def group_model(self):
with pm.Model() as gmodel:
# uniform priors on h
m = pm.DiscreteUniform('h', 0., 20.)
std = pm.InverseGamma('s', 3., 0.5)
mean = 2 * m + 1
alphas = np.arange(1., 101., 5.)
p = self.discreteNormal(alphas, mean, std)
for i in range(self.nruns):
hab_ten = pm.Categorical('h_{}'.format(i), p)
alpha = tt.as_tensor_variable([hab_ten])
probs_a, probs_r = self.inferrer(alpha)
# use a DensityDist
pm.Categorical('actions_{}'.format(i),
probs_a,
observed=self.actions[i])
pm.Categorical('rewards_{}'.format(i),
probs_r,
observed=self.rewards[i])
return gmodel
def model_static(mcmc_in, alpha_prior=(1,1), beta_prior=(0,1), asymmetric_accuracy=True, hashtag_treatment="strong", draws=500, tune=500):
'''
alpha prior = (mu,sd)
beta prior = (mu,sd)
if z_obs is present then oracle
'''
model = pm.Model()
with model:
if hashtag_treatment=="strong":
rho_prior = np.ones((2,2))
rho_prior[1,1] = 49
rho = pm.Dirichlet('rho', a=rho_prior, shape=(mcmc_in.K,2,2))
z = pm.Categorical('z',
p=rho[mcmc_in.kk_lkup, mcmc_in.flag_hashtag],
observed=np.ma.masked_values(mcmc_in.z_obs, value=-999),
testval=mcmc_in.z_init,
shape=mcmc_in.N)
if hashtag_treatment=="weak":
rho_prior = np.ones((2,2))
rho = pm.Dirichlet('rho', a=rho_prior, shape=(mcmc_in.K,2,2))
z = pm.Categorical('z',
p=rho[mcmc_in.kk_lkup, mcmc_in.flag_hashtag],
observed=np.ma.masked_values(mcmc_in.z_obs, value=-999),
testval=mcmc_in.z_init,
shape=mcmc_in.N)
elif hashtag_treatment=="oracle" or hashtag_treatment=="none":
rho_prior = np.ones((1,2))
rho = pm.Dirichlet('rho', a=rho_prior, shape=(mcmc_in.K,2))
z = pm.Categorical('z',
p=rho[mcmc_in.kk_lkup],
observed=np.ma.masked_values(mcmc_in.z_obs, value=-999),
testval=mcmc_in.z_init,
shape=mcmc_in.N)
beta_prime = pm.Normal('beta_prime', mu=beta_prior[0], sd=beta_prior[1], shape=mcmc_in.K)
if asymmetric_accuracy==True:
alpha = pm.Normal('alpha', mu=alpha_prior[0], sd=alpha_prior[1], shape=(mcmc_in.J,2))
def logp(r, z=z, alpha=alpha, beta_prime=beta_prime):
out = T.switch(T.eq(z[mcmc_in.ii],r),
-1*T.log(1+T.exp(-1*alpha[mcmc_in.jj,z[mcmc_in.ii]]*T.exp(beta_prime[mcmc_in.kk]))),
-1*alpha[mcmc_in.jj,z[mcmc_in.ii]]*T.exp(beta_prime[mcmc_in.kk]) - 1*T.log(1+T.exp(-1*alpha[mcmc_in.jj,z[mcmc_in.ii]]*T.exp(beta_prime[mcmc_in.kk])))
)
return T.sum(out)
else:
alpha = pm.Normal('alpha', mu=alpha_prior[0], sd=alpha_prior[1], shape=mcmc_in.J)
def logp(r, z=z, alpha=alpha, beta_prime=beta_prime):
out = T.switch(T.eq(z[mcmc_in.ii],r),
-1*T.log(1+T.exp(-1*alpha[mcmc_in.jj]*T.exp(beta_prime[mcmc_in.kk]))),
-1*alpha[mcmc_in.jj]*T.exp(beta_prime[mcmc_in.kk]) - 1*T.log(1+T.exp(-1*alpha[mcmc_in.jj]*T.exp(beta_prime[mcmc_in.kk])))
)
return T.sum(out)
r = pm.DensityDist('r', logp, observed=mcmc_in.r_obs, shape=len(mcmc_in.r_obs))
with model:
trace = pm.sample(draws=draws, tune=tune, chains=1)
return trace
def model_dawidskene(mcmc_in, alpha_prior, asymmetric_accuracy=True, hashtag_treatment="strong", draws=500, tune=500):
'''
alpha prior = (K,J,2) matrix of pseudocounts for dirichlet
if z_obs is present then oracle
'''
model = pm.Model()
with model:
if hashtag_treatment=="strong":
rho_prior = np.ones((2,2))
rho_prior[1,1] = 49
rho = pm.Dirichlet('rho', a=rho_prior, shape=(mcmc_in.K,2,2))
z = pm.Categorical('z',
p=rho[mcmc_in.kk_lkup, mcmc_in.flag_hashtag],
observed=np.ma.masked_values(mcmc_in.z_obs, value=-999),
testval=mcmc_in.z_init,
shape=mcmc_in.N)
elif hashtag_treatment=="weak":
rho_prior = np.ones((2,2))
rho = pm.Dirichlet('rho', a=rho_prior, shape=(mcmc_in.K,2,2))
z = pm.Categorical('z',
p=rho[mcmc_in.kk_lkup, mcmc_in.flag_hashtag],
observed=np.ma.masked_values(mcmc_in.z_obs, value=-999),
testval=mcmc_in.z_init,
shape=mcmc_in.N)
elif hashtag_treatment=="oracle" or hashtag_treatment=="none":
rho_prior = np.ones((1,2))
rho = pm.Dirichlet('rho', a=rho_prior, shape=(mcmc_in.K,2))
z = pm.Categorical('z',
