def level_model(y_old, y_new):
# PyMC3 level changepoint model
# level is modeled by Poisson RVs
# y_old: older data points since the last changepoint
# y_new: last win(10) datapoints
mean_new = y_new.mean() if len(y_new) > 0 else None
mean_old = y_old.mean() if len(y_old) > 0 else mean_new
y_ = np.concatenate((y_old, y_new))
y_obs = theano.shared(y_)
with pm.Model() as model:
w = pm.Dirichlet('w', a=np.ones(2))
lambda_ = pm.Exponential('lambda', lam=np.array([1.0 / mean_old, 1.0 / mean_new]), shape=(2,))
components = pm.Poisson.dist(mu=lambda_, shape=(2, ))
diff = pm.Deterministic('diff', lambda_[0] - lambda_[1])
obs = pm.Mixture('obs', w=w, comp_dists=components, observed=y_obs)
return model
def fit_logreturns(self, data):
def likelihood(x):
def _normal(x, sigma): # assumes a mu of 0
return pm.Normal.dist(mu=0., sd=sigma).logp(x)
nu_t = pm.math.dot(rhos, x[1:])
err = tt.reshape(x[0] - nu_t, [-1])
logps = (w[0] * pm.math.exp(_normal(err, pm.math.exp(s)))) + (w[1] * pm.math.exp(_normal(x[0], float(1e-100))))
return pm.math.log(logps)
with pm.Model() as self.model:
W = np.array([1., 1.])
w = pm.Dirichlet('w', W)
intercept = pm.Normal('intercept', mu=-5, sd=5., testval=-5.)
theta = pm.Uniform('theta', lower=0.001, upper=1.)
sigma = pm.Uniform('sigma', lower=0.001, upper=10.)
rhos = pm.Uniform('rhos', lower=-1., upper=1., shape=self.num_lags)
sde = lambda x, theta, mu: (theta * (mu-x), sigma)
s = ts.EulerMaruyama('path',
1.0,
sde,
[theta, intercept],
shape=len(data) - self.num_lags,
testval=np.ones_like(data[self.num_lags:]))
lagged_data = self._lags(data)
pm.DensityDist('obs', likelihood, observed=lagged_data)
self.trace = pm.sample(3000, tune=3000, nuts_kwargs=dict(target_accept=0.95))
pm.traceplot(self.trace, varnames=[w, intercept, rhos, theta, sigma])
self.estimated_rhos = np.mean(self.trace['rhos'], axis=0)
self.estimated_w = np.mean(self.trace['w'], axis=0)
self.estimated_intercept = np.mean(self.trace['intercept'], axis=0)
self.estimated_theta = np.mean(self.trace['theta'], axis=0)
self.estimated_sigma = np.mean(self.trace['sigma'], axis=0)
self.data = data
def run_regional_model(data,
progressbar=False,
db_file=None,
burn=2000,
samp=5000):
# Setup masks
r_dum = data.Region.str.get_dummies()
regs = r_dum.columns
r_mtx = r_dum.as_matrix()
num_reg = r_mtx.shape[1]
heads = [{'name': 'Region', 'values': regs.tolist()}]
with pm.Model() as model:
b0_mu = pm.Normal('b0_mu', mu=4, sd=3)
sigma = pm.Uniform('sigma', lower=0.7, upper=70)
thresh = pm.Dirichlet('thresh', a=np.ones(5))
mu_reg = pm.Normal('mu_reg', mu=0, sd=3, shape=num_reg)
reg_mu = b0_mu + mu_reg
reg_range = tt.arange(num_reg)
cat_ps, update = theano.scan(
fn=lambda r_i: compute_ps(thresh, reg_mu[r_i], sigma),
sequences=[reg_range])
reg_ps = pm.Deterministic('reg_ps', cat_ps)
nat_ps = pm.Deterministic('nat_ps', compute_ps(thresh, b0_mu, sigma))
cat_r = theano.dot(r_mtx, cat_ps)
resp = data.response - 1
