def start(self, noOfSamples, stepSize, dimensionality, animateStatistics=False, animateDistribution=False, gibbsBatchSize=1, desiredCovarianceMatrix=None, ACT=True, subopt=True):
accepted = 0
# get a start point
x = self.proposal.getStartPoint()
while not self.desired(x) > 0:
x = self.proposal.getStartPoint()
samples = np.array([x])
# stats variables
acceptanceWindow = 1000
covCalc = Utility.covarianceCalculator(x)
suboptimality = []
act = []
asjdList = []
asjd = 0
acceptanceRates = []
sampleX = []
gibbsFactor = 1
if self.algorithm == Name.ADAPTIVE_GIBBS:
gibbsList = [[0,0] for dimension in x]
gibbsFactor = gibbsBatchSize * x.size
if animateDistribution or animateStatistics:
animationAx = None
acceptanceRateAx = None
plt.ion()
if animateDistribution and not animateStatistics:
fig = plt.figure(figsize=(10,8))
animationAx = plt.subplot(111)
if animateDistribution and dimensionality==1:
xDesired = np.arange(-10, 10, 0.1)
pDesired = self.desired(xDesired)
binSize = 0.25
binBoundaries = np.arange(-10,10,binSize)
if animateStatistics:
if animateDistribution:
fig = plt.figure(figsize=(18,10))
animationAx = plt.subplot(231)
if dimensionality>1:
animationAx2 = plt.subplot(232)
Animation.animate2DReal(self.desired, animationAx2)
acceptanceRateAx = plt.subplot(233)
suboptimalityAx = plt.subplot(234)
actAx = plt.subplot(235)
asjdAx = plt.subplot(236)
else:
fig = plt.figure(figsize=(10,10))
acceptanceRateAx = plt.subplot(221)
suboptimalityAx = plt.subplot(222)
actAx = plt.subplot(223)
asjdAx = plt.subplot(224)
# here we go
for i in xrange(noOfSamples):
# get a proposal and calulate the acceptance rate
if self.randomWalk:
if self.algorithm == Name.ADAPTIVE_METROPOLIS_HASTINGS and samples.shape[0] > dimensionality/2.:
x_new = self.proposal.getSample(x, sampleCovariance=covCalc.getSampleCovariance(samples)* 2.38**2 * 1./dimensionality)
elif self.algorithm == Name.ADAPTIVE_GIBBS:
x_new = self.proposal.getSample(x, samples.shape[0]%x.size)
else:
x_new = self.proposal.getSample(x)
div1 = self.desired(x_new)
div2 = self.desired(x)
if not div1 >= 0 or math.isnan(div1):
div1 = 0.
if not div2 >0 or math.isnan(div2):
div2 = 0.0001
# print div1, div2
acceptance = ( float(self.desired(x_new))/float(self.desired(x)) )
else:
if self.algorithm == Name.ADAPTIVE_GIBBS:
x_new = self.proposal.getSample(x, samples.shape[0]%x.size)
acceptance = ( self.desired(x_new)/self.desired(x) )
else:
x_new = self.proposal.getSample(None)
acceptance = ( self.desired(x_new)/self.desired(x) * self.proposal.getPDF(x,None)/self.proposal.getPDF(x_new,None) )
# accept the new proposal or stick with the old one
if acceptance > np.random.random():
asjd = (asjd*(samples.shape[0]-1) + np.linalg.norm(x-x_new)) / samples.shape[0]
x = x_new
accepted+=1.
if self.algorithm == Name.ADAPTIVE_GIBBS:
gibbsList[samples.shape[0]%x.size][0] += 1.
else:
x = x
asjd = (asjd*(samples.shape[0]-1)) / samples.shape[0]
if self.algorithm == Name.ADAPTIVE_GIBBS:
gibbsList[samples.shape[0]%x.size][1] += 1.