p=rho[mcmc_in.kk_lkup],
observed=np.ma.masked_values(mcmc_in.z_obs, value=-999),
testval=mcmc_in.z_init,
shape=mcmc_in.N)
if asymmetric_accuracy==True:
alpha = pm.Dirichlet("alpha", a=alpha_prior, shape=(2,mcmc_in.K,mcmc_in.J,2))
def logp(r, z=z, alpha=alpha):
out = T.switch(T.eq(z[mcmc_in.ii],r),
T.log(alpha[z[mcmc_in.ii],mcmc_in.kk,mcmc_in.jj,1]),
T.log(1-alpha[z[mcmc_in.ii],mcmc_in.kk,mcmc_in.jj,1])
)
return T.sum(out)
else:
alpha = pm.Dirichlet("alpha", a=alpha_prior, shape=(mcmc_in.K,mcmc_in.J,2))
def logp(r, z=z, alpha=alpha):
out = T.switch(T.eq(z[mcmc_in.ii],r),
T.log(alpha[mcmc_in.kk,mcmc_in.jj,1]),
T.log(1-alpha[mcmc_in.kk,mcmc_in.jj,1])
)
return T.sum(out)
r = pm.DensityDist('r', logp, observed=mcmc_in.r_obs, shape=len(mcmc_in.r_obs))
with model:
step1 = pm.NUTS(vars=[rho, alpha])
step2 = pm.CategoricalGibbsMetropolis(vars=[z.missing_values])
trace = pm.sample(draws=draws, tune=tune, step=[step1, step2], chains=1)
return trace
def pymc3_dist(self, name, hypers):
p = self.p
if(len(hypers) == 1):
hyper_dist = hypers[0][0]
hyper_name = hypers[0][1]
p = hyper_dist.pymc3_dist(hyper_name, [])
if(self.num_elements==-1):
return pm.Categorical(name, p=p)
else:
return pm.Categorical(name, p=p, shape=self.num_elements)
def test_2d_w(self):
nd = self.nd
npop = self.npop
mus = self.mus
size = 100
with pm.Model() as model:
m = pm.NormalMixture(
"m",
w=np.ones((nd, npop)) / npop,
mu=mus,
sigma=1e-5,
comp_shape=(nd, npop),
shape=nd,
)
z = pm.Categorical("z", p=np.ones(npop) / npop, shape=nd)
mu = tt.as_tensor_variable([mus[i, z[i]] for i in range(nd)])
latent_m = pm.Normal("latent_m", mu=mu, sigma=1e-5, shape=nd)
m_val = m.random(size=size)
latent_m_val = latent_m.random(size=size)
assert m_val.shape == latent_m_val.shape
# Test that each element in axis = -1 can come from independent
# components
assert not all(np.all(np.diff(m_val) < 1e-3, axis=-1))
assert not all(np.all(np.diff(latent_m_val) < 1e-3, axis=-1))
self.samples_from_same_distribution(m_val, latent_m_val)
self.logp_matches(m, latent_m, z, npop, model=model)
def build_ann_conv(init):
network = lasagne.layers.InputLayer(shape=(None, 1, 28, 28),
input_var=input_var)
network = lasagne.layers.Conv2DLayer(
network,
num_filters=32,
filter_size=(5, 5),
nonlinearity=lasagne.nonlinearities.tanh,
W=init)
network = lasagne.layers.MaxPool2DLayer(network, pool_size=(2, 2))
network = lasagne.layers.Conv2DLayer(
network,
num_filters=32,
filter_size=(5, 5),
nonlinearity=lasagne.nonlinearities.tanh,
W=init)
network = lasagne.layers.MaxPool2DLayer(network, pool_size=(2, 2))
network = lasagne.layers.DenseLayer(
network,
num_units=256,
nonlinearity=lasagne.nonlinearities.tanh,
b=init,
W=init)
network = lasagne.layers.DenseLayer(
network,
num_units=10,
nonlinearity=lasagne.nonlinearities.softmax,
b=init,
W=init)
prediction = lasagne.layers.get_output(network)
return pm.Categorical('out', prediction, observed=target_var)
def exercise4():
with pm.Model() as basic_model:
probabilities = [0.3, 0.7, 0.95]
likelihood_params = np.array(
[np.divide(1, 3) * (1 + 2 * prob) for prob in probabilities])
group = pm.Categorical('group', p=np.array([1, 1, 1]))
p = pm.Deterministic('p', theano.shared(likelihood_params)[group])
positive_answers = pm.Binomial('positive_answers',
n=num_questions,
p=p,
observed=[7])
trace = pm.sample(4000, progressbar=True)
az.plot_trace(trace)
plt.show()
az.plot_posterior(trace)
plt.show()
az.summary(trace)
return trace
def sample_sticky_only(model_matrix, sample_kwargs=None):
# load the data
x_sc = model_matrix['x_sc']
subj_idx = model_matrix['subj_idx']
y = model_matrix['y']
n_subj = model_matrix['n_subj']
n, d = model_matrix['x_mu_kal'].shape
if sample_kwargs is None:
sample_kwargs = dict(draws=2000,
njobs=2,
tune=2000,
init='advi+adapt_diag')
with pm.Model() as hier_sticky:
mu_1 = pm.Normal('mu_beta_stick', mu=0., sd=100.)
