def sample(self, ndraw = 1000, adaptationConstant = .90,alpha = .5, steps = 10, debug = Inf, ndraw_max = 20000 , nChains = 5, burnIn = 100, thin = 1, convergenceCriteria = 1.1, mConvergence = False, mAccept = False):
"""
Samples from a posterior distribution using DREAM.
Parameters
----------
ndraw : int
minimum number of draws from the sample distribution to be returned
ndraw_max : int
maximum number of draws from the sample distribution to be returned
nChains : int
number of different chains to employ
burnInSize : int
number of iterations (meaning draws / nChains) to do before doing actual sampling.
Returns
-------
None : None
sample sets
self.history which contains the combined draws for all the chains
self.iter which is the total number of iterations
self.acceptRatio which is the acceptance ratio
self.burnIn which is the number of burn in iterations done
self.R which is the gelman rubin convergence diagnostic for each dimension
"""
startTime = time.time()
maxChainDraws = floor(ndraw_max/nChains)
self._initChains(nChains, ndraw_max)
# get the starting log likelihood and position for each of the chains
currentVectors =random.normal(loc = 1.0, scale = .01, size = (self._nChains, self.dimensions)) #self._vectors'
currentVectors[:,0] -= 1.0
self._propose(currentVectors)
currentLogPs = self._logPs
currentGradLogPs = self._gradLogPs
#initialize the history arrays
combinedHistory = zeros((nChains * maxChainDraws , self.dimensions))
sequenceHistories = zeros((nChains, self.dimensions, maxChainDraws))
logPSequences = zeros((nChains, maxChainDraws))
#add the starting positions to the history
sequenceHistories[:,:,0] = currentVectors
combinedHistory[0:nChains,:] = currentVectors
logPSequences[:, 0] = currentLogPs
# initilize the convergence diagnostic object
grConvergence = GRConvergence()
#2)now loop through and sample
minDrawIters = ceil(ndraw / nChains)
maxIters = ceil(ndraw_max /nChains)
iter = 1
acceptsRatio = 0
relevantHistoryStart = 0
relevantHistoryEnd = 1
lastRecalculation = 0
adaptedMean = 0
adaptedCov = 1.0
# continue sampling if:
# 1) we have not drawn enough samples to satisfy the minimum number of iterations
# 2) or any of the dimensions have not converged
# 3) and we have not done more than the maximum number of iterations
momentumVectors = 0
while ( relevantHistoryStart < burnIn or (relevantHistoryEnd - relevantHistoryStart) *nChains < ndraw or any(grConvergence.R > convergenceCriteria)) and relevantHistoryEnd*nChains < ndraw_max:
adaptedMean, adaptedCov = self._adapt(currentVectors,adaptationConstant/max(relevantHistoryStart-burnIn, 1), adaptedMean, adaptedCov)
# generate momentum vectors
momentumVectors = momentumVectors * alpha + .5 * (1- alpha**2) * random.normal(size = (self._nChains, self.dimensions))
stepMomentum = momentumVectors
stepGradLogPs = currentGradLogPs
scale = diagonal(adaptedCov)
if iter % debug == 0 :
print "c", currentVectors
print "cM", momentumVectors
print "cp", currentLogPs
print "cg", currentGradLogPs
for i in range(steps):
halfStepMomentum = stepMomentum + (.5/steps) * stepGradLogPs
stepVectors = currentVectors + (.5/steps) * halfStepMomentum * scale
self._propose(stepVectors)