# do not take it as a sample when it is absolutely impossible to generate from the desired distribution
if acceptance>0.0:
if dimensionality==1:
samples = np.append(samples, x)
else:
samples = np.append(samples, [x], axis=0)
# calculate stats
#if dimensionality<3:
if samples.shape[0]%acceptanceWindow !=0:
acceptanceRate = float(accepted)/(samples.shape[0]%acceptanceWindow)
# print i,acceptanceRate
else:
print i, acceptanceRate
acceptanceRates.append(acceptanceRate)
accepted = 0
if animateStatistics:
sampleX.append(samples.shape[0])
if subopt:
suboptimality.append(Utility.getSuboptimality(covCalc.getSampleCovariance(samples), desiredCovarianceMatrix))
else:
suboptimality.append(0)
if ACT:
act.append(Utility.getACT(samples[-5000:]))
else:
act.append(0)
asjdList.append(asjd)
# act.append(69)
if self.algorithm==Name.ADAPTIVE_GIBBS and samples.shape[0]%gibbsFactor == 0:
self.proposal.adjust(gibbsList, samples.shape[0]/float(gibbsFactor))
gibbsList = [[0,0] for dimension in x]
if (animateDistribution or animateStatistics) and (i+2)%(stepSize)==0:
if animateDistribution and dimensionality==1:
Animation.animate1D(samples, binBoundaries, binSize, xDesired, pDesired, animationAx)
if animateDistribution and dimensionality==2:
Animation.animate2D(samples, animationAx)
if animateStatistics:
Animation.animateStats(sampleX, acceptanceRates, acceptanceRateAx, suboptimality, suboptimalityAx, act, actAx, asjdList, asjdAx)
plt.pause(0.00001)
if dimensionality > 2:
acceptanceRate = acceptanceRates[-1]
if ACT:
act = Utility.getACT(samples)
else:
act = 0
if subopt:
suboptimality = Utility.getSuboptimality(covCalc.getSampleCovariance(samples), desiredCovarianceMatrix)
else:
suboptimality = 0
asjd = asjd
print self.algorithm
print "acc: ", acceptanceRate
print "mean acc: ", np.mean(acceptanceRates)
print "subopt: ", suboptimality
print "act: ", act
print "asjd", asjd
plt.ioff()
plt.show()
def start(self, noOfSamples, stepSize, dimensionality, animateStatistics=False, animateDistribution=False, desiredCovarianceMatrix=None):
acceptedA = 0
acceptedB = 0
propA = False
propB = False
propABatch = False
propBBatch = False
acceptanceRateA = 0
acceptanceRateB = 0
aSamples = np.array([0])
bSamples = np.array([0])
# adaptive params a and b for two regions
a=0
b=0
# number of 100 samples
n=0
# get a start point
x = np.random.multivariate_normal(np.zeros(dimensionality), np.identity(dimensionality))
while not self.desired(x) > 0:
x = np.random.multivariate_normal(np.zeros(dimensionality), np.identity(dimensionality))
samplesA = np.array([x])
samplesB = np.array([x])
samples = np.array([x])
# stats variables
acceptanceWindow = 1000
covCalc = Utility.covarianceCalculator(x)
suboptimality = []
act = []
asjdList = []
asjd = 0
sampleX = []
acceptanceRates = []
if animateDistribution or animateStatistics:
animationAx = None
acceptanceRateAx = None
plt.ion()
if animateDistribution and not animateStatistics:
fig = plt.figure(figsize=(10,8))
animationAx = plt.subplot(111)
if animateDistribution and dimensionality==1:
xDesired = np.arange(-10, 10, 0.1)
pDesired = self.desired(xDesired)
binSize = 0.25
binBoundaries = np.arange(-10,10,binSize)
if animateStatistics:
if animateDistribution:
fig = plt.figure(figsize=(18,10))
animationAx = plt.subplot(231)
if dimensionality>1:
animationAx2 = plt.subplot(232)
Animation.animate2DReal(self.desired, animationAx2)
acceptanceRateAx = plt.subplot(233)
suboptimalityAx = plt.subplot(234)
