def SMC2(td,
beta_softmax=1.,
numberOfStateSamples=200,
numberOfThetaSamples=200,
numberOfBetaSamples=50,
coefficient=.5,
latin_hyp_sampling=True):
print('\n')
print('Forward Varying Volatility Model')
print('number of theta samples ' + str(numberOfThetaSamples))
print('\n')
start_time_multi = time.time()
# uniform distribution
if latin_hyp_sampling:
d0 = uniform()
print('latin hypercube sampling')
else:
print('sobolev sampling')
# Extract parameters from task description
stimuli = td['S'] # Sequence of Stimuli
numberOfActions = td['action_num'] # Number of Actions possible
numberOfStimuli = td['state_num'] # Number of states or stimuli
rewards = td['reward']
actions = td['A_chosen']
K = np.prod(
np.arange(numberOfActions +
1)[-numberOfStimuli:]) # Number of possible Task Sets
numberOfTrials = len(stimuli) # Number of Trials
# verification
if K == 2:
if latin_hyp_sampling == False:
raise ValueError(
'Why did you change the latin_hyp_sampling? By default, it is True and has no influence when K=2.'
)
# Sampling and prior settings
betaPrior = np.array([1, 1]) # Prior on Beta, the feedback noise parameter
nuPrior = np.array([
3, 1e-3
]) # Prior on Nu, the variance on the projected gaussian random walk
gammaPrior = numpy.ones(K) # Prior on Gamma, the Dirichlet parameter
try:
tauDefault = td['tau'][0]
except:
tauDefault = td['tau']
log_proba_ = 0.
# Mapping from task set to correct action per stimulus
mapping = get_mapping.Get_TaskSet_Stimulus_Mapping(
state_num=numberOfStimuli, action_num=numberOfActions).T
betaWeights = np.zeros(numberOfBetaSamples)
betaAncestors = np.arange(numberOfBetaSamples)
# Probabilities of every actions updated at every time step -> Used to take the decision
actionLikelihood = np.zeros([numberOfBetaSamples, numberOfActions])
sum_actionLik = np.zeros(numberOfBetaSamples)
filt_actionLkd = np.zeros(
[numberOfTrials, numberOfBetaSamples, numberOfActions])
# Keep track of probability correct/exploration after switches
tsProbability = np.zeros([numberOfBetaSamples, K])
sum_tsProbability = np.zeros(numberOfBetaSamples)
# SMC particles initialisation
muSamples = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
nuSamples = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
gammaSamples = np.zeros([numberOfBetaSamples, numberOfThetaSamples, K])
if K == 24:
try:
latin_hyp_samples = pickle.load(
open('../../utils/sobol_200_26.pkl', 'rb'))
except:
latin_hyp_samples = pickle.load(
open('../../models/utils/sobol_200_26.pkl', 'rb'))
for beta_idx in range(numberOfBetaSamples):
if latin_hyp_sampling:
latin_hyp_samples = mcerp.lhd(dist=d0,
size=numberOfThetaSamples,
dims=K + 2)
muSamples[beta_idx] = betalib.ppf(latin_hyp_samples[:, 0],
betaPrior[0], betaPrior[1])
nuSamples[beta_idx] = useful_functions.ppf_inv_gamma(
latin_hyp_samples[:, 1], nuPrior[0], nuPrior[1])
gammaSamples[beta_idx] = gammalib.ppf(latin_hyp_samples[:, 2:],
gammaPrior)
gammaSamples[beta_idx] = np.transpose(
gammaSamples[beta_idx].T /
np.sum(gammaSamples[beta_idx], axis=1))
elif K == 2:
muSamples = np.random.beta(betaPrior[0], betaPrior[1],
[numberOfBetaSamples, numberOfThetaSamples])
nuSamples = useful_functions.sample_inv_gamma(
nuPrior[0], nuPrior[1],
[numberOfBetaSamples, numberOfThetaSamples])
gammaSamples = np.random.dirichlet(
gammaPrior, [numberOfBetaSamples, numberOfThetaSamples])
else:
raise IndexError('Wrong number of task sets')
muSamplesNew = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
nuSamplesNew = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
gammaSamplesNew = np.zeros([numberOfBetaSamples, numberOfThetaSamples, K])
logThetaWeightsNew = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
normalisedThetaWeights = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples])
logThetaWeights = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
currentStateSamples = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples, numberOfStateSamples],
dtype=np.intc)
currentTauSamples = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples, numberOfStateSamples],
dtype=np.double)
ancestorStateSamples = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples, numberOfStateSamples],
dtype=np.intc)
ancestorTauSamples = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples, numberOfStateSamples],
dtype=np.double)
ancestorsWeights = np.ones([numberOfThetaSamples, numberOfStateSamples
]) / numberOfStateSamples
essList = np.zeros(numberOfTrials)
# Guided SMC variables
dirichletParamCandidates = np.zeros(K)
# Loop over trials
for T in range(numberOfTrials):
# Print progress
if (T + 1) % 10 == 0:
sys.stdout.write(' ' + str(T + 1))
sys.stdout.flush()
if (T + 1) % 100 == 0: print('\n')
for beta_idx in range(numberOfBetaSamples):
ances = betaAncestors[beta_idx]
# Update theta weights
smc_c.bootstrapUpdateStep_c(currentStateSamples[beta_idx], logThetaWeights[beta_idx], currentTauSamples[beta_idx], gammaSamples[ances], muSamples[ances]/2. + 1./2, nuSamples[ances], tauDefault, T, \
np.ascontiguousarray(ancestorStateSamples[ances], dtype=np.intc), ancestorTauSamples[ances], ancestorsWeights, np.ascontiguousarray(mapping), stimuli[T-1], actions[T-1], rewards[T-1])
# Degeneray criterion
logEss = 2 * useful_functions.log_sum(
logThetaWeights[beta_idx]) - useful_functions.log_sum(
2 * logThetaWeights[beta_idx])
essList[T] = np.exp(logEss)
# Move step
normalisedThetaWeights[
beta_idx] = useful_functions.to_normalized_weights(
logThetaWeights[beta_idx])
if (essList[T] < coefficient * numberOfThetaSamples):
betaMu = np.sum(normalisedThetaWeights[beta_idx] *
muSamples[ances])
betaVar = np.sum(normalisedThetaWeights[beta_idx] *
(muSamples[ances] - betaMu)**2)
betaAlpha = ((1 - betaMu) / betaVar - 1 / betaMu) * betaMu**2
betaBeta = betaAlpha * (1 / betaMu - 1)
assert (betaAlpha > 0)
assert (betaBeta > 0)
nuMu = np.sum(normalisedThetaWeights[beta_idx] *
nuSamples[ances])
nuVar = np.sum(normalisedThetaWeights[beta_idx] *
(nuSamples[ances] - nuMu)**2)
nuAlpha = nuMu**2 / nuVar + 2
nuBeta = nuMu * (nuAlpha - 1)
assert (nuAlpha > 0)
assert (nuBeta > 0)
dirichletMeans = np.sum(normalisedThetaWeights[beta_idx] *
gammaSamples[ances].T,
axis=1)
dirichletVar = np.sum(normalisedThetaWeights[beta_idx] *
(gammaSamples[ances]**2).T,
axis=1) - dirichletMeans**2
dirichletPrecision = np.sum(dirichletMeans - dirichletMeans**2
) / (np.sum(dirichletVar)) - 1
dirichletParamCandidates[:] = np.maximum(
dirichletMeans * dirichletPrecision, 1.)