sigma_1 = pm.HalfCauchy('sigma_stick', beta=100)
b_1 = pm.Normal('beta_sticky', mu=mu_1, sd=sigma_1, shape=n_subj)
rho = tt.tile(tt.reshape(b_1[subj_idx], (n, 1)), d) * x_sc
p_hat = softmax(rho)
# Data likelihood
yl = pm.Categorical('yl', p=p_hat, observed=y)
# inference!
trace_kal_scram = pm.sample(**sample_kwargs)
return hier_sticky, trace_kal_scram
def build_softmax_linear(X, y, force_softmax=False):
"""
Sample from Bayesian Softmax Linear Regression
"""
num_features = X.shape[1]
num_classes = len(np.unique(y))
logistic_regression = num_classes == 2
Xt = theano.shared(X)
if logistic_regression and not force_softmax:
print('running logistic regression')
with pm.Model() as model:
W = pm.Normal('W', 0, sd=1e6, shape=num_features)
b = pm.Flat('b')
logit = Xt.dot(W) + b
p = tt.nnet.sigmoid(logit)
observed = pm.Bernoulli('obs', p=p, observed=y)
else:
with pm.Model() as model:
W = pm.Normal('W', 0, sd=1e6, shape=(num_features, num_classes))
b = pm.Flat('b', shape=num_classes)
logit = Xt.dot(W) + b
p = tt.nnet.softmax(logit)
observed = pm.Categorical('obs', p=p, observed=y)
return model
def get_dirichlet_multinomial_dpmixture(X, params):
n_doc, n_feat = X.shape
n_comp = params['n_trunc']
with pm.Model() as model:
# sample P ~ DP(G0)
beta = pm.Beta('beta',
1.,
params['dp_alpha'],
shape=n_comp)
p_comp = pm.Deterministic(
'p_comp',
beta * tt.concatenate([[1], tt.extra_ops.cumprod(1 - beta)[:-1]]))
pkw = pm.Dirichlet('pkw',
a=params['pkw_dirichlet_dist_alpha'] * np.ones(n_feat),
shape=(n_comp, n_feat))
# sample X ~ P
z = pm.Categorical('z',
p=p_comp,
shape=n_doc)
x = pm.Multinomial('x',
n=X.sum(axis=1),
p=pkw[z],
observed=X)
return model
def add_observations():
with hierarchical_model.pymc_model:
for i in range(hierarchical_model.n_groups):
observations.append(
pm.Categorical(f'y_{i}',
levelProbs[:, i],
observed=hierarchical_model.y[i]))
def _define_model(self):
self.model = pm.Model()
with self.model:
p = pm.Dirichlet('p', a=np.array([1., 1., 1.]), shape=self.number_of_hidden_states)
p_min_potential = pm.Potential('p_min_potential', tt.switch(tt.min(p) < .1, -np.inf, 0))
means = pm.Normal('means', mu=[0, 0, 0], sd=2.0, shape=self.number_of_hidden_states)
# break symmetry
order_means_potential = pm.Potential('order_means_potential',
tt.switch(means[1] - means[0] < 0, -np.inf, 0)
+ tt.switch(means[2] - means[1] < 0, -np.inf, 0))
sd = pm.HalfCauchy('sd', beta=2, shape=self.number_of_hidden_states)
category = pm.Categorical('category',
p=p,
shape=self.number_of_data)
points = pm.Normal('obs',
mu=means[category],
sd=sd[category],
observed=self.data)
def group_static_ucb_mes_model(X, explore_param_alpha=.01, explore_param_beta=.01,
temperature_alpha=1., temperature_beta=10., method_alpha=.001, maxk=10, samples=200):
X = X.copy().transpose((2,1,3,0))
nparticipants = X.shape[3]
nchoices = X.shape[2]
ntrials = X.shape[1]
actions = theano.shared(X[-1])
mean = theano.shared(X[0])
var = theano.shared(X[1])
mes = theano.shared(X[3])
#mes = theano.shared(X[4])
random_likelihood = theano.shared((1./nchoices)*np.ones(shape=(ntrials, maxk, nchoices, nparticipants)))
with pm.Model() as model:
explore_param = pm.Gamma('var_param', explore_param_alpha, explore_param_beta, shape=maxk)
temperature = pm.Gamma('temperature', temperature_alpha, temperature_beta, shape=maxk)
method = pm.Dirichlet('method', np.ones(3)*method_alpha, shape=(maxk,3))
alpha = pm.Gamma('alpha', 10**-10., 10**-10.)
