def run_Bernoulli_Normal():
#Cluster 1
Uh1 = pm.Uniform('UnifH1', lower=-50, upper=50)
# @UndefinedVariable
Nc1 = pm.Normal('NormC1', mu=Uh1,
tau=1) #, observed=True, value=10); # @UndefinedVariable
#Cluster 2
Uh2 = pm.Uniform('UnifH2', lower=-50, upper=50)
# @UndefinedVariable
Nc2 = pm.Normal('NormC2', mu=Uh2,
tau=1) #, observed=True, value=10); # @UndefinedVariable
#Bernoulli Nodes
B1 = pm.Bernoulli('Bern1', 0.8)
# @UndefinedVariable
B2 = pm.Bernoulli('Bern2', 0.8)
# @UndefinedVariable
B3 = pm.Bernoulli('Bern3', 0.5)
# @UndefinedVariable
#Points
p_N1 = pm.Lambda('p_Norm1', lambda k=B1, c1=Nc1, c2=Nc2: [c2, c1][int(k)])
p_N2 = pm.Lambda('p_Norm2', lambda k=B2, c1=Nc1, c2=Nc2: [c1, c2][int(k)])
p_N3 = pm.Lambda('p_Norm3', lambda k=B3, c1=Nc1, c2=Nc2: [c1, c2][int(k)])
normalObs1 = pm.Normal('NormX1', mu=p_N1, tau=1, observed=True, value=-3)
# @UndefinedVariable
normalObs2 = pm.Normal('NormX2', mu=p_N2, tau=1, observed=True, value=3)
# @UndefinedVariable
normalObsZ = pm.Normal('NormZ', mu=p_N3, tau=1)
# @UndefinedVariable
return [
Nc1, Nc2, B1, B2, B3, Uh1, Uh2, normalObs1, normalObs2, normalObsZ
]
def run_Bernoulli_Normal():
#Cluster 1
Uh1 = pm.Uniform('UnifH1', lower=-50, upper=50); # @UndefinedVariable
Nc1 = pm.Normal('NormC1', mu=Uh1, tau=1)#, observed=True, value=10); # @UndefinedVariable
#Cluster 2
Uh2 = pm.Uniform('UnifH2', lower=-50, upper=50); # @UndefinedVariable
Nc2 = pm.Normal('NormC2', mu=Uh2, tau=1)#, observed=True, value=10); # @UndefinedVariable
#Bernoulli Nodes
B1 = pm.Bernoulli('Bern1', 0.8); # @UndefinedVariable
B2 = pm.Bernoulli('Bern2', 0.8); # @UndefinedVariable
B3 = pm.Bernoulli('Bern3', 0.5); # @UndefinedVariable
#Points
p_N1 = pm.Lambda('p_Norm1', lambda k=B1, c1=Nc1, c2=Nc2: [c2,c1][int(k)]);
p_N2 = pm.Lambda('p_Norm2', lambda k=B2, c1=Nc1, c2=Nc2: [c1,c2][int(k)]);
p_N3 = pm.Lambda('p_Norm3', lambda k=B3, c1=Nc1, c2=Nc2: [c1,c2][int(k)]);
normalObs1 = pm.Normal('NormX1', mu=p_N1, tau=1, observed=True, value=-3); # @UndefinedVariable
normalObs2 = pm.Normal('NormX2', mu=p_N2, tau=1, observed=True, value=3); # @UndefinedVariable
normalObsZ = pm.Normal('NormZ', mu=p_N3, tau=1); # @UndefinedVariable
# @pm.stochastic(observed=True)
# def normalObs1(name='NormX1', parentVar=B1, parentVals=[Nc1,Nc2], value=8):
# return pm.normal_like(x=value, mu=parentVals[int(parentVar)], tau=1);
# @pm.stochastic(observed=True)
# def normalObs2(name='NormX2', parentVar=B2, parentVals=[Nc1,Nc2], value=2):
# return pm.normal_like(x=value, mu=parentVals[int(parentVar)], tau=1);
# @pm.stochastic(observed=False)
# def normalObsZ(name='NormZ', parentVar=B3, parentVals=[Nc1,Nc2], value=1):
# return pm.normal_like(x=value, mu=parentVals[int(parentVar)], tau=1);
# normalObs1 = pm.Normal('NormX1', mu=[Nc1,Nc2][int(B1)], tau=1, observed=True, value=2); # @UndefinedVariable
# normalObs2 = pm.Normal('NormX2', mu=[Nc1,Nc2][int(B2)], tau=1, observed=True, value=8); # @UndefinedVariable
# normalObsZ = pm.Normal('NormZ', mu=[Nc1,Nc2][int(B3)], tau=1); # @UndefinedVariable
return [Nc1,Nc2,B1,B2,B3,Uh1,Uh2,normalObs1,normalObs2,normalObsZ];