results = pm.Categorical('results', p=cat_r, observed=resp)
with model:
db = None
if db_file is not None:
db = pm.backends.Text(db_file)
step = pm.Metropolis()
burn = pm.sample(burn, step=step, progressbar=progressbar)
trace = pm.sample(samp,
step=step,
start=burn[-1],
progressbar=progressbar,
trace=db)
return {'heads': heads, 'trace': trace}
def build_model(data, K):
N = data.shape[0]
d = data.shape[1]
print('Building model with n=%d, d=%d, k=%d' % (N, d, K))
with pm.Model() as gmm:
#Prior over component weights
if K > 1:
p = pm.Dirichlet('p', a=np.array([1.] * K))
#Prior over component means
mus = [
pm.MvNormal('mu_%d' % i,
mu=pm.floatX(np.zeros(d)),
tau=pm.floatX(0.1 * np.eye(d)),
shape=(d, ))
#testval = pm.floatX(np.ones(d)))
for i in range(K)
]
#Cholesky decomposed LKJ prior over component covariance matrices
packed_L = [
pm.LKJCholeskyCov('packed_L_%d' % i,
n=d,
eta=2.,
sd_dist=pm.HalfCauchy.dist(1))
#testval = pm.floatX(np.ones(int(d*(d-1)/2+d))))
for i in range(K)
]
#Unpack packed_L into full array
L = [pm.expand_packed_triangular(d, packed_L[i]) for i in range(K)]
#Convert L to sigma and tau for convenience
sigma = [
pm.Deterministic('sigma_%d' % i, L[i].dot(L[i].T))
for i in range(K)
]
tau = [
pm.Deterministic('tau_%d' % i, matrix_inverse(sigma[i]))
for i in range(K)
]
#Specify the likelihood
if K > 1:
mvnl = [pm.MvNormal.dist(mu=mus[i], chol=L[i]) for i in range(K)]
Y_obs = pm.Mixture('Y_obs', w=p, comp_dists=mvnl, observed=data)
else:
Y_obs = pm.MvNormal('Y_obs', mu=mus[0], chol=L[0], observed=data)
return gmm
def test_categorical():
k = 3
ndata = 5000
v = np.random.randint(0, k, ndata)
with pymc3.Model() as model:
p = pymc3.Dirichlet(name='p', a=np.array([1., 1., 1.]), shape=k)
category = pymc3.Categorical(name='category',
p=p,
shape=ndata,
observed=v)
step = pymc3.Metropolis(vars=[p, category])
trace = pymc3.sample(3000, step=step)
pymc3.traceplot(trace)
plt.show()
def dice_toss():
n = 100
h = np.array([6,6,6,6,6,6])
h=h/sum(h)
a=np.ones((6))
niter = 1000
with pm.Model() as model: # context management
# define priors
p = pm.Dirichlet('p',a=a)
# define likelihood
y= pm.Categorical('y',p=p,observed=h)
# inference
trace = pm.sample(niter, progressbar=True)
pm.plots.traceplot(trace)
plt.show()
def run_non_sparse_initialization(self):
rat = self.allelic_counts/self.total_counts
nans = np.isnan(rat)
# Run bb-mf
with pm.Model() as bb_glm:
CONC = pm.HalfCauchy('CONC', beta=5, shape=(1,self.S), testval=self.conc_init)
ALPHA = pm.HalfCauchy('ALPHA', beta=5, shape=(1, self.S))
BETA = pm.Normal('BETA', mu=0, tau=(1.0/10.0), shape=(self.S, self.num_cov), testval=self.beta_init)
U = pm.Normal('U', mu=0, tau=(1.0/1.0), shape=(self.N, self.K), testval=self.U_init)
V = pm.Normal('V', mu=0, tau=(1.0/1.0), shape=(self.S, self.K), testval=self.V_init)
MU_A = pm.Normal("MU_A", mu=0., sd=100**2, shape=(1,self.S), testval=self.mu_a_init)