assert ((dirichletParamCandidates > 0).all())
if K == 2:
nuSamplesNew[beta_idx] = useful_functions.sample_inv_gamma(
nuAlpha, nuBeta, numberOfThetaSamples)
muSamplesNew[beta_idx] = np.random.beta(
betaAlpha, betaBeta, numberOfThetaSamples)
gammaSamplesNew[beta_idx] = np.random.dirichlet(
dirichletParamCandidates, numberOfThetaSamples)
elif K == 24:
if latin_hyp_sampling:
latin_hyp_samples = mcerp.lhd(
dist=d0, size=numberOfThetaSamples, dims=K + 2)
muSamplesNew[beta_idx] = betalib.ppf(
latin_hyp_samples[:, 0], betaAlpha, betaBeta)
nuSamplesNew[beta_idx] = useful_functions.ppf_inv_gamma(
latin_hyp_samples[:, 1], nuAlpha, nuBeta)
gammaSamplesNew[beta_idx] = gammalib.ppf(
latin_hyp_samples[:, 2:], dirichletParamCandidates)
gammaSamplesNew[beta_idx] = np.transpose(
gammaSamplesNew[beta_idx].T /
np.sum(gammaSamplesNew[beta_idx], axis=1))
logThetaWeightsNew[beta_idx] = 0.
normalisedThetaWeights[beta_idx] = 1. / numberOfThetaSamples
else:
muSamplesNew[beta_idx] = muSamples[ances]
gammaSamplesNew[beta_idx] = gammaSamples[ances]
nuSamplesNew[beta_idx] = nuSamples[ances]
logThetaWeightsNew[beta_idx] = logThetaWeights[beta_idx]
# task set probability
sum_tsProbability[:] = 0.
for ts_idx in range(K):
tsProbability[:, ts_idx] = np.sum(normalisedThetaWeights * np.sum(
(currentStateSamples == ts_idx), axis=2),
axis=1)
sum_tsProbability += tsProbability[:, ts_idx]
tsProbability[:] = np.transpose(tsProbability.T / sum_tsProbability)
# Compute action likelihood
sum_actionLik[:] = 0.
for action_idx in range(numberOfActions):
actionLikelihood[:, action_idx] = np.exp(
np.log(
np.sum(tsProbability[:, mapping[stimuli[T].astype(int)] ==
action_idx],
axis=1)) * beta_softmax)
sum_actionLik += actionLikelihood[:, action_idx]
rewards[T] = td['reward'][T]
actions[T] = td['A_chosen'][T]
actionLikelihood[:] = np.transpose(actionLikelihood.T / sum_actionLik)
betaWeights[:] = actionLikelihood[:, actions[T].astype(int)]
filt_actionLkd[T] = actionLikelihood
log_proba_ += np.log(sum(betaWeights) / numberOfBetaSamples)
betaWeights = betaWeights / sum(betaWeights)
betaAncestors[:] = useful_functions.stratified_resampling(betaWeights)
# update particles
muSamples[:] = muSamplesNew
gammaSamples[:] = gammaSamplesNew
nuSamples[:] = nuSamplesNew
logThetaWeights[:] = logThetaWeightsNew[betaAncestors]
ancestorTauSamples[:] = currentTauSamples
ancestorStateSamples[:] = currentStateSamples
elapsed_time = time.time() - start_time_multi
return log_proba_, filt_actionLkd
def SMC2(td,
show_progress=False,
numberOfStateSamples=1000,
numberOfThetaSamples=1000,
coefficient=.5):
print('\n')
print('Constant Volatility Model')
print('\n')
#Start timer
start_time_multi = time.time()
# Extract parameters from task description
stimuli = td['S'] # Sequence of Stimuli
Z_true = td['Z'] # Sequence of Task Sets
numberOfActions = td['action_num'] # Number of Actions possible
numberOfStimuli = td['state_num'] # Number of states or stimuli
K = np.prod(
np.arange(numberOfActions +
1)[-numberOfStimuli:]) # Number of possible Task Sets
numberOfTrials = len(Z_true) # Number of Trials
# Sampling and prior settings
betaPrior = np.array([1, 1]) # Prior on Beta, the feedback noise parameter
tauPrior = np.array(
[1, 1]) # Prior on Tau, the switch parameter (the volatility)
gammaPrior = numpy.ones(K) # Prior on Gamma, the Dirichlet parameter
# Mapping from task set to correct action per stimulus
mapping = get_mapping.Get_TaskSet_Stimulus_Mapping(
state_num=numberOfStimuli, action_num=numberOfActions).T
actions = np.zeros(numberOfTrials) - 1
rewards = np.zeros(numberOfTrials, dtype=bool)
# Keep track of probability correct/exploration after switches
countPerformance = np.zeros(
numberOfTrials) # Number of correct actions after i trials
countExploration = np.zeros(
numberOfTrials) # Number of exploratory actions after i trials
correct_before_switch = np.empty(0) # The correct task set before switch
tsProbability = np.zeros([numberOfTrials, K])
acceptanceProba = 0.
volTracking = np.zeros(numberOfTrials)
volStdTracking = np.zeros(numberOfTrials)
betaTracking = np.zeros(numberOfTrials)
betaStdTracking = np.zeros(numberOfTrials)
acceptance_list = [1.]
time_list = [start_time_multi]
# SMC particles initialisation
betaSamples = np.random.beta(betaPrior[0], betaPrior[1],
numberOfThetaSamples)
tauSamples = np.random.beta(tauPrior[0], tauPrior[1], numberOfThetaSamples)
gammaSamples = np.random.dirichlet(gammaPrior, numberOfThetaSamples)
logThetaWeights = np.zeros(numberOfThetaSamples)
logThetaLks = np.zeros(numberOfThetaSamples)
currentSamples = np.zeros([numberOfThetaSamples, numberOfStateSamples],
dtype=np.intc)
ancestorSamples = np.zeros([numberOfThetaSamples, numberOfStateSamples],
dtype=np.intc)
ancestorsWeights = np.ones([numberOfThetaSamples, numberOfStateSamples
]) / numberOfStateSamples
unnormalisedAncestorsWeights = np.ones(
[numberOfThetaSamples, numberOfStateSamples])
essList = np.zeros(numberOfTrials)
tasksetLikelihood = np.zeros(K)
# Guided SMC variables
betaSamplesNew = np.zeros(numberOfThetaSamples)
tauSamplesNew = np.zeros(numberOfThetaSamples)
gammaSamplesNew = np.zeros([numberOfThetaSamples, K])
stateSamplesNew = np.zeros([numberOfThetaSamples, numberOfStateSamples],
dtype=np.intc)
weightsSamplesNew = np.zeros([numberOfThetaSamples, numberOfStateSamples])
logThetaLksNew = np.zeros(numberOfThetaSamples)
dirichletParamCandidates = np.zeros(K)
stateSamplesCandidates = np.zeros(numberOfStateSamples, dtype=np.intc)
weightsSamplesCandidates = np.zeros(numberOfStateSamples)
idxTrajectories = np.zeros(numberOfThetaSamples)
# Plot progress
if show_progress: plt.figure(figsize=(12, 9))
# Loop over trials
for T in range(numberOfTrials):
# Print progress
if (T + 1) % 10 == 0:
sys.stdout.write(' ' + str(T + 1))
sys.stdout.flush()
time_list.append(time.time() - start_time_multi)
if (T + 1) % 100 == 0: print('\n')
if T > 0:
smc_c.guidedUpdateStep_c(logThetaLks, logThetaWeights, np.ascontiguousarray(currentSamples), gammaSamples, betaSamples/2. + 1./2, tauSamples/2., T, np.ascontiguousarray(ancestorSamples), ancestorsWeights, \
np.ascontiguousarray(mapping), stimuli[T-2], stimuli[T-1], rewards[T-1], actions[T-1])
ancestorSamples = np.array(currentSamples)
# Degeneray criterion
logEss = 2 * useful_functions.log_sum(
logThetaWeights) - useful_functions.log_sum(2 * logThetaWeights)
essList[T] = np.exp(logEss)
# Move step
normalisedThetaWeights = useful_functions.to_normalized_weights(
logThetaWeights)
if (essList[T] < coefficient * numberOfThetaSamples) and (
acceptance_list[-1] > 0.05):
acceptanceProba = 0.