beta = pm.Beta('beta', 1., alpha, shape=maxk)
weights = pm.Deterministic('w', stick_breaking(beta))
assignments = pm.Categorical('assignments', weights, shape=nparticipants)
obs = pm.Potential('obs', sparse_group_static_ucb_mes_likelihood(actions, mean, var, mes, random_likelihood, method, explore_param, temperature, assignments, maxk))
trace = pm.sample(samples, njobs=4)
return trace
def test_logistic_regression():
data_X = np.array([[0, 0], [1, 0], [0, 1], [1, 1]])
data_y = np.array([0, 1, 0, 1])
with pymc3.Model() as model:
X = pymc3.Normal(name='X', mu=1, sd=2, observed=data_X)
alpha1_precision = pymc3.Uniform(name='alpha1_precision')
alpha1 = pymc3.Normal(name='alpha1', mu=0, sd=1.0 / alpha1_precision)
alpha2_precision = pymc3.Uniform(name='alpha2_precision')
alpha2 = pymc3.Normal(name='alpha2', mu=0, sd=1.0 / alpha2_precision)
beta1_precision = pymc3.Uniform(name='beta1_precision')
beta2_precision = pymc3.Uniform(name='beta2_precision')
beta1 = pymc3.Normal(name='beta1',
mu=0.0,
sd=1.0 / beta1_precision,
shape=2)
beta2 = pymc3.Normal(name='beta2',
mu=0.0,
sd=1.0 / beta2_precision,
shape=2)
v1 = alpha1 + beta1.dot(X.T)
v2 = alpha2 + beta2.dot(X.T)
denom = T.exp(v1) + T.exp(v2)
sm1 = T.exp(v1) / denom
sm2 = T.exp(v2) / denom
v = T.stack(sm1, sm2)
y = pymc3.Categorical(p=v,
name='y',
observed=data_y,
shape=len(data_y))
step = pymc3.Metropolis()
trace = pymc3.sample(1000, step)
pass
def run():
data = sim()
n_rooms = len(data)
prior = [0.5, 0.25, 0.125, 0.0625, 0.03125]
prior = [0.25, 0., 0.25, 0.25, 0.5]
#p_find=np.array([0.25,0.25,0.25,0.25,0.25])
#p_find=tt.cast([0.25,0.25,0.25,0.25,0.25],'int64')
p_find = theano.shared(np.array([0.25, 0.25, 0.25, 0.25, 0.25]))
tmp_find = theano.shared(np.array([0.25, 0.25, 0.25, 0.25, 0.25]))
datas = theano.shared(data)
print(data)
with pm.Model() as model:
target_loc = pm.Categorical('target_loc', p=prior)
#Likelihood
#room_search=pm.DiscreteUniform('room_search',1,n_rooms)
#p = pm.math.switch(theano.tensor.eq(room_search,target_loc),p_find[target_loc], 0)
tmp_find = tmp_find * 0
tmp_find = tt.set_subtensor(tmp_find[target_loc], p_find[target_loc])
#theano.printing.Print('tmp_find')(tmp_find)
y = pm.Binomial('y',
p=tmp_find,
n=[5, 1., 1., 10., 10.],
observed=[0, 0, 0, 0, 0])
trace = pm.sample(5000, cores=4)
pm.plots.traceplot(trace, combined=True)
#pm.traceplot(trace,
# combined=True,
# prior=[target_loc.distribution]);
plt.show()
print(pm.summary(trace))
def test_1d_w(self):
nd = self.nd
npop = self.npop
mus = self.mus
size = 100
with pm.Model() as model:
m = pm.NormalMixture("m",
w=np.ones(npop) / npop,
mu=mus,
sigma=1e-5,
comp_shape=(nd, npop),
shape=nd)
z = pm.Categorical("z", p=np.ones(npop) / npop)
latent_m = pm.Normal("latent_m",
mu=mus[..., z],
sigma=1e-5,
shape=nd)
m_val = m.random(size=size)
latent_m_val = latent_m.random(size=size)
assert m_val.shape == latent_m_val.shape
# Test that each element in axis = -1 comes from the same mixture
# component
assert all(np.all(np.diff(m_val) < 1e-3, axis=-1))
assert all(np.all(np.diff(latent_m_val) < 1e-3, axis=-1))
self.samples_from_same_distribution(m_val, latent_m_val)
self.logp_matches(m, latent_m, z, npop, model=model)
def get_beta_bernoulli_dpmixture(X, params):
n_doc, n_feat = X.shape
n_comp = params['n_trunc']
with pm.Model() as model:
# sample P ~ DP(G0)
beta = pm.Beta('beta',
1.,
params['dp_alpha'],
shape=n_comp)
p_comp = pm.Deterministic(
'p_comp',
beta * tt.concatenate([[1], tt.extra_ops.cumprod(1 - beta)[:-1]]))
pkw = pm.Beta('pkw',
alpha=params['pkw_beta_dist_alpha'],
beta=params['pkw_beta_dist_beta'],
shape=(n_comp, n_feat))
# sample X ~ P
z = pm.Categorical('z',
p=p_comp,
shape=n_doc)
x = pm.Bernoulli('x',
p=pkw[z],
shape=(n_doc, n_feat),
observed=X)
return model
def Generate_theta_p(x, s, I, N, K, prod_f):
#print(s,N,len(x))
T = len(x)
D = len(x[0])
s = [one_hot(ss, N) for ss in s]
# x = [[xt for _ in range(N)] for xt in x]
x = np.array(x)
s = np.array(s)
model = pm.Model()
with model:
# Priors for unknown model parameters
theta = pm.Normal("theta", mu=0, sigma=1, shape=(D, K)) / np.sqrt(
K * D)
p_list = []
for t in range(T):
#print(prod_f)
#print(np.transpose(theta))
wt = dot(dot(prod_f, transpose(theta)), x[t])
swt = s[t] * wt
sum_sw = sum(swt)
p = exp(swt) / (1 + sum_sw)
p0 = 1 / (1 + sum_sw)
p_list.append(concatenate(([p0], p)))
I_obs = pm.Categorical("I_obs", p=stack(p_list, axis=0), observed=I)
with model:
step = pm.Metropolis()
trace1 = pm.sample(tune=2000, chains=1, step=step)
return trace1["theta"][-1]
def fit(self, x, y, niters=500, **kwargs):
""" Train model """
self.classes = np.sort(np.unique(y))
F = x.shape[1]
K = np.unique(y).shape[0]
with pm.Model() as linear_model:
# Creating the model
beta = pm.Normal('beta', mu=0, sd=10, shape=(F, K))
alpha = pm.Normal('alpha', mu=0, sd=10, shape=K)
mu = tt.dot(x, beta) + alpha
p = pm.Deterministic('p', tt.nnet.softmax(mu))
yl = pm.Categorical('yl', p=p, observed=y)
with linear_model:
# trace = pm.sample(niters, njobs=1, chains=1, verbose=False) # No U-turn sampler
trace = pm.sample(step=pm.Metropolis(),
draws=50000,
njobs=1,
tune=50)
self.params['beta'] = trace['beta'][-niters:].copy(
) # storing last 500 samples from sampler
self.params['alpha'] = trace['alpha'][-niters:].copy()
def build_fc_nn(X, y, output='regression', hidden_dims=[NUM_HIDDEN]):
"""
Build basic fully connected Bayesian neural network
Args:
X: data matrix
y: targets
output: one of SUPPORTED_OUTPUTS to specify the kind of outputs
hidden_dims: integer list indicating the size of the hidden layers
Returns:
PyMC3 Bayesian neural network model
"""
if output not in SUPPORTED_OUTPUTS:
raise ValueError(
'Unsupported neural network output: {}\nSupported outputs: {}'.