SIGMA_A = pm.HalfCauchy("SIGMA_A", beta=5.0, shape=(1,self.S), testval=self.sigma_a_init)
mu_a_mat = pm.math.dot(np.ones((self.I,1)), MU_A)
sigma_a_mat = pm.math.dot(np.ones((self.I,1)), SIGMA_A)
A = pm.Normal('A', mu=mu_a_mat, sigma=sigma_a_mat, shape=(self.I,self.S), testval=self.A_init)
p = pm.math.invlogit(pm.math.dot(self.cov, BETA.T) + pm.math.dot(U,V.T) + A[self.Z,:])
conc_mat = pm.math.dot(np.ones((self.N,1)), CONC)
w = pm.Dirichlet('w', a=np.ones((self.S,2)))
beta_null_mat = pm.math.dot(np.ones((self.N,1)), ALPHA)
BB_GLM = pm.BetaBinomial.dist(alpha=(p*conc_mat), beta=((1.0-p)*conc_mat), n=self.total_counts)
BB_NULL = pm.BetaBinomial.dist(alpha=(np.ones((self.N,self.S))), beta=7.0+beta_null_mat, n=self.total_counts)
mixmod = pm.Mixture('mixmodel', w=w, comp_dists=[BB_GLM, BB_NULL], observed=self.allelic_counts, shape=2)
approx = pm.fit(method='advi', n=2000)
#pickle.dump(approx, open(self.output_root + '_model', 'wb'))
#approx = pickle.load( open(self.output_root + '_model', "rb" ) )
means_dict = approx.bij.rmap(approx.params[0].eval())
y = means_dict['w_stickbreaking__'].T
y = np.concatenate([y, -np.sum(y, 0, keepdims=True)])
e_y = np.exp(y - np.max(y, 0, keepdims=True))
w_learned = e_y / np.sum(e_y, 0, keepdims=True)
self.conc_init = np.exp(means_dict['CONC_log__'])
self.alpha_init = np.exp(means_dict['ALPHA_log__'])
self.beta_init = means_dict['BETA']
self.U_init = means_dict['U']
self.V_init = means_dict['V']
self.mu_a_init = means_dict['MU_A']
self.sigma_a_init = np.exp(means_dict['SIGMA_A_log__'])
self.A_init = means_dict['A']
self.w_init = w_learned.T
def laser_late_trials(data, num_emissions):
# Make the pymc3 model
with pm.Model() as model:
# Dirichlet prior on the emission/spiking probabilities - 4 states
p = pm.Dirichlet('p', np.ones(num_emissions), shape=(4, num_emissions))
# Discrete Uniform switch times
# Switch from detection to identity firing
t1 = pm.DiscreteUniform('t1', lower=20, upper=60)
# Switch from identity to palatability firing
t2 = pm.DiscreteUniform('t2', lower=t1 + 20, upper=120)
# Switch from palatability firing to end
t3 = pm.DiscreteUniform('t3', lower=t2 + 30, upper=150)
# Add potentials to keep the switch times from coming too close to each other
#t_pot1 = pm.Potential('t_pot1', tt.switch(t2 - t1 >= 20, 0, -np.inf))
#t_pot2 = pm.Potential('t_pot2', tt.switch(t3 - t2 >= 20, 0, -np.inf))
#t_pot3 = pm.Potential('t_pot3', tt.switch(t3 - t1 >= 40, 0, -np.inf))
# Get the actual state numbers based on the switch times
states1 = tt.switch(t1 >= np.arange(150), 0, 1)
states2 = tt.switch(t2 >= np.arange(150), states1, 2)
states = tt.switch(t3 >= np.arange(150), states2, 3)
# Categorical observations
obs = pm.Categorical('obs',
p=p[states],
observed=np.append(data[:140], data[190:]))
# Inference button :D
with model:
tr = pm.sample(300000,
init=None,
step=pm.Metropolis(),
njobs=2,
start={
't1': 25,
't2': 75,
't3': 125
},
progressbar=False)