tauMu = np.sum(normalisedThetaWeights * tauSamples)
tauVar = np.sum(normalisedThetaWeights * (tauSamples - tauMu)**2)
tauAlpha = ((1 - tauMu) / tauVar - 1 / tauMu) * tauMu**2
tauBeta = tauAlpha * (1 / tauMu - 1)
assert (tauAlpha > 0)
assert (tauBeta > 0)
betaMu = np.sum(normalisedThetaWeights * betaSamples)
betaVar = np.sum(normalisedThetaWeights *
(betaSamples - betaMu)**2)
betaAlpha = ((1 - betaMu) / betaVar - 1 / betaMu) * betaMu**2
betaBeta = betaAlpha * (1 / betaMu - 1)
assert (betaAlpha > 0)
assert (betaBeta > 0)
dirichletMeans = np.sum(normalisedThetaWeights * gammaSamples.T,
axis=1)
dirichletVar = np.sum(normalisedThetaWeights * (gammaSamples**2).T,
axis=1) - dirichletMeans**2
dirichletPrecision = np.sum(dirichletMeans - dirichletMeans**2) / (
np.sum(dirichletVar)) - 1
dirichletParamCandidates = dirichletMeans * dirichletPrecision
assert ((dirichletParamCandidates > 0).all())
idxTrajectories = useful_functions.stratified_resampling(
normalisedThetaWeights)
for theta_idx in range(numberOfThetaSamples):
tauCandidate = np.random.beta(tauAlpha, tauBeta)
betaCandidate = np.random.beta(betaAlpha, betaBeta)
gammaCandidate = np.random.dirichlet(dirichletParamCandidates)
# Launch guidedSMC
logLksCandidate = smc_c.guidedSmc_c(np.ascontiguousarray(stateSamplesCandidates), weightsSamplesCandidates, gammaCandidate, betaCandidate/2. + 1./2, tauCandidate/2., np.ascontiguousarray(mapping), \
np.ascontiguousarray(stimuli[:T], dtype=np.intc), np.ascontiguousarray(rewards[:T], dtype=np.intc), np.ascontiguousarray(actions[:T], dtype=np.intc), numberOfStateSamples)
# Update a trajectory
idx_traj = idxTrajectories[theta_idx]
priorsLogRatio = useful_functions.log_dirichlet_pdf(
gammaCandidate,
gammaPrior) - useful_functions.log_dirichlet_pdf(
gammaSamples[idx_traj], gammaPrior)
transLogRatio = useful_functions.log_beta_pdf(tauSamples[idx_traj], tauAlpha, tauBeta) + useful_functions.log_beta_pdf(betaSamples[idx_traj], betaAlpha, betaBeta) + useful_functions.log_dirichlet_pdf(gammaSamples[idx_traj], dirichletParamCandidates) - \
useful_functions.log_beta_pdf(tauCandidate, tauAlpha, tauBeta) - useful_functions.log_beta_pdf(betaCandidate, betaAlpha, betaBeta) - useful_functions.log_dirichlet_pdf(gammaCandidate, dirichletParamCandidates)
logLkdRatio = logLksCandidate - logThetaLks[idx_traj]
logAlpha = min(0, priorsLogRatio + transLogRatio + logLkdRatio)
U = np.random.rand()
# Accept or Reject
if np.log(U) < logAlpha:
acceptanceProba += 1.
betaSamplesNew[theta_idx] = betaCandidate
tauSamplesNew[theta_idx] = tauCandidate
gammaSamplesNew[theta_idx] = gammaCandidate
stateSamplesNew[theta_idx] = stateSamplesCandidates
logThetaLksNew[theta_idx] = logLksCandidate
weightsSamplesNew[theta_idx] = weightsSamplesCandidates
else:
betaSamplesNew[theta_idx] = betaSamples[idx_traj]
tauSamplesNew[theta_idx] = tauSamples[idx_traj]
gammaSamplesNew[theta_idx] = gammaSamples[idx_traj]
stateSamplesNew[theta_idx] = ancestorSamples[idx_traj]
logThetaLksNew[theta_idx] = logThetaLks[idx_traj]
weightsSamplesNew[theta_idx] = ancestorsWeights[idx_traj]
print('\n')
print('acceptance ratio is ')
print(acceptanceProba / numberOfThetaSamples)
print('\n')
acceptance_list.append(acceptanceProba / numberOfThetaSamples)
ancestorsWeights = np.array(weightsSamplesNew)
logThetaLks = np.array(logThetaLksNew)
logThetaWeights = np.zeros(numberOfThetaSamples)
ancestorSamples = np.array(stateSamplesNew)
betaSamples = np.array(betaSamplesNew)
tauSamples = np.array(tauSamplesNew)
gammaSamples = np.array(gammaSamplesNew)
normalisedThetaWeights = useful_functions.to_normalized_weights(
logThetaWeights)
# Launch bootstrap update
smc_c.bootstrapUpdateStep_c(np.ascontiguousarray(currentSamples),
gammaSamples, betaSamples / 2. + 1. / 2,
tauSamples / 2., T,
np.ascontiguousarray(ancestorSamples),
ancestorsWeights,
np.ascontiguousarray(mapping),
stimuli[T - 1])
# Take decision
for ts_idx in range(K):
tsProbability[T, ts_idx] = np.sum(normalisedThetaWeights * np.sum(
(currentSamples == ts_idx), axis=1))
# Select action and compute vol
volTracking[T] = np.sum(normalisedThetaWeights * tauSamples)
volStdTracking[T] = np.sum(normalisedThetaWeights *
(tauSamples - volTracking[T])**2)
betaTracking[T] = np.sum(normalisedThetaWeights * betaSamples)
betaStdTracking[T] = np.sum(normalisedThetaWeights *
(betaSamples - betaTracking[T])**2)
rewards[T] = td['reward'][T]
actions[T] = td['A_chosen'][T]
if show_progress:
plt.subplot(3, 2, 1)
plt.imshow(tsProbability[:T].T, aspect='auto')
plt.hold(True)
plt.plot(Z_true[:T], 'w--')
plt.axis([0, T - 1, 0, K - 1]) # For speed
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('p(TS|past) at current time')
plt.subplot(3, 2, 2)
plt.plot(volTracking[:T], 'b')
plt.hold(True)
plt.fill_between(np.arange(T),
volTracking[:T] - volStdTracking[:T],
volTracking[:T] + volStdTracking[:T],
facecolor=[.5, .5, 1],
color=[.5, .5, 1])
plt.plot(td['tau'], 'b--', linewidth=2)
plt.axis([0, T - 1, 0, .5]) # For speed
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('Volatility')
plt.subplot(3, 2, 3)
x = np.linspace(0.01, .99, 100)
plt.plot(x, normlib.pdf(x, betaTracking[T], betaStdTracking[T]),
'r')
plt.hold(True)
plt.plot([betaTracking[T], betaTracking[T]],
plt.gca().get_ylim(),
