def stretch1DModel():
steep = 5
weight = (np.array([-3, -2, -1, 0]) * steep).tolist()
bias = (np.array([6, 5, 3, 0]) * steep).tolist()
low = 0
high = 5
res = 100
#Define Likelihood Model
a = Softmax(weight, bias)
a.plot1D(low=low, high=high)
#weight = (np.array([[-1,0],[0,0]])*steep).tolist();
#bias = (np.array([3,0])*steep).tolist();
for i in range(0, len(weight)):
weight[i] = [weight[i], 0]
b = Softmax(weight, bias)
b.plot2D(low=[0, 0], high=[5, 5])
def testVL():
#plotting parameters
low = 0
high = 5
res = 100
#Define Likelihood Model
weight = [-30, -20, -10, 0]
bias = [60, 50, 30, 0]
softClass = 1
likelihood = Softmax(weight, bias)
#Define Prior
prior = GM()
prior.addG(Gaussian(3, 0.25, 1))
startTime = time.clock()
postVL = VL(prior, likelihood, softClass, low, high, res)
timeVL = time.clock() - startTime
postVB = likelihood.runVB(prior, softClassNum=softClass)
timeVB = time.clock() - timeVL
#Normalize postVB
#postVB.normalizeWeights();
#share weights
#postVL[0].weight = postVB[0].weight;
postVB[0].weight = 1
[x0, classes] = likelihood.plot1D(res=res, vis=False)
[x1, numApprox] = likelihood.numericalProduct(prior,
softClass,
low=low,
high=high,
res=res,
vis=False)
softClassLabels = ['Far left', 'Left', 'Far Right', 'Right']
labels = [
'likelihood', 'prior', 'Normed VB Posterior', 'Normed VL Posterior',
'Numerical Posterior', 'Normed True Posterior'
]
[x2, pri] = prior.plot(low=low, high=high, num=res, vis=False)
[x3, pos] = postVB.plot(low=low, high=high, num=res, vis=False)
[x4, pos2] = postVL.plot(low=low, high=high, num=res, vis=False)
plt.plot(x0, classes[softClass])
plt.plot(x2, pri)
plt.plot(x3, pos)
plt.plot(x4, pos2)
plt.plot(x1, numApprox)
plt.ylim([0, 3.1])
plt.xlim([low, high])
plt.title("Fusion of prior with: " + softClassLabels[softClass])
SSE_VL = 0
SSE_VB = 0
for i in range(0, len(numApprox)):
SSE_VL += (numApprox[i] - pos2[i])**2
SSE_VB += (numApprox[i] - pos[i])**2
var_VL = postVL.getVars()[0]
var_VB = postVB.getVars()[0]
var_True = 0
mean_True = 0
mean_True = x1[numApprox.index(max(numApprox))]
for i in range(0, len(numApprox)):
var_True += numApprox[i] * (x1[i] - mean_True)**2
TruePostNorm = GM()
TruePostNorm.addG(Gaussian(mean_True, var_True, 1))
[x5, postTrue] = TruePostNorm.plot(low=low, high=high, num=res, vis=False)
plt.plot(x5, postTrue)
print("Variational Laplace:")
print("Time: " + str(timeVL))
print("Mean Error: " + str(postVL.getMeans()[0] - mean_True))
print("Variance Error: " + str(postVL.getVars()[0] - var_True))
print("ISD from Normed True: " + str(TruePostNorm.ISD(postVL)))
print("")
print("Variational Bayes:")
print("Time: " + str(timeVB))
print("Mean Error: " + str(postVB.getMeans()[0] - mean_True))
print("Variance Error: " + str(postVB.getVars()[0] - var_True))
print("ISD from Normed True: " + str(TruePostNorm.ISD(postVB)))
print("")
print("Time Ratio (L/B): " + str(timeVL / timeVB))
plt.legend(labels)
plt.show()