def _create_bayesian_gbmodel(self, database, initial_parameters):
"""
Generates the PyMC model to sample within one GB model (no Reversible Jump)
Arguments
---------
database : dict
Database of FreeSolv solvation free energy data
initial_parameters : dict
Dict containing the starting set of parameters for the model
Returns
-------
gbffmodel : dict
A dict containing the nodes of a PyMC model to sample
"""
gbffmodel = dict()
log_sigma_min = math.log(0.01) # kcal/mol
log_sigma_max = math.log(10.0) # kcal/mol
log_sigma_guess = math.log(0.2)
cid_list = database.keys()
def RMSE(**args):
nmolecules = len(cid_list)
error = np.zeros([nmolecules], np.float64)
for (molecule_index, cid) in enumerate(cid_list):
entry = database[cid]
error[molecule_index] = args['dg_gbsa'][
molecule_index] - float(entry['expt'])
mse = np.mean((error - np.mean(error))**2)
return np.sqrt(mse)
gbffmodel['log_sigma'] = pymc.Uniform('log_sigma',
lower=log_sigma_min,
upper=log_sigma_max,
value=log_sigma_guess)
gbffmodel['sigma'] = pymc.Lambda(
'sigma',
lambda log_sigma=gbffmodel['log_sigma']: math.exp(log_sigma))
gbffmodel['tau'] = pymc.Lambda(
'tau', lambda sigma=gbffmodel['sigma']: sigma**(-2))
gbffmodel.update(self.parameter_model)
gbffmodel_with_mols = self._add_parallel_gbffmodel(database, gbffmodel)
gbffmodel_with_mols['RMSE'] = pymc.Deterministic(
eval=RMSE,
name='RMSE',
parents={'dg_gbsa': gbffmodel_with_mols['dg_gbsa']},
doc='RMSE',
dtype=float,
trace=True,
verbose=1)
return gbffmodel_with_mols
def mymodel():
mu = pm.Normal('mu', 0, 1)
N = [pm.Normal('N_%i' % i, mu, 1) for i in xrange(3)]
z1 = pm.Lambda('z1', lambda n=N: np.sum(n))
z2 = pm.Lambda('z2', lambda n=N: np.sum(n))
@pm.potential
def y(z1=z1, z2=z2, mu=mu):
return 0
return mu, N, z1, z2, y
def __setup_obs(self):
self.obs = pymc.Container(
[pymc.Normal('obs_%s' % i,
mu=pymc.Lambda('omu_%s' % i,
lambda cls=self.eqv[i]: self.mu[cls]),
tau=pymc.Lambda('otau_%s' % i,
lambda cls=self.eqv[i]:
1.0 / (self.sigma[cls]**2)),
value=self.logit(acc),
observed=True)
for i, acc in enumerate(self.observations)])
def create_nodes_for_normal_normal(self, add_shift, tau_0, mu_0, sigma_beta,
sigma_y, true_mu, n_subjs, avg_samples):
""" create the normal normal nodes"""
mu = pm.Normal('mu',mu_0,tau_0)
nodes = {'mu': mu}
size = [None]*n_subjs
x_values = [None]*n_subjs
if add_shift:
b = []
else:
b = None
for i in range(n_subjs):
size[i] = int(max(1, avg_samples + randn()*10))