'r',
linewidth=2)
plt.plot([td['beta'], td['beta']],
plt.gca().get_ylim(),
'r--',
linewidth=2)
plt.hold(False)
plt.xlabel('Parameters')
plt.ylabel('Gaussian pdf')
plt.subplot(3, 2, 4)
plt.plot(np.arange(T) + 1, essList[:T], 'g', linewidth=2)
plt.hold(True)
plt.plot(plt.gca().get_xlim(), [
coefficient * numberOfThetaSamples,
coefficient * numberOfThetaSamples
],
'g--',
linewidth=2)
plt.axis([0, T - 1, 0, numberOfThetaSamples])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('ESS')
plt.subplot(3, 2, 5)
plt.plot(np.divide(countPerformance[:T],
np.arange(T) + 1),
'k--',
linewidth=2)
plt.hold(True)
plt.axis([0, T - 1, 0, 1])
plt.hold(False)
plt.xlabel('Trials')
plt.ylabel('Performance')
plt.draw()
elapsed_time = time.time() - start_time_multi
return [
td, tauSamples, volTracking, volStdTracking, betaSamples, betaTracking,
betaStdTracking, gammaSamples, tsProbability, countPerformance,
actions, acceptance_list, essList, time_list, elapsed_time
]
def SMC2(td,
show_progress=True,
numberOfStateSamples=1000,
numberOfThetaSamples=1000,
coefficient=.5,
beta_softmax=None):
print('Varying Volatility Model')
print('number of theta samples ' + str(numberOfThetaSamples))
print('\n')
#Start timer
start_time_multi = time.time()
# Extract parameters from task description
stimuli = td['S'] # Sequence of Stimuli
Z_true = td['Z'] # Sequence of Task Sets
numberOfActions = td['action_num'] # Number of Actions possible
numberOfStimuli = td['state_num'] # Number of states or stimuli
K = np.prod(
np.arange(numberOfActions +
1)[-numberOfStimuli:]) # Number of possible Task Sets
numberOfTrials = len(Z_true) # Number of Trials
# Sampling and prior settings
betaPrior = np.array([1, 1]) # Prior on Beta, the feedback noise parameter
nuPrior = np.array([
3, 1e-3
]) # Prior on Nu, the variance on the projected gaussian random walk
gammaPrior = numpy.ones(K) # Prior on Gamma, the Dirichlet parameter
try:
tauDefault = td['tau'][0]
except:
tauDefault = td['tau']
# Mapping from task set to correct action per stimulus
mapping = get_mapping.Get_TaskSet_Stimulus_Mapping(
state_num=numberOfStimuli, action_num=numberOfActions).T
# Probabilities of every actions updated at every time step -> Used to take the decision
actionLikelihood = np.zeros(
numberOfActions
) # For 1 observation, likelihood of the action. Requires a marginalisation over all task sets
actions = np.zeros(numberOfTrials) - 1
rewards = np.zeros(numberOfTrials, dtype=bool)
# Keep track of probability correct/exploration after switches
countPerformance = np.zeros(
numberOfTrials) # Number of correct actions after i trials
countExploration = np.zeros(
numberOfTrials) # Number of exploratory actions after i trials
correct_before_switch = np.empty(0) # The correct task set before switch
tsProbability = np.zeros([numberOfTrials, K])
volTracking = np.zeros(numberOfTrials) # Volatility with time
volStdTracking = np.zeros(numberOfTrials)
nuTracking = np.zeros(numberOfTrials)
nuStdTracking = np.zeros(numberOfTrials)
betaTracking = np.zeros(numberOfTrials)
betaStdTracking = np.zeros(numberOfTrials)
acceptanceProba = 0. # Acceptance proba
time_list = [start_time_multi]
# SMC particles initialisation
betaSamples = np.random.beta(betaPrior[0], betaPrior[1],
numberOfThetaSamples)
nuSamples = useful_functions.sample_inv_gamma(nuPrior[0], nuPrior[1],
numberOfThetaSamples)
gammaSamples = np.random.dirichlet(gammaPrior, numberOfThetaSamples)
logThetaWeights = np.zeros(numberOfThetaSamples)
currentStateSamples = np.zeros(
[numberOfThetaSamples, numberOfStateSamples], dtype=np.intc)
currentTauSamples = np.zeros([numberOfThetaSamples, numberOfStateSamples],
dtype=np.double)
ancestorStateSamples = np.zeros(
[numberOfThetaSamples, numberOfStateSamples], dtype=np.intc)
ancestorTauSamples = np.zeros([numberOfThetaSamples, numberOfStateSamples],
dtype=np.double)
ancestorsWeights = np.ones([numberOfThetaSamples, numberOfStateSamples
]) / numberOfStateSamples
unnormalisedAncestorsWeights = np.ones(
[numberOfThetaSamples, numberOfStateSamples])
essList = np.zeros(numberOfTrials)
tasksetLikelihood = np.zeros(K)
# Guided SMC variables
dirichletParamCandidates = np.zeros(K)
# Plot progress
if show_progress:
plt.figure(figsize=(12, 9))
plt.ion()
# Loop over trials
for T in range(numberOfTrials):
# Print progress
if (T + 1) % 10 == 0:
sys.stdout.write(' ' + str(T + 1))
sys.stdout.flush()
time_list.append(time.time() - start_time_multi)
if (T + 1) % 100 == 0: print('\n')
# Update theta weights
smc_c.bootstrapUpdateStep_c(currentStateSamples, logThetaWeights, currentTauSamples, gammaSamples, betaSamples/2. + 1/2., nuSamples, tauDefault, T, \
np.ascontiguousarray(ancestorStateSamples, dtype=np.intc), ancestorTauSamples, ancestorsWeights, np.ascontiguousarray(mapping), stimuli[T-1], actions[T-1], rewards[T-1])
ancestorTauSamples = np.array(currentTauSamples)
ancestorStateSamples = np.array(currentStateSamples)
# Degeneray criterion
logEss = 2 * useful_functions.log_sum(
logThetaWeights) - useful_functions.log_sum(2 * logThetaWeights)
essList[T] = np.exp(logEss)
# Move step
normalisedThetaWeights = useful_functions.to_normalized_weights(
logThetaWeights)
if (essList[T] < coefficient * numberOfThetaSamples):
acceptanceProba = 0.