format(output, SUPPORTED_OUTPUTS))
if 'regression' == output:
num_output_units = 1
elif 'classification' == output:
num_output_units = len(np.unique(y))
floatX = theano.config.floatX
Xt = theano.shared(X)
num_features = X.shape[1]
layer_dims = [num_features] + hidden_dims
# initialize weights (switch to Xavier initiallization?)
Ws = []
for i in range(len(layer_dims) - 1):
in_dim = layer_dims[i]
out_dim = layer_dims[i + 1]
Ws.append(np.random.randn(in_dim, out_dim).astype(floatX))
with pm.Model() as model_nn:
for i in range(len(Ws)):
# priors
W_i = pm.Normal('W' + str(i),
0,
sd=WEIGHT_SD,
shape=Ws[i].shape,
testval=Ws[i])
b_i = pm.Flat('b' + str(i), shape=Ws[i].shape[1])
# deterministic transformations
in_layer = a_i if i > 0 else Xt
z_i = in_layer.dot(W_i) + b_i
a_i = pm.math.tanh(z_i)
# format output and plug in data
# uses pre-activation of last layer
if 'regression' == output:
observed = pm.Normal('obs', mu=z_i, sd=LIKELIHOOD_SD, observed=y)
elif 'classification' == output:
p = tt.nnet.softmax(z_i)
observed = pm.Categorical('obs', p=p, observed=y)
return model_nn
def bms(L, hdi_prob=0.95, **sample_kwargs):
"""This function computes the exceedance probabilities (xp)
and expected relative frequencies (r) from an array of log-evidences.
Args:
L (numpy.ndarray): Array of model log-evidences (higher is better fit).
Array shape should be (K models; N subjects)
**sample_kwargs: Additional arguments to the pymc.sample function.
Currently `cores=1` seems to be necessary.
Returns:
dict: Dictionary with values xp and r.
Reference:
Stephan, K. E., Penny, W. D., Daunizeau, J., Moran, R. J., & Friston, K. J. (2009). Bayesian model selection for group studies. Neuroimage, 46(4), 1004-1017.
"""
K, N = L.shape
with pm.Model() as bms:
def lookup_L(L, N):
"""This function looks up the log-evidences for all N subjects,
given the current model labels m.
"""
return L[tt.cast(m, dtype="int32"),
tt.cast(tt.arange(N), dtype="int32")]
# Priors
alpha = pm.Uniform("alpha", 0, N, shape=K, testval=np.ones(K))
# Model
r = pm.Dirichlet("r", a=alpha, testval=np.ones(K) / K)
m = pm.Categorical("m", p=r, shape=N, testval=0)
# Look up log evidence
ll = pm.DensityDist("ll", logp=lookup_L, observed=dict(L=L, N=N))
# Sample
inferencedata = pm.sample(return_inferencedata=True, **sample_kwargs)
# Build results
result = {}
result["summary"] = az.summary(inferencedata,
hdi_prob=hdi_prob,
var_names=["alpha", "r"])
result["xp"] = np.array([
np.mean(inferencedata.posterior["r"].data[:, :, k] ==
inferencedata.posterior["r"].data.max(axis=-1))
for k in range(K)
])
r_unscaled = np.array([
np.mean(inferencedata.posterior["r"].data[:, :, k]) for k in range(K)
])
result["r"] = r_unscaled / r_unscaled.sum()
return result
def test_FFBSStep():
with pm.Model(), pytest.raises(ValueError):
P_rv = np.eye(2)[None, ...]
S_rv = DiscreteMarkovChain("S_t", P_rv, np.r_[1.0, 0.0], shape=10)
S_2_rv = DiscreteMarkovChain("S_2_t", P_rv, np.r_[0.0, 1.0], shape=10)
PoissonZeroProcess("Y_t",
9.0,
S_rv + S_2_rv,
observed=np.random.poisson(9.0, size=10))
# Only one variable can be sampled by this step method
ffbs = FFBSStep([S_rv, S_2_rv])
with pm.Model(), pytest.raises(TypeError):
S_rv = pm.Categorical("S_t", np.r_[1.0, 0.0], shape=10)
PoissonZeroProcess("Y_t",
9.0,
S_rv,
observed=np.random.poisson(9.0, size=10))
# Only `DiscreteMarkovChains` can be sampled with this step method
ffbs = FFBSStep([S_rv])
with pm.Model(), pytest.raises(TypeError):
P_rv = np.eye(2)[None, ...]