if add_shift:
x_values[i] = randn()*sigma_beta
value = randn(size[i]) * sigma_y + true_mu + x_values[i]
x = pm.Lambda('x%d' % i, lambda x=x_values[i]:x)
y = pm.Normal('y%d' % i,mu+x, sigma_y**-2, value=value,observed=True)
nodes['x%d' % i] = x
b.append(x)
else:
value = randn(size[i]) * sigma_y + true_mu
y = pm.Normal('y%d' % i,mu, sigma_y**-2, value=value,observed=True)
nodes['y%d' % i] = y
return nodes, size, x_values
def run_Categorical_Normal():
nC = 3
#Num. Clusters
aD = [0, 1, 8, 9, 20, 21]
#Data Points
nPts = len(aD) + 1
#Clusters
aUh = [
pm.Uniform('UnifH' + str(i), lower=-50, upper=50) for i in range(nC)
]
# @UndefinedVariable
aNc = [pm.Normal('NormC' + str(i), mu=aUh[i], tau=1) for i in range(nC)]
# @UndefinedVariable
#Dirichlet & Categorical Nodes
Dir = pm.Dirichlet('Dirichlet', theta=[1] * nC)
# @UndefinedVariable
aC = [pm.Categorical('Cat' + str(i), Dir) for i in range(nPts)]
# @UndefinedVariable
aL = [
pm.Lambda('p_Norm' + str(i), lambda k=aC[i], aNcl=aNc: aNcl[int(k)])
for i in range(nPts)
]
# @UndefinedVariable
#Points
aN = [
pm.Normal('NormX' + str(i),
mu=aL[i],
tau=1,
observed=True,
value=aD[i]) for i in range(nPts - 1)
]
# @UndefinedVariable
Nz = pm.Normal('NormZ', mu=aL[-1], tau=1)
# @UndefinedVariable
return np.concatenate([[Nz, Dir], aUh, aNc, aC, aN])
def model():
# Priors
sigma_y = pymc.Uniform('sigma_y', lower=0, upper=100)
tau_y = pymc.Lambda('tau_y', lambda s=sigma_y: s**-2)
xi = pymc.Uniform('xi', lower=0, upper=100, value=np.zeros(K))
mu_raw = pymc.Normal('mu_raw', mu=0., tau=0.0001, value=np.zeros(K))
Tau_B_raw = pymc.Wishart('Tau_B_raw', df, Tau=np.diag(np.ones(K)))
B_raw = pymc.MvNormal('B_raw', mu_raw, Tau_B_raw, value=np.zeros((J, K)))
# Model
@pymc.deterministic(plot=True)
def B(xi=xi, B_raw=B_raw):
return xi * B_raw
@pymc.deterministic
def mu(xi=xi, mu_raw=mu_raw):
return xi * mu_raw
@pymc.deterministic(plot=False)
def y_hat(B=B, X=X, i=index_c):
return np.sum(B[i, ] * X, axis=1)
# Likelihood
@pymc.stochastic(observed=True)
def y_i(value=y, mu=y_hat, tau=tau_y):
return pymc.normal_like(value, mu, tau)
return vars()
def run_Bernoulli_Normal():
B = pm.Bernoulli('Bern', 0.8)
# @UndefinedVariable
p_N1 = pm.Lambda('p_Norm', lambda k=B: [-5, 5][int(k)])
N = pm.Normal('Norm', mu=p_N1, tau=1)
# @UndefinedVariable
return [B, N]
def run_Categorical_Normal():
C = pm.Categorical('Cat', [0.2, 0.4, 0.1, 0.3])
# @UndefinedVariable
p_N = pm.Lambda('p_Norm', lambda node=C: [-5, 0, 5, 10][node])
N = pm.Normal('Norm', mu=p_N, tau=1)
# @UndefinedVariable
return [C, N]
def test_age_pattern_model_sim():
# simulate normal data
a = np.arange(0, 100, 5)
pi_true = .0001 * (a * (100. - a) + 100.)
sigma_true = .025 * np.ones_like(pi_true)
p = np.maximum(0., mc.rnormal(pi_true, 1. / sigma_true**2.))