betaMu = np.sum(normalisedThetaWeights * betaSamples)
betaVar = np.sum(normalisedThetaWeights *
(betaSamples - betaMu)**2)
betaAlpha = ((1 - betaMu) / betaVar - 1 / betaMu) * betaMu**2
betaBeta = betaAlpha * (1 / betaMu - 1)
assert (betaAlpha > 0)
assert (betaBeta > 0)
nuMu = np.sum(normalisedThetaWeights * nuSamples)
nuVar = np.sum(normalisedThetaWeights * (nuSamples - nuMu)**2)
nuAlpha = nuMu**2 / nuVar + 2
nuBeta = nuMu * (nuAlpha - 1)
assert (nuAlpha > 0)
assert (nuBeta > 0)
dirichletMeans = np.sum(normalisedThetaWeights * gammaSamples.T,
axis=1)
dirichletVar = np.sum(normalisedThetaWeights * (gammaSamples**2).T,
axis=1) - dirichletMeans**2
dirichletPrecision = np.sum(dirichletMeans - dirichletMeans**2) / (
np.sum(dirichletVar)) - 1
dirichletParamCandidates = np.maximum(
dirichletMeans * dirichletPrecision, 1.)
assert ((dirichletParamCandidates > 0).all())
nuSamples = useful_functions.sample_inv_gamma(
nuAlpha, nuBeta, numberOfThetaSamples)
betaSamples = np.random.beta(betaAlpha, betaBeta,
numberOfThetaSamples)
gammaSamples = np.random.dirichlet(dirichletParamCandidates,
numberOfThetaSamples)
logThetaWeights[:] = 0
normalisedThetaWeights = useful_functions.to_normalized_weights(
logThetaWeights)
# Take decision
for ts_idx in range(K):
tsProbability[T, ts_idx] = np.sum(normalisedThetaWeights * np.sum(
(currentStateSamples == ts_idx),
axis=1)) # Todo : change!!! take out currentAncestorsWeights
if beta_softmax is None:
# Compute action likelihood
for action_idx in range(numberOfActions):
actionLikelihood[action_idx] = np.sum(
tsProbability[T, mapping[stimuli[T]] == action_idx])
# Select action
actions[T] = np.argmax(actionLikelihood)
else:
# Compute action likelihood
tsProbability[T] /= sum(tsProbability[T])
for action_idx in range(numberOfActions):
actionLikelihood[action_idx] = np.exp(
np.log(
np.sum(tsProbability[
T, mapping[stimuli[T].astype(int)] == action_idx]))
* beta_softmax)
actionLikelihood /= sum(actionLikelihood)
# Select action
actions[T] = np.where(
np.random.multinomial(1, actionLikelihood, size=1)[0])[0][0]
# Select action and compute vol, nu, beta for tracking
volTracking[T] = np.sum(
normalisedThetaWeights *
(np.sum(currentTauSamples, axis=1) / numberOfStateSamples))
volStdTracking[T] = np.sum(normalisedThetaWeights *
(np.sum(currentTauSamples**2, axis=1) /
numberOfStateSamples)) - volTracking[T]**2
nuTracking[T] = np.sum(normalisedThetaWeights * nuSamples)
nuStdTracking[T] = np.sum(normalisedThetaWeights *
(nuSamples - nuTracking[T])**2)
betaTracking[T] = np.sum(normalisedThetaWeights * betaSamples)
betaStdTracking[T] = np.sum(normalisedThetaWeights *
(betaSamples - betaTracking[T])**2)
# Update performance
if K == 2:
assert (mapping[stimuli[T].astype(int),
Z_true[T].astype(int)] == Z_true[T])
if (K == 2) and (actions[T] == mapping[stimuli[T].astype(int),
Z_true[T].astype(int)]):
rewards[T] = not td['trap'][T]
countPerformance[T:] += 1
elif (K == 24) and (actions[T] == td['A_correct'][T]):
rewards[T] = not td['trap'][T]
countPerformance[T:] += 1
else:
rewards[T] = td['trap'][T]
if show_progress:
plt.subplot(3, 2, 1)
plt.imshow(tsProbability[:T].T, aspect='auto')
plt.hold(True)
plt.plot(Z_true[:T], 'w--')
plt.axis([0, T - 1, 0, K - 1])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('p(TS|past) at current time')
plt.subplot(3, 2, 2)
plt.plot(volTracking[:T], 'b')
plt.hold(True)
plt.fill_between(np.arange(T),
volTracking[:T] - volStdTracking[:T],
volTracking[:T] + volStdTracking[:T],
facecolor=[.5, .5, 1],
color=[.5, .5, 1])
plt.plot(td['tau'], 'b--', linewidth=2)
plt.axis([0, T - 1, 0, .5])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('Volatility')
plt.subplot(3, 2, 3)
x = np.linspace(0.01, .99, 100)
plt.plot(x, normlib.pdf(x, nuTracking[T], nuStdTracking[T]), 'b')
plt.hold(True)
plt.plot([nuTracking[T], nuTracking[T]],
plt.gca().get_ylim(),
'b',
linewidth=2)
plt.plot(x, normlib.pdf(x, betaTracking[T], betaStdTracking[T]),
'r')
plt.plot([betaTracking[T], betaTracking[T]],
plt.gca().get_ylim(),
'r',
linewidth=2)
plt.plot([td['beta'], td['beta']],
plt.gca().get_ylim(),
'r--',
linewidth=2)
plt.hold(False)
plt.xlabel('Parameters')
plt.ylabel('Gaussian pdf')
plt.subplot(3, 2, 4)
plt.plot(np.arange(T) + 1, essList[:T], 'g', linewidth=2)
plt.hold(True)
plt.plot(plt.gca().get_xlim(), [
coefficient * numberOfThetaSamples,
coefficient * numberOfThetaSamples
],
'g--',
linewidth=2)
plt.axis([0, T - 1, 0, numberOfThetaSamples])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('ESS')
plt.subplot(3, 2, 5)
plt.plot(np.divide(countPerformance[:T],
np.arange(T) + 1),
'k--',
linewidth=2)
plt.hold(True)
plt.axis([0, T - 1, 0, 1])
plt.hold(False)
plt.xlabel('Trials')
plt.ylabel('Performance')
plt.draw()
plt.show()
plt.pause(0.1)
elapsed_time = time.time() - start_time_multi
return [
td, nuSamples, nuTracking, nuStdTracking, volTracking, volTracking,
betaSamples, betaTracking, betaStdTracking, gammaSamples,
tsProbability, countPerformance, actions, essList, time_list,
elapsed_time
]
def SMC2(td,
show_progress=True,
lambdaa=.9,
eta=0.,
inertie_noise=0.,
numberOfStateSamples=2000,
numberOfThetaSamples=1000,
coefficient=.5,
beta_softmax=None,
espilon_softmax=0.):
print(
'precision model with lambda = {0} and eta = {1}, epsilon= {4}, inertie_noise={5}. Number of state samples : {2} and number of theta samples : {3}'
.format(lambdaa, eta, numberOfStateSamples, numberOfThetaSamples,
espilon_softmax, inertie_noise))
#Start timer
start_time_multi = time.time()
# Extract parameters from task description
stimuli = np.ascontiguousarray(td['S'],
dtype=np.intc) # Sequence of Stimuli
Z = td['Z'] # Sequence of Task Sets
numberOfActions = td['action_num'] # Number of Actions possible
numberOfStimuli = td['state_num'] # Number of states or stimuli
K = np.prod(
np.arange(numberOfActions +
1)[-numberOfStimuli:]) # Number of possible Task Sets
numberOfTrials = len(Z) # Number of Trials
# Sampling and prior settings
betaPrior = np.array([1, 1]) # Prior on Beta, the feedback noise parameter
dirichletPrior = np.ones(K)
# Mapping from task set to correct action per stimulus
mapping = np.ascontiguousarray(get_mapping.Get_TaskSet_Stimulus_Mapping(
state_num=numberOfStimuli, action_num=numberOfActions).T,
dtype=np.intc)
Z_true = Z
# Probabilities of every actions updated at every time step -> Used to take the decision
actionLikelihood = np.zeros(
numberOfActions
) # For 1 observation, likelihood of the action. Requires a marginalisation over all task sets
actions = np.ascontiguousarray(np.zeros(numberOfTrials) - 1, dtype=np.intc)
rewards = np.ascontiguousarray(np.zeros(numberOfTrials), dtype=np.intc)
# Keep track of probability correct/exploration after switches
countPerformance = np.zeros(
numberOfTrials) # Number of correct actions after i trials
countExploration = np.zeros(
numberOfTrials) # Number of exploratory actions after i trials
correct_before_switch = np.empty(0) # The correct task set before switch
tsProbability = np.zeros([numberOfTrials, K])
acceptanceProba = 0.