# Return the inference!
return model, tr[250000:]
def run_national_model(data):
with pm.Model() as model:
mu = pm.Normal('mu', mu=4, sd=3)
sigma = pm.Uniform('sigma', lower=0.7, upper=70)
thresh = pm.Dirichlet('thresh', a=np.ones(5))
cat_p = compute_ps(thresh, mu, sigma)
resp = data.response - 1
results = pm.Categorical('results', p=cat_p, observed=resp)
with model:
step = pm.Metropolis()
burn = pm.sample(2000, step=step)
trace = pm.sample(5000, step=step, start=burn[-1])
return trace
def test_multivariate2(self):
# Added test for issue #3271
mn_data = np.random.multinomial(n=100, pvals=[1 / 6.0] * 6, size=10)
with pm.Model() as dm_model:
probs = pm.Dirichlet("probs", a=np.ones(6))
obs = pm.Multinomial("obs", n=100, p=probs, observed=mn_data)
burned_trace = pm.sample(20,
tune=10,
cores=1,
return_inferencedata=False,
compute_convergence_checks=False)
sim_priors = pm.sample_prior_predictive(samples=20, model=dm_model)
sim_ppc = pm.sample_posterior_predictive(burned_trace,
samples=20,
model=dm_model)
assert sim_priors["probs"].shape == (20, 6)
assert sim_priors["obs"].shape == (20, ) + mn_data.shape
assert sim_ppc["obs"].shape == (20, ) + mn_data.shape
def getAngelRate(data, n_sample=10000, n_chain=3, ax=None):
# データの整理
data_0 = data.query('campaign != 1')
data_1 = data.query('campaign == 1')
d = np.array([[
sum(data_0['angel'] == 0),
sum(data_0['angel'] == 1),
sum(data_0['angel'] == 2)
],
[
sum(data_1['angel'] == 0),
sum(data_1['angel'] == 1),
sum(data_1['angel'] == 2)
]])
weight = np.array([[1.0, 1.0, 1.0], [1.0, 0.0, 2.0]])
# パラメータ推定
with pm.Model() as model:
alpha = [1., 1., 1.] # hyper-parameter of DirichletDist.
pi = pm.Dirichlet('pi', a=np.array(alpha))
for i in np.arange(d.shape[0]):
piw = pi * weight[i]
m = pm.Multinomial('m_%s' % (i),
n=np.sum(d[i]),
p=piw,
observed=d[i])
trace = pm.sample(n_sample, chains=n_chain)
np.savetxt('trace_pi.csv', trace['pi'], delimiter=',')
# Silver
hpd_l, hpd_u = pm.hpd(trace['pi'][:, 1])
print('Silver : 95% HPD : {}-{}'.format(hpd_l, hpd_u))
print('Silver ExpectedValue : {}'.format(trace['pi'][:, 1].mean()))
# Gold
hpd_l, hpd_u = pm.hpd(trace['pi'][:, 2])
print('Gold : 95% HPD : {}-{}'.format(hpd_l, hpd_u))
print('Gold ExpectedValue : {}'.format(trace['pi'][:, 2].mean()))
# save fig
if ax is not None:
pm.plot_posterior(trace['pi'][:, 0], ax=ax[0])
pm.plot_posterior(trace['pi'][:, 1], ax=ax[1])
pm.plot_posterior(trace['pi'][:, 2], ax=ax[2])
ax[0].set_title('Nothing')
ax[1].set_title('SilverAngel')
ax[2].set_title('GoldAngel')
return trace
def fun_infer_model_learn(df,
tune=100,
samples=10,
K=2,
path="./",
name="",
run=1):
print("Write: " + path + name + "learner_" + str(K) + ".txt")
print("Write: " + path + name + "question_" + str(K) + ".txt")
print("Write: " + path + name + "concentration_" + str(K) + ".txt")
ch = 1
N = df.shape[0]
Q = df.shape[1]
# for K in Krange:
with pm.Model() as model:
learner = pm.Uniform('learner', shape=(N, K))
concentration = pm.Uniform('concentration', testval=.5)