# create model and priors
vars = {}
vars.update(
dismod_mr.model.spline.spline('test',
ages=np.arange(101),
knots=np.arange(0, 101, 5),
smoothing=.1))
vars['pi'] = mc.Lambda('pi', lambda mu=vars['mu_age'], a=a: mu[a])
vars.update(
dismod_mr.model.likelihood.normal('test', vars['pi'], 0., p,
sigma_true))
# fit model
m = mc.MCMC(vars)
m.sample(2)
def getModel():
nA, nK = 0.05, 4
aDir = [nA / nK] * nK
D = pm.Dirichlet('1-Dirichlet', theta=aDir)
#@UndefinedVariable
C1 = pm.Categorical('2-Cat', D)
#@UndefinedVariable
# C2 = pm.Categorical('10-Cat', D); #@UndefinedVariable
# C3 = pm.Categorical('11-Cat', D); #@UndefinedVariable
# C4 = pm.Categorical('14-Cat', D); #@UndefinedVariable
# C5 = pm.Categorical('15-Cat', D); #@UndefinedVariable
# G0_0 = pm.Gamma('4-Gamma0_1', alpha=1, beta=1.5); #@UndefinedVariable
N0_1 = pm.Normal('5-Norm0_1', mu=10, tau=1)
#@UndefinedVariable
N0_2 = pm.Normal('6-Norm0_2', mu=-10, tau=1)
#@UndefinedVariable
N0_3 = pm.Normal('7-Norm0_3', mu=30, tau=1)
#@UndefinedVariable
N0_4 = pm.Normal('16-Norm0_3', mu=-30, tau=1)
#@UndefinedVariable
aMu = [N0_1.value, N0_2.value, N0_3.value, N0_4.value]
p_N1 = pm.Lambda('p_Norm1', lambda n=C1: aMu[n], doc='Pr[Norm|Cat]')
# p_N2 = pm.Lambda('p_Norm2', lambda n=C2: aMu[n], doc='Pr[Norm|Cat]');
# p_N3 = pm.Lambda('p_Norm3', lambda n=C3: aMu[n], doc='Pr[Norm|Cat]');
# p_N4 = pm.Lambda('p_Norm4', lambda n=C4: aMu[n], doc='Pr[Norm|Cat]');
# p_N5 = pm.Lambda('p_Norm6', lambda n=C5: aMu[n], doc='Pr[Norm|Cat]');
N = pm.Normal('3-Norm', mu=p_N1, tau=1)
#@UndefinedVariable
# obsN1 = pm.Normal('8-Norm', mu=p_N2, tau=1, observed=True, value=40); #@UndefinedVariable @UnusedVariable
# obsN2 = pm.Normal('9-Norm', mu=p_N3, tau=1, observed=True, value=40); #@UndefinedVariable @UnusedVariable
# obsN3 = pm.Normal('12-Norm', mu=p_N4, tau=1, observed=True, value=-40); #@UndefinedVariable @UnusedVariable
# obsN4 = pm.Normal('13-Norm', mu=p_N5, tau=1, observed=True, value=-40); #@UndefinedVariable @UnusedVariable
return pm.Model([D, C1, N, N0_1, N0_2, N0_3, N0_4, N])
def __setup_predictive(self):
for j in xrange(0, self.num_equiv):
self.predictive.append(
pymc.Lambda('predictive_%s' % j,
lambda p=pymc.Normal('log_pred_%s' % j,
mu=self.mu[j],
tau=1.0/self.sigma[j]**2):
self.inv_logit(p)))
def performInference(graph, responses):
#this is a really hacky solution for now until I can spend more time figuring out how to do this more programatically
pStr = "p%s"
def _build_probabilities(cid):
#return memoized bernoulli variable
if "_bp" in graph[cid]: return graph[cid]["_bp"]
#hack since pymc seems to require ascii (and not unicode)
cida = str(cid).encode('ascii')
if graph[cid]["dependencies"]:
# process dependencies first
deps = map(_build_probabilities, graph[cid]["dependencies"])
cp = calculateProbability(pStr % cida, deps)
_bp = mc.Bernoulli(cida, cp, value=1)
else:
# roots get special treatment
_bp = mc.Bernoulli(cida, .5, value=1)
#memoize bernoulli variable
graph[cid]["_bp"] = _bp
return _bp
concepts = map(_build_probabilities, graph)
#variables = mc.Bernoulli('variables', .5, value=1)
#concepts.append(variables);
#pConditionals = calculateProbability('pConditionals', [variables])
#conditionals = mc.Bernoulli('conditionals', pConditionals, value=1)
#concepts.append(conditionals);
otherQuestions = []
for example in responses:
# more pymc ascii hacks
cida = str(example[0]).encode('ascii')
tmp = graph[example[0]]["_bp"]
prob = mc.Lambda(pStr % cida,
lambda tmp=tmp: pl.where(tmp, 1 - pS, pG))
otherQuestions.append(
mc.Bernoulli(cida, prob, value=example[1], observed=True))
##################some simple tests##########
model = mc.Model(concepts + otherQuestions)
samples = mc.MCMC(model)
knownNodes = []
samples.sample(1000)
for concept in concepts:
if concept.trace().mean() > 0.75:
knownNodes.append(concept.__name__)
return knownNodes
def calculateProbability(name, dependencies, weights=0):
#given that no specific weights are specified
if weights == 0:
weights = [1] * len(dependencies)
assert len(weights) == len(dependencies)
#get the current values of the dependencies
return mc.Lambda(name,
lambda dependencies=dependencies, weights=weights:
(pK - pM) * sum(pl.multiply(dependencies, weights)) / sum(
weights) + pM)
def _lambda_heats_model(self, q_name='q_n_model'):
"""Model the heat using expected_injection_heats, providing all input by using a lambda function
q_name is the name for the model
"""
return pymc.Lambda(
q_name,
lambda P0=self.P0, Ls=self.Ls, DeltaG=self.DeltaG, DeltaH=self.