betaTracking = np.zeros(numberOfTrials)
betaStdTracking = np.zeros(numberOfTrials)
temperatureTracking = np.zeros(numberOfTrials)
temperatureStdTracking = np.zeros(numberOfTrials)
acceptance_list = [1.]
transitionProba = np.zeros([numberOfThetaSamples, K, K])
# SMC particles initialisation
betaSamples = np.random.beta(betaPrior[0], betaPrior[1],
numberOfThetaSamples)
gammaSamples = np.random.dirichlet(dirichletPrior, numberOfThetaSamples)
logThetaWeights = np.zeros(numberOfThetaSamples)
logThetaLks = np.zeros(numberOfThetaSamples)
currentTaskSetSamples = np.zeros(
[numberOfThetaSamples, numberOfStateSamples], dtype=np.intc)
ancestorTaskSetSamples = np.zeros(
[numberOfThetaSamples, numberOfStateSamples], dtype=np.intc)
weightsList = np.zeros([numberOfThetaSamples, numberOfStateSamples])
essList = np.zeros(numberOfTrials)
tasksetLikelihood = np.zeros(K)
currentTemperatures = np.zeros(numberOfTrials)
entropies = np.zeros(numberOfTrials)
temperature = 0.5
# variables for speed-up
ante_proba_local = np.zeros(K)
post_proba_local = np.zeros(K)
sum_weightsList = np.zeros(numberOfThetaSamples)
ancestorsIndexes = np.zeros(numberOfStateSamples, dtype=np.intc)
gammaAdaptedProba = np.zeros(K)
likelihoods = np.zeros(K)
positiveStates = np.zeros(K, dtype=np.intc)
distances = np.zeros([numberOfThetaSamples, 1])
currentNoises = np.zeros([numberOfThetaSamples, numberOfStateSamples])
noise_amount = np.zeros(numberOfTrials)
# Plot progress
if show_progress:
plt.figure(figsize=(12, 9))
plt.ion()
# Loop over trials
for T in range(numberOfTrials):
# Print progress
if (T + 1) % 10 == 0:
sys.stdout.write(' ' + str(T + 1))
sys.stdout.flush()
if (T + 1) % 100 == 0: print('\n')
noise_amount[T] = smc_c.bootstrap_smc_step_c(logThetaWeights, distances, betaSamples/2. + 1/2., lambdaa, eta, inertie_noise, gammaSamples, currentTaskSetSamples, ancestorTaskSetSamples, weightsList, \
mapping, stimuli[T-1], rewards[T-1], actions[T-1], T, likelihoods, positiveStates, ante_proba_local,\
post_proba_local, ancestorsIndexes, gammaAdaptedProba, sum_weightsList, currentNoises, float(temperature))
if temperature is None:
assert (False)
entropies[T] = entropy(
np.asarray([np.sum(currentTaskSetSamples == i)
for i in range(K)]) * 1. /
(numberOfThetaSamples * numberOfStateSamples))
ancestorTaskSetSamples[:] = currentTaskSetSamples
# Degeneray criterion
logEss = 2 * useful_functions.log_sum(
logThetaWeights) - useful_functions.log_sum(2 * logThetaWeights)
essList[T] = np.exp(logEss)
# Move step
normalisedThetaWeights = useful_functions.to_normalized_weights(
logThetaWeights)
if essList[T] < coefficient * numberOfThetaSamples and acceptance_list[
-1] > 0.05:
acceptanceProba = 0.
betaMu = np.sum(normalisedThetaWeights * betaSamples)
betaVar = np.sum(normalisedThetaWeights *
(betaSamples - betaMu)**2)
betaAlpha = np.maximum(
((1 - betaMu) / betaVar - 1 / betaMu) * betaMu**2, 1)
betaBeta = np.maximum(betaAlpha * (1 / betaMu - 1), 1.)
assert (betaAlpha > 0)
assert (betaBeta > 0)
dirichletMeans = np.sum(normalisedThetaWeights * gammaSamples.T,
axis=1)
dirichletVar = np.sum(normalisedThetaWeights * (gammaSamples**2).T,
axis=1) - dirichletMeans**2
dirichletPrecision = np.sum(dirichletMeans - dirichletMeans**2) / (
np.sum(dirichletVar)) - 1
dirichletParamCandidates = dirichletMeans * dirichletPrecision
dirichletParamCandidates = np.maximum(dirichletParamCandidates, 1.)
