def test1DSoftmax():
# weight = [-30,-20,-10,0];
# bias = [60,50,30,0];
weight = [-5, 0]
bias = [5, 0]
softClass = 0
low = 0
high = 5
res = 100
#Define Likelihood Model
a = Softmax(weight, bias)
#build a prior gaussian
prior = GM([2, 4], [1, 0.5], [1, 0.5])
#Get the posterior
post = a.runVB(prior, softClassNum=softClass)
a.plot1D(res=res, low=0, high=5)
#Plot Everything
[x0, classes] = a.plot1D(res=res, vis=False)
[x1, numApprox] = a.numericalProduct(prior,
softClass,
low=low,
high=high,
res=res,
vis=False)
softClassLabels = ['Far left', 'Left', 'Far Right', 'Right']
labels = ['likelihood', 'prior', 'VB Posterior', 'Numerical Posterior']
[x2, pri] = prior.plot(low=low, high=high, num=res, vis=False)
[x3, pos] = post.plot(low=low, high=high, num=res, vis=False)
plt.plot(x0, classes[softClass])
plt.plot(x2, pri)
plt.plot(x3, pos)
plt.plot(x1, numApprox)
plt.ylim([0, 1.1])
plt.xlim([low, high])
plt.title("Fusion of prior with: " + softClassLabels[softClass])
plt.legend(labels)
plt.show()
print(i.action);
i.plot(low=-20,high=20);
'''
xs = [i for i in range(-20, 21)]
gs = [0] * len(xs)
for i in range(0, len(xs)):
gs[i] = GM()
gs[i].addG(Gaussian(i - 20, 5, 1))
acts = [-1] * len(xs)
for i in range(0, len(xs)):
acts[i] = getAction(gs[i], Gamma)
print(acts)
'''
al1 = [GM()];
al1 = copy.deepcopy(r[2]);
al1.scalerMultiply(1/(.1));
al1 = [al1];
al2 = backup(al1,modes,delA,delAVar,pz,r,maxMix,b)
al2.plot(low=-20,high=20);
'''
'''
b.plot(low = -20,high=20);
b = beliefUpdate(modes,delA,delAVar,pz,b,act,obs,5);
b.plot(low = -20,high=20);
'''
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()
alpha1 = GM();
alpha1.addG(Gaussian(1,1,2));
alpha1.addG(Gaussian(2,0.5,-1));
alpha2 = GM();
alpha2.addG(Gaussian(3,0.25,0.5));
alpha2.addG(Gaussian(4,0.5,-1));
alpha3 = GM();
alpha3.addG(Gaussian(5,2,2));
alpha3.addG(Gaussian(3,0.5,-1));
[x,c] = alpha1.plot(low=0,high=5,vis = False);
[x2,c2] = alpha2.plot(low=0,high=5,vis = False);
[x3,c3] = alpha3.plot(low=0,high=5,vis = False);
plt.plot(x,c,linewidth=5,color='r');
plt.plot(x2,c2,linewidth=5,color='g');
plt.plot(x3,c3,linewidth=5,color='y');
plt.axhline(y=0, xmin=0, xmax=5, linewidth=2, color = 'k')
plt.title('Alpha Functions',fontsize=30);
plt.xlabel('Position',fontsize = 20);
plt.ylabel('Value',fontsize=20);
plt.legend(['Move Right','Stay','Move Left']);