DeltaH, DeltaH_0=self.DeltaH_0: self.expected_injection_heats(
self.V0, self.DeltaVn, P0, Ls, DeltaG, DeltaH, DeltaH_0, self.
beta, self.N))
def main():
x = pm.Normal("x", 4, 10)
y = pm.Lambda("y", lambda x=x: 10 - x, trace=True)
ex_mcmc = pm.MCMC(pm.Model([x, y]))
ex_mcmc.sample(500)
plt.plot(ex_mcmc.trace("x")[:])
plt.plot(ex_mcmc.trace("y")[:])
plt.title("Displaying (extreme) case of dependence between unknowns")
plt.show()
def construct(self):
first = pymc.Bernoulli('F', .6, value=pl.ones(self.obs))
p_first = pymc.Lambda('p_F',
lambda R=R: pl.where(R, .005, .8),
doc='Pr[S|R]')
second = pymc.Bernoulli('S', p_first, value=pl.ones(self.obs))
p_G = mc.Lambda('p_G',
lambda S=S, R=R: pl.where(S, pl.where(R, .99, .9),
pl.where(R, .8, 0.)),
doc='Pr[G|S,R]')
G = mc.Bernoulli('G', p_G, value=G_obs, observed=True)
def getModel():
D = pm.Dirichlet('1-Dirichlet', theta=[3,2,4]); #@UndefinedVariable
C1 = pm.Categorical('2-Cat', D); #@UndefinedVariable
C2 = pm.Categorical('10-Cat', D); #@UndefinedVariable
C3 = pm.Categorical('11-Cat', D); #@UndefinedVariable
W0_0 = pm.WishartCov('4-Wishart0_1', n=5, C=np.eye(2)); #@UndefinedVariable
N0_1 = pm.MvNormalCov('5-Norm0_1', mu=[-20,-20], C=np.eye(2)); #@UndefinedVariable
N0_2 = pm.MvNormalCov('6-Norm0_2', mu=[0,0], C=np.eye(2)); #@UndefinedVariable
N0_3 = pm.MvNormalCov('7-Norm0_3', mu=[20,20], C=np.eye(2)); #@UndefinedVariable
aMu = [N0_1.value, N0_2.value, N0_3.value];
fL1 = lambda n=C1: np.select([n==0, n==1, n==2], aMu);
fL2 = lambda n=C2: np.select([n==0, n==1, n==2], aMu);
fL3 = lambda n=C3: np.select([n==0, n==1, n==2], aMu);
p_N1 = pm.Lambda('p_Norm1', fL1, doc='Pr[Norm|Cat]');
p_N2 = pm.Lambda('p_Norm2', fL2, doc='Pr[Norm|Cat]');
p_N3 = pm.Lambda('p_Norm3', fL3, doc='Pr[Norm|Cat]');
N = pm.MvNormalCov('3-Norm', mu=p_N1, C=W0_0); #@UndefinedVariable
obsN1 = pm.MvNormalCov('8-Norm', mu=p_N2, C=W0_0, observed=True, value=[-20,-20]); #@UndefinedVariable @UnusedVariable
obsN2 = pm.MvNormalCov('9-Norm', mu=p_N3, C=W0_0, observed=True, value=[20,20]); #@UndefinedVariable @UnusedVariable
return pm.Model([D,C1,C2,C3,N,W0_0,N0_1,N0_2,N0_3,N,obsN1,obsN2]);
def run_Categorical_Normal():
C = pm.Categorical('1-Cat', [0.2, 0.4, 0.1, 0.3]); # @UndefinedVariable
p_N = pm.Lambda('p_Norm', lambda node=C: np.select([node==0, node==1, node==2, node==3],
[-5, 0, 5, 10]), doc='Pr[Norm|Cat]');
N = pm.Normal('2-Norm', mu=p_N, tau=1); # @UndefinedVariable
model = pm.Model([C,N]);
mcmc = pm.MCMC(model);
mcmc.sample(5000, progress_bar=True);
print "C:", C.stats()["mean"], C.value;
print "N:", N.stats()["mean"], N.value;
plot_Samples(mcmc, aBins=[2,500]);
def __init__(self, G=nx.balanced_tree(2, 3, create_using=nx.DiGraph())):
self.G = G
self.n = len(G)
roots = [n for n, d in G.in_degree().items() if d == 0]
# root random variables
self.roots = [pm.Bernoulli(str(v), 0.5, value=0) for v in roots]
self.node_top_sort = nx.topological_sort(G)
node_variables = dict(zip(roots, self.roots))
self.others = []
for node in self.node_top_sort:
if node not in roots:
Pa_v = [
node_variables[key] for key in node_variables.keys()
if key in G.predecessors(node)
]
weight = [
G[key][node]['weight'] for key in G.predecessors(node)
]
bias = G.node[node]['bias']
# energy = w*Pa(v) + bias
energy = pm.Lambda(
'energy_%d' % (node),
lambda Pa_v=Pa_v, weight=weight, bias=bias: pm.
LinearCombination('weighted_sum', x=Pa_v, y=weight) + bias)
# Pr(v=1) = sigmoid(energy)
# use pymc.Lambda deterministic function
sigmoid_cond_prob = pm.Lambda('sigmoid_%d_cond' % (node),
lambda energy=energy: 1 /
(1 + exp(-energy)))
node_variables[node] = pm.Bernoulli(str(node),
sigmoid_cond_prob,
value=0)
self.others.append(node_variables[node])
self.node_variables = node_variables
pm.MCMC.__init__(self, [self.roots, self.others])
def get_z_data(self, p, p_pos, q):
K = 2 # Num topics
M = p # Num documents
N = q # Total num of unique words across all documents
alpha = 1.0 # Concentration parameter for distribution over
# distributions over words (one for each topic)
beta = 1.0 # Concentration parameter for distribution over
# distributions over topics (one for each
# document)
phi = pymc.Container([
pymc.CompletedDirichlet(
name="phi_" + str(k),
D=pymc.Dirichlet(name="phi_temp_" + str(k),
theta=beta * numpy.ones(N)),
) for k in range(K)
])
theta = pymc.Container([
pymc.CompletedDirichlet(
name="theta_" + str(m),
D=pymc.Dirichlet(name="theta_temp_" + str(m),
theta=alpha * numpy.ones(K)),
) for m in range(M)
])
z = pymc.Container([
pymc.Categorical(name="z_" + str(m), p=theta[m], size=N)
for m in range(M)
])
w = pymc.Container([
pymc.Categorical(
name="w_" + str(m) + "_" + str(n),
p=pymc.Lambda(
"phi_z_" + str(m) + str(n),
lambda z_in=z[m][n], phi_in=phi: phi_in[z_in],
),
) for m in range(M) for n in range(N)
])
lda = pymc.Model([w, z, theta, phi])
z_rvs = []
for m in range(M):
metadata = {"doc_idx": m, "num_unique_words": N}
rv = WordCountVecRV(
model=lda, name="w_0_0",
metadata=metadata) # Note: w_0_0 is just a dummy
# argument that must be present in
# the pymc.Model
z_rvs += [rv]
return z_rvs
def run_HDP():
nG, nA, nC = 2, 2, 2
#Gamma, Alpha & Max No. Clusters
aDir = [nG / nC] * nC
Dir0 = pm.Dirichlet('Dirichlet0', theta=aDir)
# @UndefinedVariable
lDir0 = pm.Lambda('p_Dir0',
lambda d=Dir0: np.concatenate([d, [1 - sum(d)]]) * nA)
# @UndefinedVariable
aNodes1 = get_DP('1', lDir0, [0, 1, 20, 21])
aNodes2 = get_DP('2', lDir0, [50, 51, 70, 71, 72])
return np.concatenate([[Dir0], aNodes1, aNodes2])
def getModel():
C = pm.Categorical('1-Cat', [0.2, 0.4, 0.1, 0.3])
#@UndefinedVariable
# C = pm.Categorical('1-Cat', [0.2, 0.4, 0.1, 0.3], observed=True, value=3); #@UndefinedVariable
p_N = pm.Lambda('p_Norm',
lambda n=C: np.select([n == 0, n == 1, n == 2, n == 3],
[-5, 0, 5, 10]),
doc='Pr[Norm|Cat]')
N = pm.Normal('2-Norm', mu=p_N, tau=1)
#@UndefinedVariable
# N = pm.Normal('2-Norm', mu=p_N, tau=1, observed=True, value=2.5); #@UndefinedVariable
return pm.Model([C, N])
def __init__(self, submod, V, eps_p_f, ti=None, tally=True, verbose=0):