stepGradLogPs = self._gradLogPs
stepMomentum = halfStepMomentum + (.5/steps) * stepGradLogPs
if ( iter %debug == 0):
print i
print "s", stepVectors
print "sM", stepMomentum
print "sg", stepGradLogPs
proposalVectors = stepVectors
proposalLogPs = self._logPs
proposalGradLogPs = stepGradLogPs
#apply the metrop decision to decide whether to accept or reject each chain proposal
decisions, acceptance = self._metropolis_hastings(currentLogPs + sum(momentumVectors**2 / (2 )* scale, axis = 1),
proposalLogPs+ sum(stepMomentum**2 / (2 )* scale, axis = 1))
weighting = 1 - exp(-1.0/60)
acceptsRatio = weighting * sum(acceptance)/nChains + (1-weighting) * acceptsRatio
if mAccept and iter % 20 == 0:
print acceptsRatio
#make the current vectors the previous vectors
previousVectors = currentVectors
currentVectors = choose(decisions[:,newaxis], (currentVectors, proposalVectors))
currentLogPs = choose(decisions, (currentLogPs, proposalLogPs))
currentGradLogPs = choose(decisions[:, newaxis], (currentGradLogPs, proposalGradLogPs))
#need to repropose these because some of these may have been rolled back more than 1 "proposal"
self._propose(currentVectors)
# we only want to recalculate convergence criteria when we are past the burn in period
# and then only every so often (currently every 10% increase in iterations)
if (relevantHistoryStart > burnIn and
(relevantHistoryEnd - relevantHistoryStart) * nChains > ndraw and
iter > lastRecalculation * 1.1):
lastRecalculation = iter
# calculate the Gelman Rubin convergence diagnostic
grConvergence.update(sequenceHistories, relevantHistoryEnd, relevantHistoryStart, self.dimensions, nChains)
if mConvergence:
print mean(grConvergence.R), std(grConvergence.R), max(grConvergence.R), argmax(grConvergence.R)
#record the vector for each chain
if iter % thin == 0:
sequenceHistories[:,:,relevantHistoryEnd] = currentVectors
combinedHistory[(relevantHistoryEnd *nChains) :(relevantHistoryEnd *nChains + nChains),:] = currentVectors
logPSequences[:, relevantHistoryEnd] = currentLogPs
relevantHistoryEnd += 1
relevantHistoryStart += .5
iter += 1
#3) finalize
# only make the second half of draws available because that's the only part used by the convergence diagnostic
self.history = combinedHistory[relevantHistoryStart*nChains:relevantHistoryEnd*nChains,:]
self.iter = iter
self.acceptRatio = acceptsRatio
self.burnIn = burnIn
self.time = time.time() - startTime
self.R = grConvergence.R
self._finalizeChains()
def sample(self, ndraw = 1000, samplesPerAdapatationParameter = 5, adaptationDecayLength = 250, variables_of_interest = None,minimum_scale = .1, maxGradient = 1.0, ndraw_max = None , nChains = 5, burnIn = 1000, thin = 2, convergenceCriteria = 1.1, monitor_convergence = True, monitor_acceptence = True):
"""Samples from a posterior distribution using Adaptive Metropolis Adjusted Langevin Algorithm (AMALA).
Parameters
----------
ndraw : int
minimum number of draws from the sample distribution to be returned
ndraw_max : int
maximum number of draws from the sample distribution to be returned
nChains : int
number of different chains to employ
burnInSize : int
number of iterations (meaning draws / nChains) to do before doing actual sampling.
