/
samplingComp.py
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/
samplingComp.py
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import sys
sys.path.append('./tdf/Venture')
import calcPost as cp
import ppUtils as pu
import cPickle
import random
import numpy as np
import scipy.stats
from matplotlib import pyplot as plt
corp = []
def getCorp(ind):
global corp
if len(corp) > ind:
return corp[ind]
else:
start = len(corp) + 1
end = start + max(len(corp)*2,1000)
corp = corp + [float(int(s,2)) / 2**(len(s)) for s in [bin(i)[2:][::-1] for i in range(start,end)]]
return corp[ind]
pd = None
fac=None
maxPd = None
def getLL(ys, d, dof=4, fn="tdf/Venture/posteriorDict"):
global pd
global fac
global maxPd
if dof == 4:
if pd == None:
#print "loading Dict"
with open(fn,'r') as f:
fac, pd = cPickle.load(f)
maxPd = max(pd.values())
try:
return pd[round(d*fac)]
except:
return float("-inf")
elif dof == 21:
if pd == None:
#print "loading Dict"
with open(fn + "21",'r') as f:
fac, pd = cPickle.load(f)
maxPd = max(pd.values())
try:
return pd[round(d*fac)]
except:
return float("-inf")
else:
return cp.logLiks(ys, d, base=2)
def metropolis(ll, prop, stop): # assume proposal distribution is symmetric
samples = [prop([])]
curLL = ll(samples[-1])
while not stop(samples):
curProp = prop(samples)
propLL = ll(curProp)
if propLL >= curLL:
samples.append(curProp)
curLL = propLL
else:
accProb = 2**(propLL - curLL)
if random.random() < accProb:
samples.append(curProp)
curLL = propLL
else:
samples.append(samples[-1])
return samples
def metropolisTdf(ys, iters, eps, dof=4):
if dof == 4:
mode = 4.214
elif dof == 21:
mode = 11.5
ll = lambda sample: getLL(ys, sample, dof)
prop = lambda _: 2 + random.random()*98
stop = lambda samples: samples[-1] >= mode-eps and samples[-1] < mode+eps
lens = []
for i in range(iters):
samples = metropolis(ll, prop, stop)
lens.append(len(samples))
#print samples
return np.mean(lens), np.std(lens)
def metropolisMixTdf(ys, sampleNo, dof=4):
if dof == 4:
mode = 4.214
elif dof == 21:
mode = 11.5
ll = lambda sample: getLL(ys, sample, dof)
prop = lambda s: 2 + random.random()*98 if len(s) > 0 else mode
stop = lambda samples: len(samples) >= sampleNo
return metropolis(ll, prop, stop)
def metropolisTdfSim(iters):
mode = 4.214
eps = 0.25
ll = lambda sample: -1 * abs(sample - mode)
prop = lambda s: random.random()*100
stop = lambda samples: samples[-1] >= mode-eps and samples[-1] < mode+eps
lens = []
for i in range(iters):
lens.append(len(metropolis(ll, prop, stop)))
print np.mean(lens), np.std(lens)
def metropolisTdfCorp(ys, iters, eps, dof=4):
if dof == 4:
mode = 4.214
elif dof == 21:
mode = 11.5
ll = lambda sample: getLL(ys, sample, dof)
prop = lambda s : getCorp(len(s))*100
stop = lambda samples: samples[-1] >= mode-eps and samples[-1] < mode+eps
lens = []
for i in range(iters):
samples = metropolis(ll, prop, stop)
lens.append(len(samples))
#print samples
return np.mean(lens), np.std(lens)
def sliceSampling(lik, x, iw, stop): # assume proposal distribution is symmetric
samples = [x]
llCalc = 0
rejected = 0
while not stop(samples, llCalc):
llCalc += 2 # not 3 because one likelihood calculation implicit in the samples' existence
y = random.uniform(0, lik(samples[-1]))
r = random.random()
xl = samples[-1] - r*iw
xr = samples[-1] + (1-r)*iw
w = iw
while lik(xl) > y:
llCalc += 1
xl -= w
w *= 2
w = iw
while lik(xr) > y:
llCalc += 1
xr += w
w *= 2
#print samples[-1], y, xl, xr
while True:
prop = random.uniform(xl, xr)
propLik = lik(prop)
if propLik > y:
samples.append(prop)
break
else:
rejected += 1
llCalc += 1
if prop > samples[-1]:
xr = prop
else:
xl = prop
return samples, llCalc + len(samples)
def sliceSamplingTdf(ys, iters, eps, w = 1, dof=4):
if dof == 4:
mode = 4.214
elif dof == 21:
mode = 11.5
ll = lambda sample: 2**(getLL(ys, sample, dof) - maxPd)
stop = lambda samples, _: samples[-1] >= mode-eps and samples[-1] < mode+eps
lens = []
for i in range(iters):
init = 2 + random.random()*98
samples, _ = sliceSampling(ll, init, w, stop)