self.f_eval = submod.f_eval
self.f = submod.f
pm.StepMethod.__init__(self, [self.f, self.f_eval], tally=tally)
self.children_no_data = copy.copy(self.children)
if isinstance(eps_p_f, pm.Variable):
self.children_no_data.remove(eps_p_f)
self.eps_p_f = eps_p_f
else:
for epf in eps_p_f:
self.children_no_data.remove(epf)
self.eps_p_f = pm.Lambda('eps_p_f',
lambda e=eps_p_f: np.hstack(e),
trace=False)
self.V = pm.Lambda('%s_vect' % V.__name__,
lambda V=V: np.resize(V, len(submod.mesh)))
self.C_eval = submod.C_eval
self.M_eval = submod.M_eval
self.S_eval = submod.S_eval
M_eval_shape = pm.utils.value(self.M_eval).shape
C_eval_shape = pm.utils.value(self.C_eval).shape
self.ti = ti or np.arange(M_eval_shape[0])
# Work arrays
self.scratch1 = np.asmatrix(np.empty(C_eval_shape, order='F'))
self.scratch2 = np.asmatrix(np.empty(C_eval_shape, order='F'))
self.scratch3 = np.empty(M_eval_shape)
# Initialize hidden attributes
self.accepted = 0.
self.rejected = 0.
self._state = ['rejected', 'accepted', 'proposal_distribution']
self._tuning_info = []
self.proposal_distribution = None
self.verbose = verbose
def getModel():
C = pm.Categorical('1-Cat', [0.2, 0.4, 0.1, 0.3])
#@UndefinedVariable
# C = pm.Categorical('1-Cat', [0.2, 0.4, 0.1, 0.3], observed=True, value=3); #@UndefinedVariable
p_N = pm.Lambda(
'p_Norm',
lambda n=C: np.select([n == 0, n == 1, n == 2, n == 3],
[[-5, -5], [0, 0], [5, 5], [10, 10]]),
doc='Pr[Norm|Cat]')
N = pm.MvNormal('2-Norm_2D', mu=p_N, tau=np.eye(2, 2))
#@UndefinedVariable
# N = pm.MvNormal('2-Norm', mu=p_N, tau=np.eye(2,2), observed=True, value=[2.5,2.5]); #@UndefinedVariable
return pm.Model([C, N])
def __init__(self, corpus, K=10, iterations=1000, burn=100):
print("Building model ...")
self.K = K
self.V = corpus.wordCount + 1
self.M = corpus.documentCount
self.alpha = np.ones(self.K)
self.beta = np.ones(self.V)
self.corpus = corpus
self.observations = np.array(corpus.observations)
self.phi = np.empty(self.K, dtype=object)
for i in range(self.K):
self.phi[i] = pm.CompletedDirichlet(
"Phi[%i]" % i, pm.Dirichlet("phi[%i]" % i, theta=self.beta))
self.phi = pm.Container(self.phi)
self.theta = np.empty(self.M, dtype=object)
for i in range(self.M):
self.theta[i] = pm.CompletedDirichlet(
"Theta[%i]" % i, pm.Dirichlet("theta[%i]" % i,
theta=self.alpha))
self.theta = pm.Container(self.theta)
self.z = np.empty(self.observations.shape, dtype=object)
for i in range(self.M):
self.z[i] = pm.Categorical("z[%i]" % i,
size=len(self.observations[i]),
p=self.theta[i],
value=np.random.randint(
self.K,
size=len(self.observations[i])))
self.z = pm.Container(self.z)
self.w = []
for i in range(self.M):
self.w.append([])
for j in range(len(self.observations[i])):
self.w[i].append(
pm.Categorical(
"w[%i][%i]" % (i, j),
p=pm.Lambda(
"phi[z[%i][%i]]" % (i, j),
lambda z=self.z[i][j], phi=self.phi: phi[z]),
value=self.observations[i][j],
observed=True))
self.w = pm.Container(self.w)
self.mcmc = pm.MCMC(pm.Model([self.theta, self.phi, self.z, self.w]))
print("Fitting model ...")
