

Example #6

X2 = BetaDistr(4, 4, sym="X2")
Y1 = BetaDistr(4, 4, sym="Y1")
Y2 = BetaDistr(4, 4, sym="Y2")

C1 = FrankCopula2d(theta=5, marginals=[X1, X2])
C2 = FrankCopula2d(theta=2, marginals=[Y1, Y2])
C1.contour()
C2.contour()
figure()

# C1 = FrankCopula2d(theta=2, marginals=[X1, X2])
# C2 = FrankCopula2d(theta=2.5, marginals=[Y1, Y2])

#C1 = GumbelCopula2d(theta=2, marginals=[X1, X2])
#C1 = PiCopula(marginals=[X1, X2])

Z1 = X1 + Y1
Z1.setSym("Z1")
Z2 = X2 + Y2
Z2.setSym("Z2")

M = Model([C1, C2], [Z1, Z2])
#M = Model([C1,Y1,Y2], [Z1, Z2])
#M = Model([X1,X2,Y1,Y2], [Z1, Z2])
print(M)

M2 = M.inference([Z1, Z2])
print(M2)
M2.plot()
show()

Example #7

print M
M.eliminate_other(E + Y + O + [A, Y0] + U)
print M
M.toGraphwiz(f=open('bn.dot', mode="w+"))

#!
#! Joint distribution of initial condition and parameter of equation
#! -----------------------------------------------------------------

i = 0
ay0 = []
ui = [0.0] * n
figure()
for yend in [0.25, 1.25, 2.25]:
    M2 = M.inference(wanted_rvs=[A, Y0],
                     cond_rvs=[O[-1]] + U,
                     cond_X=[yend] + ui)
    subplot(1, 3, i + 1)
    title("O_{0}={1}".format(n, yend))
    M2.plot()
    ay0.append(M2.nddistr.mode())  # "most probable" state
    print "yend=", yend, ",  MAP  est. of A, Y0 =", ay0[i]
    i += 1
show()
#!
#! Trajectory
#! ----------

figure()
styles = ['-', '--', '-.', ':']
for j in range(len(ay0)):

Example #8

yi = 0.0
ydenoise = 0.0
ynoise = 0.0
y = 0.0
figure()
for i in range(nT):
    t[i] = i
    # Deterministic simultation
    u[i] = 0.1 * sign(sin(4 * pi * i / nT))
    y = y * K + u[i]
    Yorg[i] = y
    Ynoised[i] = y + E[0].rand()
    # Inference (Y[i] | O[i-n+1], ..., O[i]
    if i > n - 1:
        MY = M.inference(wanted_rvs=[Y[-1]],
                         cond_rvs=O + U,
                         cond_X=concatenate(
                             (Ynoised[i - n + 1:i + 1], u[i - n + 1:i + 1])))
        ydenoised = MY.as1DDistr().median()
        Ydenoised[i] = ydenoised
        #MY.as1DDistr().boxplot(i, width=0.2, useci=0.1)
plot(t, u, 'k-', label="U", linewidth=1.0)
plot(t, Ynoised, 'k.--', label="O", linewidth=1.0)
plot(t, Yorg, 'k-.', label="Y original", linewidth=3.0)
plot(t, Ydenoised, 'k-', label="Y denoised", linewidth=2.0)
legend(loc='lower left')

#! Error of estimation using median
#! --------------------------------
print "mse=", sqrt(mean((Yorg - Ynoised)**2)), sqrt(mean(
    (Yorg - Ydenoised)**2))
print "mae=", mean(abs(Yorg - Ynoised)), mean(abs(Yorg - Ydenoised))

Example #9

File: vec_sum.py Project: jszymon/pacal

X2 = BetaDistr(4,4, sym="X2")
Y1 = BetaDistr(4,4, sym="Y1")
Y2 = BetaDistr(4,4, sym="Y2")


C1 = FrankCopula2d(theta=5, marginals=[X1, X2])
C2 = FrankCopula2d(theta=2, marginals=[Y1, Y2])
C1.contour()
C2.contour()
figure()

# C1 = FrankCopula2d(theta=2, marginals=[X1, X2])
# C2 = FrankCopula2d(theta=2.5, marginals=[Y1, Y2])

#C1 = GumbelCopula2d(theta=2, marginals=[X1, X2])
#C1 = PiCopula(marginals=[X1, X2])


Z1 = X1 + Y1; Z1.setSym("Z1")
Z2 = X2 + Y2; Z2.setSym("Z2")

M = Model([C1,C2], [Z1, Z2])
#M = Model([C1,Y1,Y2], [Z1, Z2])
#M = Model([X1,X2,Y1,Y2], [Z1, Z2])
print(M)

M2 = M.inference([Z1, Z2])
print(M2)
M2.plot()
show()

Example #10

File: linreg_m.py Project: dkasak/pacal

# MXY.plot()
# plot([0.0, 1.0], [0.7, 0.7+a], "k-", linewidth=2.0)
# plot(Xobs, Yobs, "ko")
# plot()
# show()

#print ar, br
print Xobs, Yobs
print X + Y
print concatenate((Xobs, Yobs))