actAx = plt.subplot(235)
asjdAx = plt.subplot(236)
else:
fig = plt.figure(figsize=(10,10))
acceptanceRateAx = plt.subplot(221)
suboptimalityAx = plt.subplot(222)
actAx = plt.subplot(223)
asjdAx = plt.subplot(224)
for i in xrange(noOfSamples):
acceptance = 0
#if self.desired.one.getPDF(x) <= self.desired.two.getPDF(x):
if np.linalg.norm(x) <= dimensionality:
propA = True
propABatch = True
x_new = np.random.multivariate_normal(x, np.identity(dimensionality)*np.exp(2*a))
#if self.desired.one.getPDF(x_new) <= self.desired.two.getPDF(x_new):
if np.linalg.norm(x_new) <= dimensionality:
acceptance = self.desired(x_new)/self.desired(x)
else:
acceptance = self.desired(x_new)/self.desired(x) * np.exp(dimensionality*(a-b)-0.5*np.dot(x,x_new)*(np.exp(-2*b)-np.exp(-2*a)))
else:
propB = True
propBBatch = True
x_new = np.random.multivariate_normal(x, np.identity(dimensionality)*np.exp(2*b))
#if self.desired.one.getPDF(x_new) > self.desired.two.getPDF(x_new):
if np.linalg.norm(x_new) > dimensionality:
acceptance = self.desired(x_new)/self.check(self.desired(x))
else:
acceptance = self.desired(x_new)/self.check(self.desired(x)) * np.exp(dimensionality*(b-a)-0.5*np.dot(x,x_new)*(np.exp(-2*a)-np.exp(-2*b)))
acceptance = min(1,acceptance);
# accept the new proposal or stick with the old one
if acceptance > np.random.random():
asjd = (asjd*(samples.shape[0]-1) + np.linalg.norm(x-x_new)) / samples.shape[0]
x = x_new
if dimensionality==1:
samples = np.append(samples, x)
else:
samples = np.append(samples, [x], axis=0)
if propA:
if acceptance > np.random.random():
acceptedA+=1
samplesA = np.append(samplesA, [x], axis=0)
acceptanceRateA = float(acceptedA)/samplesA.shape[0]
elif propB:
if acceptance > np.random.random():
acceptedB+=1
samplesB = np.append(samplesB, [x], axis=0)
acceptanceRateB = float(acceptedB)/samplesB.shape[0]
if i % 100 == 0:
n += 1
if propABatch:
a = self.delta(a,n,acceptanceRateA)
if propBBatch:
b = self.delta(b,n,acceptanceRateB)
aSamples = np.append(aSamples, a)
bSamples = np.append(bSamples, b)
propA = False
propB = False
# calculate stats
if samplesA.shape[0]%acceptanceWindow !=0:
acceptanceRateA = float(acceptedA)/(samplesA.shape[0]%acceptanceWindow)
#acceptanceRateB = float(acceptedB)/(samples.shape[0]%acceptanceWindow)
else:
print i, acceptanceRateA
acceptanceRates.append(acceptanceRateA)
accepted = 0
if animateStatistics:
sampleX.append(samples.shape[0])
suboptimality.append(Utility.getSuboptimality(covCalc.getSampleCovariance(samples), desiredCovarianceMatrix))
act.append(Utility.getACT(samples[-5000:]))
asjdList.append(asjd)
if (animateDistribution or animateStatistics) and (i+2)%(stepSize)==0:
if animateDistribution and dimensionality==1:
Animation.animate1D(samples, binBoundaries, binSize, xDesired, pDesired, animationAx)
if animateDistribution and dimensionality==2:
Animation.animate2D(samples, animationAx)
if animateStatistics:
Animation.animateStats(sampleX, acceptanceRates, acceptanceRateAx, suboptimality, suboptimalityAx, act, actAx, asjdList, asjdAx)
plt.pause(0.00001)
if dimensionality > 2:
acceptanceRate = acceptanceRates[-1]
act = Utility.getACT(samples)
suboptimality = Utility.getSuboptimality(covCalc.getSampleCovariance(samples), desiredCovarianceMatrix)
asjd = asjd
print self.algorithm
print "acc: ", acceptanceRate
print "mean acc: ", np.mean(acceptanceRates)
print "subopt: ", suboptimality
print "act: ", act
print "asjd", asjd