self.mcmc.sample(iter=iterations, burn=burn)
def getModel():
D = pm.Dirichlet('1-Dirichlet', theta=[3, 2, 4])
#@UndefinedVariable
C1 = pm.Categorical('2-Cat', D)
#@UndefinedVariable
C2 = pm.Categorical('10-Cat', D)
#@UndefinedVariable
C3 = pm.Categorical('11-Cat', D)
#@UndefinedVariable
G0_0 = pm.Gamma('4-Gamma0_1', alpha=1, beta=1.5)
#@UndefinedVariable
U1 = pm.Uniform('12-Unif', lower=-100, upper=500)
#@UndefinedVariable
U2 = pm.Uniform('13-Unif', lower=-100, upper=500)
#@UndefinedVariable
U3 = pm.Uniform('14-Unif', lower=-100, upper=500)
#@UndefinedVariable
N0_1 = pm.Normal('5-Norm0_1', mu=U1, tau=1)
#@UndefinedVariable
N0_2 = pm.Normal('6-Norm0_2', mu=U2, tau=1)
#@UndefinedVariable
N0_3 = pm.Normal('7-Norm0_3', mu=U3, tau=1)
#@UndefinedVariable
aMu = [N0_1.value, N0_2.value, N0_3.value]
fL1 = lambda n=C1: np.select([n == 0, n == 1, n == 2], aMu)
fL2 = lambda n=C2: np.select([n == 0, n == 1, n == 2], aMu)
fL3 = lambda n=C3: np.select([n == 0, n == 1, n == 2], aMu)
p_N1 = pm.Lambda('p_Norm1', fL1, doc='Pr[Norm|Cat]')
p_N2 = pm.Lambda('p_Norm2', fL2, doc='Pr[Norm|Cat]')
p_N3 = pm.Lambda('p_Norm3', fL3, doc='Pr[Norm|Cat]')
N = pm.Normal('3-Norm', mu=p_N1, tau=1)
#@UndefinedVariable
obsN1 = pm.Normal('8-Norm', mu=p_N2, tau=1, observed=True, value=0)
#@UndefinedVariable @UnusedVariable
obsN2 = pm.Normal('9-Norm', mu=p_N3, tau=1, observed=True, value=150)
#@UndefinedVariable @UnusedVariable
return pm.Model(
[D, C1, C2, C3, N, G0_0, N0_1, N0_2, N0_3, N, obsN1, obsN2])
def run_HDP():
nC = 3
#Max No. Clusters
Gam = pm.Uniform('Gamma0', lower=0, upper=15)
# @UndefinedVariable
aDir = [Gam / nC] * nC
Dir0 = pm.Dirichlet('Dirichlet0', theta=aDir)
# @UndefinedVariable
lDir0 = pm.Lambda('p_Dir0',
lambda d=Dir0: np.concatenate([d, [1 - sum(d)]]))
# @UndefinedVariable
aNodes1 = get_DP('1', lDir0, [0, 1, 20, 21])
aNodes2 = get_DP('2', lDir0, [50, 51, 70, 71, 72])
return np.concatenate([[Dir0], aNodes1, aNodes2])
def run_Bernoulli():
B = pm.Bernoulli('Bern', 0.4)
# @UndefinedVariable
p_N = pm.Lambda('p_Norm',
lambda B=B: np.where(B, -5, 5),
doc='Pr[Norm|Bern]')
N = pm.Normal('Norm', mu=p_N, tau=1)
# @UndefinedVariable
model = pm.Model([B, N])
mcmc = pm.MCMC(model)
mcmc.sample(1000, progress_bar=True)
print "B:", B.stats()["mean"], B.value
print "N:", N.stats()["mean"], N.value
plot_Samples(mcmc)