#print M
#MAB = M.inference([A,B]+E, X + Y,  concatenate((Xobs, Yobs)))
#print MAB
#MAB = MAB.inference([A,B], X + Y,  concatenate((Xobs, Yobs)))
MW = M.inference(W, X + Y,  concatenate((Xobs, Yobs)))
print "-------------------"
MW0 = MW.inference([W[0]],[],[])
#MB = MW.inference([B],[],[])

#M = M.inference([A,B], [X[0], Y[0]], [0.2, 0.4])
print MW
        
print MW0
figure()
subplot(211)
MW0.plot()
#print MB
#subplot(212)
#MB.plot()
#print "mean   est. A=", MA.as1DDistr().mean(),   "est. B=", MB.as1DDistr().mean()

Example #11

File: sums.py Project: sczesla/pacal

for i in range(n):
    print("X{}".format(i))
    X[i] = BetaDistr(2, 2, sym = "X{}".format(i))
    if i==0:
        S[i] = X[0]        
    else:
        S[i] = S[i-1] + X[i]
        S[i].setSym("S{}".format(i))

M = Model(X, S[1:])
print(M)
M.toGraphwiz()
#M = M.inference([S[-1], S[-4]], [S[-3]], [1])
#M = M.inference([X[0], X[1]], [S[-1]], [3.5])
print("====================")
M1 = M.inference(wanted_rvs =[X[0], X[1]], cond_rvs=[S[-1]], cond_X=[1])
print("====================",M1)
M2 = M.inference(wanted_rvs =[S[1], S[4]])
print("====================",M2)
M3 = M.inference(wanted_rvs =[S[1], S[4]], cond_rvs=[S[3]], cond_X=[2])
print("====================",M3)
MC_X0 = M.inference(wanted_rvs =[X[0]], cond_rvs=[S[-1]], cond_X=[1])
print("====================")

print(M1)
figure()
M1.plot(cont_levels=10)
figure()
M1.plot(have_3d=True)

print(M2)

Example #12

File: diffeq.py Project: ntankovic/pacal

        pass
    else:
        Y[i] = Y[i - 1] * K
        Y[i].setSym("Y" + str(i))
P = NDProductDistr([Factor1DDistr(A), Factor1DDistr(Y[0])])
M = Model(P, Y[1:])
M.eliminate_other([K] + Y)

#M2 = M.inference2([Y[0], A], [Y[n]], [1])
#M2.plot(); print M2; show()
#M2 = M.inference2([Y[0]], [Y[n]], [0.5])
#figure()
#M2.plot(); print M2;
figure()
Y[-1].plot(color='r', linewidth=5)
M3 = M.inference([Y[-1]], [], [])

M3.plot()
print M3

X0 = BetaDistr(2, 2)
y = X0 * exp(A)
y.summary()
y.plot(label="Y0*exp(A)")
Y[-1].plot('r')
figure()
err = y.get_piecewise_pdf() - M3.as1DDistr().get_piecewise_pdf()
err.plot()
show()

stop

Example #13

File: lotka_volterra.py Project: sczesla/pacal

for i in range(n):
    print(i)
    if i==0:
        X[i] = BetaDistr(3, 3, sym = "X0")
        Y[i] = BetaDistr(3, 3, sym = "Y0")
    else:
        X[i] = X[i-1] + h*(A*X[i-1] - B*Y[i-1])
        Y[i] = Y[i-1] + h*(-C*X[i-1] + D*Y[i-1])
        
        X[i].setSym("X{}".format(i))
        Y[i].setSym("Y{}".format(i))



M = Model([X[0], Y[0], A, B, C, D], X[1:] + Y[1:] )
print(M)
M.eliminate_other([X[0], Y[0], A, B, C, D] + X[1:] + Y[1:])
print(M)
print(Y[1].range())

#M1 = M.inference([X[2], Y[2]], [X[0], Y[0]], [0.5, 0.2])\
figure()
    
for i in range(n):
    M1 = M.inference([X[i], Y[i]], [A, B, C, D], [0.9, 0.2, 0.3, 0.6])
    print(M1)
    M1.plot(cont_levels=1)
    #figure()
    #M1.plot(have_3d=True)
show()

Example #14

File: lotka_volterra.py Project: dkasak/pacal

h=0.1
for i in range(n):
    print i
    if i==0:
        X[i] = BetaDistr(3, 3, sym = "X0")
        Y[i] = BetaDistr(3, 3, sym = "Y0")
    else:
        X[i] = X[i-1] + h*(A*X[i-1] - B*Y[i-1])
        Y[i] = Y[i-1] + h*(-C*X[i-1] + D*Y[i-1])
        
        X[i].setSym("X{}".format(i))
        Y[i].setSym("Y{}".format(i))



M = Model([X[0], Y[0], A, B, C, D], X[1:] + Y[1:] )
print M
M.eliminate_other([X[0], Y[0], A, B, C, D] + X[1:] + Y[1:])
print M
print Y[1].range()

#M1 = M.inference([X[2], Y[2]], [X[0], Y[0]], [0.5, 0.2])\
figure()
    
for i in range(n):
    M1 = M.inference([X[i], Y[i]], [A, B, C, D], [0.9, 0.2, 0.3, 0.6])
    print M1
    M1.plot(cont_levels=1)
    #figure()
    #M1.plot(have_3d=True)
show()