lens.append(len(samples))
#print samples
return np.mean(lens), np.std(lens)
def sliceSamplingMixTdf(ys, sampleNo, w = 1, dof=4):
if dof == 4:
mode = 4.214
elif dof == 21:
mode = 11.5
ll = lambda sample: 2**(getLL(ys, sample, dof) - maxPd)
stop = lambda samples, rej: len(samples) + rej >= sampleNo
return sliceSampling(ll, mode, w, stop)
def sliceSamplingGauss(iters, eps, gauss, w = 1):
ll = lambda sample: gauss.pdf(sample)
stop = lambda samples, _: samples[-1] >= gauss.mean()-eps and samples[-1] < gauss.mean()+eps
lens = []
calcs = []
for i in range(iters):
init = random.random() * 100
samples, calc = sliceSampling(ll, init, w, stop)
calcs.append(calc)
lens.append(len(samples))
#print i
mLens = np.mean(lens)
mStds = np.std(lens)
mCalcs = np.mean(calcs)
return mLens, mStds, (mLens + mCalcs) / float(mLens)
def plotLogs(fn = "samplingLogs"):
dicLogs = {}
with open("samplingTests/" + fn, 'r') as f:
logs = f.read().strip().split("===")
for log in logs:
rows = log.strip().split('\n')
tp = rows[0].strip()
if len(tp) > 0:
dicLogs[tp] = ([],[])
for row in rows[1:]:
eps, mode, var = map(float, row.strip().split())
dicLogs[tp][0].append(eps * 2)
dicLogs[tp][1].append(mode)
daxs = {}
count = 0
cols = ['b','r','k','c']
for title,log in dicLogs.items():
ax, = plt.plot(log[0],log[1], cols[count], linewidth=3)
daxs[title] = ax
count += 1
axs = [ax for _, ax in sorted(daxs.items())]
titles = [title for title, _ in sorted(daxs.items())]
plt.legend(axs,titles)
plt.yscale("log")
plt.xlabel("Size of target neighbourhood", size=20)
plt.ylabel("Number of samples", size=20)
plt.title("Avg. samples to mode neighbourhood", size=30)
plt.show()
def plotSimpleLog(fn, xl, yl, ti):
xs = []
ys = []
zs = []
with open("samplingTests/" + fn, 'r') as f:
for row in f:
try:
key, mode, var, rej = map(float, row.strip().split())
xs.append(key)
ys.append(mode)
zs.append(rej)
plt.xscale("log")
except:
key, mode, var = map(float, row.strip().split())
xs.append(key)
zs.append(mode)
plt.plot(xs,zs, linewidth=3)
plt.ylim([0,20])
plt.xlabel(xl, size=20)
plt.ylabel(yl, size=20)
plt.title(ti, size=30)
plt.show()
def plotGauss(mean, std):
n = scipy.stats.norm(mean,std)
xs = []
ys = []
for s in np.arange(0,100.001,0.1):
xs.append(s)
ys.append(n.pdf(s))
plt.plot(xs,ys, linewidth=3)
plt.xlabel("x", size=20)
plt.ylabel("Likelihood", size=20)
plt.title("Gauss. w/ mean " + str(mean) + " and stDev " + str(std), size=30)
plt.show()
def printSamples(samples):
for s in range(len(samples)):
print s, samples[s]
if __name__ == "__main__":
#ys = pu.readData("tdf/tdfData")
#iters = 100
#dof = 4
#print len(sliceSamplingMixTdf(ys, 100, w = 1)[0])
#printSamples(sliceSamplingMixTdf(ys, 10000, w = 1)[0])
#printSamples(metropolisMixTdf(ys, 10000))
"""
cur = 0
eps = 0.5
mode = 4.214
ind = 0
lenToModes = {}
while len(lenToModes) < 100:
cur = getCorp(ind)*100
ind += 1
mode = round(cur+eps)
if mode not in lenToModes:
lenToModes[mode] = ind
print lenToModes
print np.mean(lenToModes.values())
"""
#for eps in np.arange(1,0,-0.1):
# print eps, metropolisTdf(ys, iters, eps, dof)
# print eps, metropolisTdfCorp(ys, iters, eps, dof)
# print eps, sliceSamplingTdf(ys, iters, eps, dof)
#for std in range(2,21):
# print std, sliceSamplingGauss(iters, 0.5, scipy.stats.norm(50,std))
#for mean in range(1,100):
# print mean, sliceSamplingGauss(iters, 0.5, scipy.stats.norm(mean,3))
#for w in np.logspace(-1,3,50):
# print w, sliceSamplingGauss(iters, 0.5, scipy.stats.norm(50,2), w)
#plotSimpleLog("slicePerfWidth", "Slice sampling initial width", "Likelihood comps", "Avg. likelihood comps. per sample")
#plotSimpleLog("slicePerfStd", "Likelihood's standard deviation", "Burn-in length", "Avg. samples to reach mode neigh.")
#plotSimpleLog("slicePerfMean", "Likelihood's mean", "Burn-in length", "Avg. samples to reach mode neigh.")
#plotSimpleLog("sliceMix", "Likelihood's mean", "Burn-in length", "Avg. samples to reach mode neigh.")
plotLogs()
#plotGauss(50,20)
#sliceSamplingTdf(ys, iters, eps, dof)