minimum_scale : float
the minimum that the scaling constant can fall to (default .1)
monitor_convergence : bool
determines whether to periodically print out convergence statistics (True)
monitor_acceptence : bool
determines whether to periodically print out the average acceptance ratio and adapted scale
Returns
-------
None : None
sample sets
self.history which contains the combined draws for all the chains
self.iter which is the total number of iterations
self.burnIn which is the number of burn in iterations done
self.R which is the gelman rubin convergence diagnostic for each dimension
"""
startTime = time.time()
if ndraw_max is None:
ndraw_max = 10 * ndraw
maxChainDraws = floor(ndraw_max/nChains)
self._initChains(nChains, ndraw_max)
history = SimulationHistory(self.slices, maxChainDraws,self._nChains, self.dimensions)
if variables_of_interest is not None:
slices = []
for var in variables_of_interest:
slices.append(self.slices[var])
else:
slices = [slice(None,None)]
history.add_group('interest', slices)
# initilize the convergence diagnostic object
convergence_diagnostics = [GRConvergence(.1, history),
CovarianceConvergence(.3, history),
CovarianceConvergence(.2, history, 'interest')]
monitor_diagnostics = [convergence_diagnostics[0], convergence_diagnostics[2]]
iter = 1
lastRecalculation = 0
# try to find some approximate modes for starting the chain
for chain in self._chains:
inv_hessian = find_mode(self,chain)
adaptationConstant = min(self._nChains*1.0/(self.dimensions * samplesPerAdapatationParameter), 1)
adapted_approximation = AdaptedApproximation(self._chains[1].vector, inv_hessian)
adapted_scale = AdaptedScale(self.optimalAcceptance, minimum_scale)
accepts_ratio_weighting = 1 - exp(-1.0/30)
adaptationDecay = 1.0/adaptationDecayLength
# continue sampling if:
# 1) we have not drawn enough samples to satisfy the minimum number of iterations
# 2) or any of the dimensions have not converged
# 3) and we have not done more than the maximum number of iterations
while ( (history.nsamples < ndraw or
not all((diagnostic.converged() for diagnostic in convergence_diagnostics))) and
history.ncomplete_sequence_histories < maxChainDraws - 1):
if iter == burnIn:
history.start_sampling()
current_logps = self.logps
jump_logp, reverse_logp = propose_amala(self,adapted_approximation, adapted_scale, maxGradient)
acceptance = self.metropolis_hastings(current_logps,self.logps, jump_logp, reverse_logp)
self._update_accepts_ratio(accepts_ratio_weighting, acceptance)
if monitor_acceptence and iter % 20 == 0:
print "accepts ratio: ", self.accepts_ratio, " adapted scale: ", adapted_scale.scale
if history.nsamples > ndraw and history.nsamples > lastRecalculation * 1.1:
lastRecalculation = history.nsamples
for diagnostic in convergence_diagnostics:
diagnostic.update()
for diagnostic in monitor_diagnostics:
print diagnostic.state()
if iter % thin == 0:
history.record(self.vectors, self.logps, .5)
adaptation_rate = exp(-adaptationConstant/exp(history.nsamples * adaptationDecay))
adapted_approximation.update(self.vectors, adaptation_rate)
mean(self.vectors)
adapted_scale.update(acceptance, adaptation_rate)
iter += 1
self.finalize_chains()
return history , time.time() - startTime
def sample(self, ndraw = 1000, ndraw_max = 20000 , nChains = 5, burnIn = 100, thin = 5, convergenceCriteria = 1.1,variables_of_interest = None, nCR = 3, DEpairs = 1, adaptationRate = .65, eps = 5e-6, mConvergence = False, mAccept = False):
"""
Samples from a posterior distribution using DREAM.
Parameters
----------
ndraw : int
minimum number of draws from the sample distribution to be returned
ndraw_max : int
maximum number of draws from the sample distribution to be returned
nChains : int
number of different chains to employ
burnInSize : int
number of iterations (meaning draws / nChains) to do before doing actual sampling.