assert ((dirichletParamCandidates > 0).all())
logThetaWeights[:] = 0
betaSamples = np.random.beta(betaAlpha, betaBeta,
numberOfThetaSamples)
gammaSamples = np.random.dirichlet(dirichletParamCandidates,
numberOfThetaSamples)
normalisedThetaWeights = useful_functions.to_normalized_weights(
logThetaWeights)
# Take decision
for ts_idx in range(K):
tsProbability[T, ts_idx] = np.sum(normalisedThetaWeights * np.sum(
(currentTaskSetSamples == ts_idx), axis=1))
if beta_softmax is None:
# Compute action likelihood
for action_idx in range(numberOfActions):
actionLikelihood[action_idx] = np.sum(
tsProbability[T, mapping[stimuli[T]] == action_idx])
# Select action
actions[T] = np.argmax(actionLikelihood)
else:
# Compute action likelihood
tsProbability[T] /= sum(tsProbability[T])
for action_idx in range(numberOfActions):
actionLikelihood[action_idx] = np.exp(
np.log(
np.sum(tsProbability[
T, mapping[stimuli[T].astype(int)] == action_idx]))
* beta_softmax)
actionLikelihood /= sum(actionLikelihood)
actionLikelihood = actionLikelihood * (
1 - espilon_softmax) + espilon_softmax / K
# Select action
actions[T] = np.where(
np.random.multinomial(1, actionLikelihood, size=1)[0])[0][0]
betaTracking[T] = np.sum(normalisedThetaWeights * betaSamples)
betaStdTracking[T] = np.sum(normalisedThetaWeights *
(betaSamples - betaTracking[T])**2)
temperatureTracking[T] = np.mean(currentNoises)
temperatureStdTracking[T] = np.std(currentNoises)
if K == 2:
assert (mapping[stimuli[T].astype(int),
Z_true[T].astype(int)] == Z_true[T])
if (K == 2) and (actions[T] == mapping[stimuli[T].astype(int),
Z_true[T].astype(int)]):
rewards[T] = not td['trap'][T]
countPerformance[T:] += 1
elif (K == 24) and (actions[T] == td['A_correct'][T]):
rewards[T] = not td['trap'][T]
countPerformance[T:] += 1
else:
rewards[T] = td['trap'][T]
if show_progress:
plt.subplot(3, 2, 1)
plt.imshow(tsProbability[:T].T, aspect='auto')
plt.hold(True)
plt.plot(Z_true[:T], 'w--')
plt.axis([0, T - 1, 0, K - 1])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('p(TS|past) at current time')
plt.subplot(3, 2, 2)
plt.plot(temperatureTracking[:T])
plt.fill_between(
np.arange(T),
temperatureTracking[:T] - temperatureStdTracking[:T],
temperatureTracking[:T] + temperatureStdTracking[:T],
facecolor=[.5, .5, 1],
color=[.5, .5, 1])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('Temperature')
plt.subplot(3, 2, 3)
x = np.linspace(0.01, .99, 100)
plt.plot(x, normlib.pdf(x, betaTracking[T], betaStdTracking[T]),
'r')
plt.hold(True)
plt.plot([betaTracking[T], betaTracking[T]],
plt.gca().get_ylim(),
'r',
linewidth=2)
plt.plot([td['beta'], td['beta']],
plt.gca().get_ylim(),
'r--',
linewidth=2)
plt.hold(False)
plt.xlabel('Parameters')
plt.ylabel('Gaussian pdf')
plt.subplot(3, 2, 4)
plt.plot(np.arange(T) + 1, essList[:T], 'g', linewidth=2)
plt.hold(True)
plt.plot(plt.gca().get_xlim(), [
coefficient * numberOfThetaSamples,
coefficient * numberOfThetaSamples
],
'g--',
linewidth=2)
plt.axis([0, T - 1, 0, numberOfThetaSamples])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('ESS')
plt.subplot(3, 2, 5)
plt.plot(np.divide(countPerformance[:T],
np.arange(T) + 1),
'k--',
linewidth=2)
plt.hold(True)
plt.axis([0, T - 1, 0, 1])
plt.hold(False)
plt.xlabel('Trials')
plt.ylabel('Performance')
plt.draw()
plt.show()
plt.pause(0.1)
elapsed_time = time.time() - start_time_multi
return [
td, noise_amount, lambdaa, eta, betaSamples, betaTracking,
betaStdTracking, currentTemperatures, temperatureTracking,
temperatureStdTracking, gammaSamples, tsProbability, countPerformance,
actions, acceptance_list, elapsed_time
]
def SMC2(td,
beta_softmax=1.,
lambda_noise=.4,
eta_noise=.1,
epsilon_softmax=0.,
noise_inertie=0.,
numberOfStateSamples=200,
numberOfThetaSamples=200,
numberOfBetaSamples=20,
coefficient=.5,
latin_hyp_sampling=True):
print('\n')
print('Noisy Forward Model')
print('number of theta samples ' + str(numberOfThetaSamples))
print('\n')
#Start timer
start_time_multi = time.time()
# uniform distribution
if latin_hyp_sampling:
d0 = uniform()
print('latin hypercube sampling')
else:
print('sobolev sampling')
# Extract parameters from task description
stimuli = td['S'] # Sequence of Stimuli
Z_true = td['Z'] # Sequence of Task Sets
numberOfActions = td['action_num'] # Number of Actions possible
numberOfStimuli = td['state_num'] # Number of states or stimuli
rewards = td['reward']
actions = td['A_chosen']
K = np.prod(
np.arange(numberOfActions +
1)[-numberOfStimuli:]) # Number of possible Task Sets
numberOfTrials = len(Z_true) # Number of Trials
distances = np.zeros([numberOfThetaSamples, 1])
# Sampling and prior settings
betaPrior = np.array([1, 1]) # Prior on Beta, the feedback noise parameter
gammaPrior = np.ones(K) # Prior on Gamma, the Dirichlet parameter
log_proba_ = 0.
# verification
if K == 2:
if latin_hyp_sampling == False:
raise ValueError(
'Why did you change the latin_hyp_sampling? By default, it is True and has no influence when K=2.'
)
# Mapping from task set to correct action per stimulus
mapping = get_mapping.Get_TaskSet_Stimulus_Mapping(
state_num=numberOfStimuli, action_num=numberOfActions).T
betaWeights = np.zeros(numberOfBetaSamples)
betaLog = np.zeros(numberOfBetaSamples)
logbetaWeights = np.zeros(numberOfBetaSamples)
betaAncestors = np.arange(numberOfBetaSamples)
# Probabilities of every actions updated at every time step -> Used to take the decision
actionLikelihood = np.zeros([numberOfBetaSamples, numberOfActions])
sum_actionLik = np.zeros(numberOfBetaSamples)
filt_actionLkd = np.zeros(
[numberOfTrials, numberOfBetaSamples, numberOfActions])
# Keep track of probability correct/exploration after switches
tsProbability = np.zeros([numberOfBetaSamples, K])
sum_tsProbability = np.zeros(numberOfBetaSamples)
dirichletParamCandidates = np.zeros(K)
# SMC particles initialisation
muSamples = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples]
) #np.random.beta(betaPrior[0], betaPrior[1], [numberOfBetaSamples, numberOfThetaSamples])
gammaSamples = np.zeros([numberOfBetaSamples, numberOfThetaSamples, K])
if K == 24:
try:
latin_hyp_samples = pickle.load(
open('../../utils/sobol_200_25.pkl', 'rb'))
except:
latin_hyp_samples = pickle.load(
open('../../models/utils/sobol_200_25.pkl', 'rb'))
for beta_idx in range(numberOfBetaSamples):
if latin_hyp_sampling:
latin_hyp_samples = mcerp.lhd(dist=d0,
size=numberOfThetaSamples,
dims=K + 1)
muSamples[beta_idx] = betalib.ppf(latin_hyp_samples[:, 0],
betaPrior[0], betaPrior[1])
gammaSamples[beta_idx] = gammalib.ppf(latin_hyp_samples[:, 1:],
gammaPrior)
gammaSamples[beta_idx] = np.transpose(
gammaSamples[beta_idx].T /
np.sum(gammaSamples[beta_idx], axis=1))
elif K == 2:
muSamples = np.random.beta(betaPrior[0], betaPrior[1],
[numberOfBetaSamples, numberOfThetaSamples])
gammaSamples = np.random.dirichlet(
gammaPrior, [numberOfBetaSamples, numberOfThetaSamples])
else:
raise IndexError('Wrong number of task sets')
logThetaWeights = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
currentSamples = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples, numberOfStateSamples],
dtype=np.intc)
ancestorSamples = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples, numberOfStateSamples],
dtype=np.intc)
weightsList = np.ones([numberOfThetaSamples, numberOfStateSamples
]) / numberOfStateSamples
currentNoises = np.zeros([numberOfThetaSamples, numberOfStateSamples])
log_proba_corr = 0.