S_rv = DiscreteMarkovChain("S_t", P_rv, np.r_[1.0, 0.0], shape=10)
pm.Poisson("Y_t", S_rv, observed=np.random.poisson(9.0, size=10))
# Only `SwitchingProcess`es can used as dependent variables
ffbs = FFBSStep([S_rv])
np.random.seed(2032)
poiszero_sim, _ = simulate_poiszero_hmm(30, 150)
y_test = poiszero_sim["Y_t"]
with pm.Model() as test_model:
p_0_rv = pm.Dirichlet("p_0", np.r_[1, 1], shape=2)
p_1_rv = pm.Dirichlet("p_1", np.r_[1, 1], shape=2)
P_tt = at.stack([p_0_rv, p_1_rv])
P_rv = pm.Deterministic("P_tt", at.shape_padleft(P_tt))
pi_0_tt = compute_steady_state(P_rv)
S_rv = DiscreteMarkovChain("S_t", P_rv, pi_0_tt, shape=y_test.shape[0])
PoissonZeroProcess("Y_t", 9.0, S_rv, observed=y_test)
with test_model:
ffbs = FFBSStep([S_rv])
test_point = test_model.test_point.copy()
test_point["p_0_stickbreaking__"] = poiszero_sim["p_0_stickbreaking__"]
test_point["p_1_stickbreaking__"] = poiszero_sim["p_1_stickbreaking__"]
res = ffbs.step(test_point)
assert np.array_equal(res["S_t"], poiszero_sim["S_t"])
def test_pymc3_convert_dists():
"""Just a basic check that all PyMC3 RVs will convert to and from Theano RVs."""
tt.config.compute_test_value = "ignore"
theano.config.cxx = ""
with pm.Model() as model:
norm_rv = pm.Normal("norm_rv", 0.0, 1.0, observed=1.0)
mvnorm_rv = pm.MvNormal("mvnorm_rv",
np.r_[0.0],
np.c_[1.0],
shape=1,
observed=np.r_[1.0])
cauchy_rv = pm.Cauchy("cauchy_rv", 0.0, 1.0, observed=1.0)
halfcauchy_rv = pm.HalfCauchy("halfcauchy_rv", 1.0, observed=1.0)
uniform_rv = pm.Uniform("uniform_rv", observed=1.0)
gamma_rv = pm.Gamma("gamma_rv", 1.0, 1.0, observed=1.0)
invgamma_rv = pm.InverseGamma("invgamma_rv", 1.0, 1.0, observed=1.0)
exp_rv = pm.Exponential("exp_rv", 1.0, observed=1.0)
halfnormal_rv = pm.HalfNormal("halfnormal_rv", 1.0, observed=1.0)
beta_rv = pm.Beta("beta_rv", 2.0, 2.0, observed=1.0)
binomial_rv = pm.Binomial("binomial_rv", 10, 0.5, observed=5)
dirichlet_rv = pm.Dirichlet("dirichlet_rv",
np.r_[0.1, 0.1],
observed=np.r_[0.1, 0.1])
poisson_rv = pm.Poisson("poisson_rv", 10, observed=5)
bernoulli_rv = pm.Bernoulli("bernoulli_rv", 0.5, observed=0)
betabinomial_rv = pm.BetaBinomial("betabinomial_rv",
0.1,
0.1,
10,
observed=5)
categorical_rv = pm.Categorical("categorical_rv",
np.r_[0.5, 0.5],
observed=1)
multinomial_rv = pm.Multinomial("multinomial_rv",
5,
np.r_[0.5, 0.5],
observed=np.r_[2])
# Convert to a Theano `FunctionGraph`
fgraph = model_graph(model)
rvs_by_name = {
n.owner.inputs[1].name: n.owner.inputs[1]
for n in fgraph.outputs
}
pymc_rv_names = {n.name for n in model.observed_RVs}
assert all(
isinstance(rvs_by_name[n].owner.op, RandomVariable)
for n in pymc_rv_names)
# Now, convert back to a PyMC3 model
pymc_model = graph_model(fgraph)
new_pymc_rv_names = {n.name for n in pymc_model.observed_RVs}
pymc_rv_names == new_pymc_rv_names
def _create_model(self):
with pm.Model() as self.model:
# getting the location primers
for layer_index in range(self.num_layers):
setattr(self, 'w%d' % layer_index, self.__get_weights(layer_index, self.weight_shapes[layer_index]))
setattr(self, 'b%d' % layer_index, self.__get_biases(layer_index, self.bias_shapes[layer_index]))
if layer_index == 0:
fc = pm.Deterministic('fc%d' % layer_index, pm.math.tanh(pm.math.dot(self.network_input, self.weight(layer_index)) + self.bias(layer_index)))
setattr(self, 'fc%d' % layer_index, fc)
elif 0 < layer_index < self.num_layers - 1:
fc = pm.Deterministic('fc%d' % layer_index, pm.math.tanh(pm.math.dot(getattr(self, 'fc%d' % (layer_index - 1)), self.weight(layer_index)) + self.bias(layer_index)))
setattr(self, 'fc%d' % layer_index, fc)
else:
self._loc = pm.Deterministic('bnn_out', pm.math.sigmoid(pm.math.dot(getattr(self, 'fc%d' % (layer_index - 1)), self.weight(layer_index)) + self.bias(layer_index)) )
# getting the precision / standard deviation / variance
self.tau_rescaling = np.zeros((self.num_obs, self.network_input.shape[1]))
for obs_index in range(self.num_obs):
self.tau_rescaling[obs_index] += self.var_e_ranges
self.tau_rescaling = self.tau_rescaling**2
tau = pm.Gamma('tau', self.num_obs**2, 1., shape = (self.num_obs, self.network_input.shape[1]))
self.tau = tau / self.tau_rescaling
self.scale = pm.Deterministic('scale', 1. / pm.math.sqrt(self.tau))
# learn the floats
self.loc = pm.Deterministic('loc', (self.upper_rescalings - self.lower_rescalings) * self._loc + self.lower_rescalings)
self.out_floats = pm.Normal('out_floats', self.loc[:, self.floats], tau = self.tau[:, self.floats], observed = self.network_output[:, self._floats])
# learn the integers
self.int_scale = pm.Deterministic('int_scale', 1. * self.scale)
self.out_ints = DiscreteLaplace('out_ints', loc = self.loc[:, self.ints], scale = self.int_scale[:, self.ints], observed = self.network_output[:, self._ints])
# learn the categories
dist_counter, cat_var_index = 0, 0
self.alpha = pm.Deterministic('alpha', (self.loc + 1.) * self.scale)
self.num_cats = 0
for var_e_index, var_e_type in enumerate(self.var_e_types):
if var_e_type == 'categorical' and self.var_e_begin[var_e_index] == var_e_index:
begin, end = self.var_e_begin[var_e_index], self.var_e_end[var_e_index]
var_e_name = self.var_e_names[var_e_index]
param_index = np.argwhere(self.var_p_names == var_e_name)[0, 0]
self.param_index = param_index
out_dirichlet = pm.Dirichlet('dirich_%d' % dist_counter, a = self.alpha[:, begin : end], shape = (self.num_obs, int(end - begin)) )
out_cats = pm.Categorical('out_cats_%d' % dist_counter, p = out_dirichlet, observed = self.network_output[:, param_index])
self.num_cats += 1
dist_counter += 1
def sample_heir_rbf_kal(model_matrix, sample_kwargs=None):
# load the data
x_mu_rbf = model_matrix['x_mu_rbf']
x_sd_rbf = model_matrix['x_sd_rbf']
x_mu_kal = model_matrix['x_mu_kal']
x_sd_kal = model_matrix['x_sd_kal']
x_sc = model_matrix['x_sc']
subj_idx = model_matrix['subj_idx']
y = model_matrix['y']
n_subj = model_matrix['n_subj']
n, d = x_mu_rbf.shape
if sample_kwargs is None:
sample_kwargs = dict(draws=2000,
njobs=2,
tune=2000,
init='advi+adapt_diag')
with pm.Model() as hier_rbf_kal:
mu_1 = pm.Normal('mu_beta_rbf_mean', mu=0., sd=100.)
mu_2 = pm.Normal('mu_beta_rbf_stdv', mu=0., sd=100.)
mu_3 = pm.Normal('mu_beta_kal_mean', mu=0., sd=100.)
mu_4 = pm.Normal('mu_beta_kal_stdv', mu=0., sd=100.)
mu_5 = pm.Normal('mu_beta_stick', mu=0., sd=100.)
sigma_1 = pm.HalfCauchy('sigma_rbf_means', beta=100)
sigma_2 = pm.HalfCauchy('sigma_rbf_stdev', beta=100)
sigma_3 = pm.HalfCauchy('sigma_kal_means', beta=100)
sigma_4 = pm.HalfCauchy('sigma_kal_stdev', beta=100)
sigma_5 = pm.HalfCauchy('sigma_stick', beta=100)
b_1 = pm.Normal('beta_rbf_mu', mu=mu_1, sd=sigma_1, shape=n_subj)
b_2 = pm.Normal('beta_rbf_std', mu=mu_2, sd=sigma_2, shape=n_subj)
b_3 = pm.Normal('beta_kal_mu', mu=mu_3, sd=sigma_3, shape=n_subj)
b_4 = pm.Normal('beta_kal_std', mu=mu_4, sd=sigma_4, shape=n_subj)
b_5 = pm.Normal('beta_sc', mu=mu_5, sd=sigma_5, shape=n_subj)
rho = \
tt.tile(tt.reshape(b_1[subj_idx], (n, 1)), d) * x_mu_rbf + \
tt.tile(tt.reshape(b_2[subj_idx], (n, 1)), d) * x_sd_rbf + \
tt.tile(tt.reshape(b_3[subj_idx], (n, 1)), d) * x_mu_kal + \
tt.tile(tt.reshape(b_4[subj_idx], (n, 1)), d) * x_sd_kal + \
tt.tile(tt.reshape(b_5[subj_idx], (n, 1)), d) * x_sc
p_hat = softmax(rho)
# Data likelihood
yl = pm.Categorical('yl', p=p_hat, observed=y)