nCR : int
number of intervals to use to adjust the crossover probability distribution for efficiency
DEpairs : int
number of pairs of chains to base movements off of
eps : float
used in jittering the chains
Returns
-------
None : None
sample sets
self.history which contains the combined draws for all the chains
self.iter which is the total number of iterations
self.acceptRatio which is the acceptance ratio
self.burnIn which is the number of burn in iterations done
self.R which is the gelman rubin convergence diagnostic for each dimension
"""
startTime = time.time()
maxChainDraws = floor(ndraw_max/nChains)
self._initChains(nChains, ndraw_max)
history = SimulationHistory(maxChainDraws, self._nChains, self.dimensions)
if variables_of_interest is not None:
slices = []
for var in variables_of_interest:
slices.append(self.slices[var])
else:
slices = [slice(None,None)]
history.add_group('interest', slices)
# initialize the temporary storage vectors
currentVectors = zeros((nChains, self.dimensions))
currentLogPs = zeros(nChains)
#) make a list of starting chains that at least spans the dimension space
# in this case it will be of size 2*dim
nSeedChains = int(ceil(self.dimensions* 2/nChains) * nChains)
nSeedIterations = int(nSeedChains/nChains)
model = self._model_generator()
for i in range(nSeedIterations - 1):
vectors = zeros((nChains, self.dimensions))
for j in range(nChains):
#generate a vector drawn from the prior distributions
for variable in model:
if isinstance(variable,Stochastic) and not variable.observed:
drawFromPrior = variable.random()
if isinstance(drawFromPrior , np.matrix):
drawFromPrior = drawFromPrior.A.ravel()
elif isinstance(drawFromPrior, np.ndarray):
drawFromPrior = drawFromPrior.ravel()
else:
drawFromPrior = drawFromPrior
vectors[j,self.slices[str(variable)]] = drawFromPrior
history.record(vectors,0,0)
#use the last nChains chains as the actual chains to track
vectors = self._vectors
#add the starting positions to the history
history.record(vectors,self._logPs,0)
gamma = None
# initilize the convergence diagnostic object
grConvergence = GRConvergence()
covConvergence = CovarianceConvergence()
# get the starting log likelihood and position for each of the chains
currentVectors = vectors
currentLogPs = self._logPs
#2)now loop through and sample
minDrawIters = ceil(ndraw / nChains)
maxIters = ceil(ndraw_max /nChains)
iter = 0
accepts_ratio_weighting = 1 - exp(-1.0/30)
lastRecalculation = 0
# continue sampling if:
# 1) we have not drawn enough samples to satisfy the minimum number of iterations
# 2) or any of the dimensions have not converged
# 3) and we have not done more than the maximum number of iterations
while ( history.nsamples < ndraw or any(grConvergence.R > convergenceCriteria)) and history.ncombined_history < ndraw_max:
if iter == burnIn:
history.start_sampling()
#every5th iteration allow a big jump
if random.randint(5) == 0.0:
gamma = array([1.0])
else:
gamma = array([2.38 / sqrt( 2 * DEpairs * self.dimensions)])
proposalVectors = dream_components.dream_proposals(currentVectors, history,self.dimensions, nChains, DEpairs, gamma, .05, eps)
# get the log likelihoods for the proposal chains
self._propose(proposalVectors)
proposalLogPs = self._logPs
#apply the metrop decision to decide whether to accept or reject each chain proposal
decisions, acceptance = self._metropolis_hastings(currentLogPs,proposalLogPs)
self._update_accepts_ratio(accepts_ratio_weighting, acceptance)
if mAccept and iter % 20 == 0:
print self.accepts_ratio
self._reject(decisions)
#make the current vectors the previous vectors
previousVectors = currentVectors
currentVectors = choose(decisions[:,newaxis], (currentVectors, proposalVectors))
currentLogPs = choose(decisions, (currentLogPs, proposalLogPs))
# we only want to recalculate convergence criteria when we are past the burn in period
if history.nsamples > 0 and iter > lastRecalculation * 1.1 and history.nsequence_histories > self.dimensions:
lastRecalculation = iter
grConvergence.update(history)
covConvergence.update(history,'all')
covConvergence.update(history,'interest')
if mConvergence:
print mean(grConvergence.R), std(grConvergence.R), max(grConvergence.R), argmax(grConvergence.R)
print covConvergence.relativeVariances['interest']
if iter % thin == 0:
historyStartMovementRate = adaptationRate
#try to adapt more when the acceptance rate is low and less when it is high
if adaptationRate == 'auto':
historyStartMovementRate = min((.234/self.accepts_ratio)*.5, .95)
history.record(currentVectors, currentLogPs, historyStartMovementRate)
iter += 1
#3) finalize
# only make the second half of draws available because that's the only part used by the convergence diagnostic
self.history = history.samples
self.iter = iter
self.burnIn = burnIn
self.time = time.time() - startTime
self.R = grConvergence.R
self._finalizeChains()