ante_proba_local = np.zeros(K)
post_proba_local = np.zeros(K)
sum_weightsList = np.zeros(numberOfThetaSamples)
ancestorsIndexes = np.zeros(numberOfStateSamples, dtype=np.intc)
gammaAdaptedProba = np.zeros(K)
likelihoods = np.zeros(K)
positiveStates = np.zeros(K, dtype=np.intc)
# Guided SMC variables
muSamplesNew = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
gammaSamplesNew = np.zeros([numberOfBetaSamples, numberOfThetaSamples, K])
logThetaWeightsNew = np.zeros([numberOfBetaSamples, numberOfThetaSamples])
normalisedThetaWeights = np.zeros(
[numberOfBetaSamples, numberOfThetaSamples])
temperatures = np.zeros(numberOfBetaSamples)
temperatureAncestors = np.zeros(numberOfBetaSamples) + .5
# Loop over trials
for T in range(numberOfTrials):
# Print progress
if (T + 1) % 10 == 0:
sys.stdout.write(' ' + str(T + 1))
sys.stdout.flush()
if (T + 1) % 100 == 0: print('\n')
for beta_idx in range(numberOfBetaSamples):
ances = betaAncestors[beta_idx]
temperatures[beta_idx] = smc_c.bootstrap_smc_step_c(logThetaWeights[beta_idx], distances, muSamples[ances]/2. + 1./2, lambda_noise, eta_noise, noise_inertie, gammaSamples[ances], currentSamples[beta_idx], ancestorSamples[ances], weightsList, \
np.ascontiguousarray(mapping), stimuli[T-1], rewards[T-1], actions[T-1], T, likelihoods, positiveStates, ante_proba_local,\
post_proba_local, ancestorsIndexes, gammaAdaptedProba, sum_weightsList, currentNoises, temperatureAncestors[ances])
# Move step
normalisedThetaWeights[
beta_idx] = useful_functions.to_normalized_weights(
logThetaWeights[beta_idx])
ess = 1. / np.sum(normalisedThetaWeights[beta_idx]**2)
if (ess < coefficient * numberOfThetaSamples):
acceptanceProba = 0.
betaMu = np.sum(normalisedThetaWeights[beta_idx] *
muSamples[ances])
betaVar = np.sum(normalisedThetaWeights[beta_idx] *
(muSamples[ances] - betaMu)**2)
betaAlpha = ((1 - betaMu) / betaVar - 1 / betaMu) * betaMu**2
betaBeta = betaAlpha * (1 / betaMu - 1)
assert (betaAlpha > 0)
assert (betaBeta > 0)
dirichletMeans = np.sum(normalisedThetaWeights[beta_idx] *
gammaSamples[ances].T,
axis=1)
dirichletVar = np.sum(normalisedThetaWeights[beta_idx] *
(gammaSamples[ances]**2).T,
axis=1) - dirichletMeans**2
dirichletPrecision = np.sum(dirichletMeans - dirichletMeans**2
) / (np.sum(dirichletVar)) - 1
dirichletParamCandidates[:] = np.maximum(
dirichletMeans * dirichletPrecision, 1.)
assert ((dirichletParamCandidates > 0).all())
if K == 2:
muSamplesNew[beta_idx] = np.random.beta(
betaAlpha, betaBeta, numberOfThetaSamples)
gammaSamplesNew[beta_idx] = np.random.dirichlet(
dirichletParamCandidates, numberOfThetaSamples)
if K == 24:
if latin_hyp_sampling:
latin_hyp_samples = mcerp.lhd(
dist=d0, size=numberOfThetaSamples, dims=K + 1)
muSamplesNew[beta_idx] = betalib.ppf(
latin_hyp_samples[:, 0], betaAlpha, betaBeta)
gammaSamplesNew[beta_idx] = gammalib.ppf(
latin_hyp_samples[:, 1:], dirichletParamCandidates)
gammaSamplesNew[beta_idx] = np.transpose(
gammaSamplesNew[beta_idx].T /
np.sum(gammaSamplesNew[beta_idx], axis=1))
logThetaWeightsNew[beta_idx] = 0.
normalisedThetaWeights[beta_idx] = 1. / numberOfThetaSamples
else:
muSamplesNew[beta_idx] = muSamples[ances]
gammaSamplesNew[beta_idx] = gammaSamples[ances]
logThetaWeightsNew[beta_idx] = logThetaWeights[beta_idx]
# task set probability
sum_tsProbability[:] = 0.
for ts_idx in range(K):
tsProbability[:, ts_idx] = np.sum(normalisedThetaWeights * np.sum(
(currentSamples == ts_idx), axis=2),
axis=1)
sum_tsProbability += tsProbability[:, ts_idx]
tsProbability[:] = np.transpose(tsProbability.T / sum_tsProbability)
# Compute action likelihood
sum_actionLik[:] = 0.
for action_idx in range(numberOfActions):
actionLikelihood[:, action_idx] = np.exp(
np.log(
np.sum(tsProbability[:, mapping[stimuli[T].astype(int)] ==
action_idx],
axis=1)) * beta_softmax)
sum_actionLik += actionLikelihood[:, action_idx]
rewards[T] = td['reward'][T]
actions[T] = td['A_chosen'][T]
actionLikelihood[:] = np.transpose(
actionLikelihood.T / sum_actionLik) * (
1 - epsilon_softmax) + epsilon_softmax / numberOfActions
betaWeights[:] = actionLikelihood[:, actions[T].astype(int)]
filt_actionLkd[T] = actionLikelihood
log_proba_ += np.log(sum(betaWeights) / numberOfBetaSamples)
betaWeights = betaWeights / sum(betaWeights)
betaAncestors[:] = useful_functions.stratified_resampling(betaWeights)
# update particles
muSamples[:] = muSamplesNew
gammaSamples[:] = gammaSamplesNew
logThetaWeights[:] = logThetaWeightsNew[betaAncestors]
ancestorSamples[:] = currentSamples
temperatureAncestors[:] = temperatures
elapsed_time = time.time() - start_time_multi
return log_proba_