# inference!
trace_gprbf_kal = pm.sample(**sample_kwargs)
return hier_rbf_kal, trace_gprbf_kal
def test_discrete_not_allowed():
mu_true = np.array([-2, 0, 2])
z_true = np.random.randint(len(mu_true), size=100)
y = np.random.normal(mu_true[z_true], np.ones_like(z_true))
with pm.Model():
mu = pm.Normal('mu', mu=0, sigma=10, shape=3)
z = pm.Categorical('z', p=tt.ones(3) / 3, shape=len(y))
pm.Normal('y_obs', mu=mu[z], sigma=1., observed=y)
with pytest.raises(opvi.ParametrizationError):
pm.fit(n=1) # fails
def build_model(self, n=None, name='archimedian_model'):
with pm.Model(name=name) as self.model:
if n is None:
# one n per galaxy, or per arm?
self.n_choice = pm.Categorical('n_choice', [1, 1, 0, 1, 1],
testval=1,
shape=len(self.galaxies))
self.n = pm.Deterministic('n', self.n_choice - 2)
self.chirality_correction = tt.switch(self.n < 0, -1, 1)
else:
msg = 'Parameter $n$ must be a nonzero float'
try:
n = float(n)
except ValueError:
pass
finally:
assert isinstance(n, float) and n != 0, msg
self.n_choice = None
self.n = pm.Deterministic('n',
np.repeat(n, len(self.galaxies)))
self.chirality_correction = tt.switch(self.n < 0, -1, 1)
self.a = pm.HalfCauchy('a', beta=1, testval=1, shape=self.n_arms)
self.psi = pm.Normal(
'psi',
mu=0,
sigma=1,
testval=0.1,
shape=self.n_arms,
)
self.sigma_r = pm.InverseGamma('sigma_r', alpha=2, beta=0.5)
# Unfortunately, as we need to reverse the theta points for arms
# with n < 1, and rotate all arms to start at theta = 0,
# we need to do some model-mangling
self.t_mins = Series({
i: self.data.query('arm_index == @i')['theta'].min()
for i in np.unique(self.data['arm_index'])
})
r_stack = [
self.a[i] * tt.power(
(self.data.query('arm_index == @i')['theta'].values -
self.t_mins[i] + self.psi[i]),
1 / self.n[int(self.gal_arm_map[i])])
[::self.chirality_correction[int(self.gal_arm_map[i])]]
for i in np.unique(self.data['arm_index'])
]
r = pm.Deterministic('r', tt.concatenate(r_stack))
self.likelihood = pm.StudentT(
'Likelihood',
mu=r,
sigma=self.sigma_r,
observed=self.data['r'].values,
)
def single_model(self, idx):
minimum = 0.
maximum = 8.
sample_space = np.arange(minimum, maximum + 1, 1)
sample_space = 1. / 10**(sample_space / 4.)
with pm.Model() as smodel:
# uniform priors on h
hab_ten = pm.DiscreteUniform('h', 0., 8.)
# convert to a tensor
alpha = tt.as_tensor_variable([10**(hab_ten / 4.)])
probs_a, probs_r = self.inferrer(alpha)
# use a DensityDist
pm.Categorical('actions', probs_a, observed=self.actions[idx])
pm.Categorical('rewards', probs_r, observed=self.rewards[idx])
return smodel, sample_space
def test_bernoulli_process(self):
"""Testing the Bridge Sampler with a Beta-Bernoulli-Process model"""
# prior parameters
alpha = np.random.gamma(1.0, 2.0)
beta = np.random.gamma(1.0, 2.0)
n = 100
draws = 10000
tune = 1000
print("Testing with alpha = ", alpha, "and beta = ", beta)
# random data
p0 = np.random.random()
expected_error = np.sqrt(p0 * (1 - p0) / n) # reasonable approximation
observations = (np.random.random(n) <= p0).astype("int")
with pm.Model() as BernoulliBeta:
theta = pm.Beta('pspike', alpha=alpha, beta=beta)
obs = pm.Categorical('obs',
p=pm.math.stack([theta, 1.0 - theta]),
observed=observations)
trace = pm.sample(draws=draws, tune=tune)
# calculate exact marginal likelihood
n = len(observations)
k = sum(observations)
print(n, k)
exact_log_marg_ll = spf.betaln(alpha + k, beta +
(n - k)) - spf.betaln(alpha, beta)
# estimate with bridge sampling
logml_dict = marginal_llk(trace, model=BernoulliBeta, maxiter=10000)
expected_p = 1.0 - trace["pspike"].mean()
# should be true in 95% of the runs
self.assertTrue(
np.abs(expected_p - p0) < 2 * expected_error,
msg=
"Estimated probability is {0:5.3f}, exact is {1:5.3f}, estimated standard deviation is {2:5.3f}. Is this OK?"
.format(expected_p, p0, expected_error))
estimated_log_marg_ll = logml_dict["logml"]
# 3.2 corresponds to a bayes factor of 'Not worth more than a bare mention'
self.assertTrue(
np.abs(estimated_log_marg_ll - exact_log_marg_ll) < np.log(3.2),
msg=
"Estimated marginal log likelihood {0:2.5f}, exact marginal log likelihood {1:2.5f}. Is this OK?"
.format(estimated_log_marg_ll, exact_log_marg_ll))
def _set_clustering_model(self):
with pm.Model() as model:
logger.info("Using {} cluster centers".format(self.n_states))
p = pm.Dirichlet("p",
a=np.repeat(1, self.n_states),
shape=self.n_states)
pm.Potential("p_pot", var=tt.switch(tt.min(p) < 0.05, -np.inf, 0.))
z = pm.Categorical("z", p=p, shape=self.n_genes)
tau_g, mean_g, gamma = self._gamma_mix(model, z)
param_hlm = self._hlm(model, gamma)
self._set_steps(model, z, p, tau_g, mean_g, gamma, *param_hlm)
return self