question = pm.Dirichlet('question',
a=np.repeat(concentration, K),
shape=(Q, K))
# difficulty=pm.Uniform ('difficulty',0.1,4,shape=(Q,1),testval=np.repeat(.5,Q).reshape(Q,1))
x = pm.math.dot(learner, question.T)
results = pm.Bernoulli('rezults', p=x, shape=(N, Q), observed=df)
if run:
with model:
trace = pm.sample(samples,
chains=ch,
tune=tune,
discard_tuned_samples=True)
# a=pm.math.dot(trace['learner'].mean(0), trace['question'][:,:].mean(0).T)
pd.DataFrame(trace['learner'].mean(0)).to_csv(
path + name + "learner_" + str(K) + ".txt", sep="\t")
pd.DataFrame(trace['question'].mean(0)).to_csv(
path + name + "question_" + str(K) + ".txt", sep="\t")
# pd.DataFrame(a.eval()).to_csv(path+name+"estim_"+str(K)+".txt",sep="\t")
pd.DataFrame(trace['concentration']).to_csv(
path + name + "concentration_" + str(K) + ".txt", sep="\t")
print("finished: " + str(K))
return [model, trace]
return [model, None]
def predict_proba(self, X, return_std=False):
"""
Predicts probabilities of new data with a trained GaussianMixture Model
Parameters
----------
X : numpy array, shape [n_samples, n_features]
cats : numpy array, shape [n_samples, ]
return_std : Boolean flag of whether to return standard deviations with
mean probabilities. Defaults to False.
"""
if self.trace is None:
raise NotFittedError('Run fit on the model before predict.')
# num_samples = X.shape[0]
if self.cached_model is None:
self.cached_model = self.create_model()
self._set_shared_vars({'model_input': X})
K = self.num_components
with self.cached_model:
pi = pm.Dirichlet("probability",
a=np.array([1.0, 1.0, 1.0]),
shape=K)
_vars = [pi]
ppc = pm.sample_ppc(
self.trace,
# model=self.cached_model,
vars=_vars,
samples=2000,
size=len(X))
if return_std:
return ppc['probability'].mean(axis=0), \
ppc['probability'].std(axis=0)
else:
return ppc['probability'].mean(axis=0)
def get_beta_bernoulli_mixture(X, params):
n_doc, n_feat = X.shape
n_comp = params['n_comp']
with pm.Model() as model:
pkw = pm.Beta('pkw',
alpha=params['pkw_beta_dist_alpha'],
beta=params['pkw_beta_dist_beta'],
shape=(n_comp, n_feat))
p_comp = pm.Dirichlet('p_comp',
a=params['pcomp_dirichlet_dist_alpha'] * np.ones(n_comp))
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 run_mcmc(self, n_generations, n_burn):
logger.info("{} subpaths in total".format(
len(self.traversome.all_sub_paths)))
isomer_num = self.traversome.num_of_isomers
with pm.Model() as isomer_model:
isomer_percents = pm.Dirichlet(name="props",
a=np.ones(isomer_num),
shape=(isomer_num, ))
loglike_expression = self.traversome.get_multinomial_like_formula(
isomer_percents=isomer_percents,
log_func=tt.log).loglike_expression
pm.Potential("likelihood", loglike_expression)
# pm.Deterministic("likelihood", likes)
# pm.DensityDist?
# pm.Mixture(name="likelihood", w=np.ones(len(components)), comp_dists=components, observed=data)
# pm.Binomial("path_last", n=n__num_reads_in_range, p=this_prob, observed=x__num_matched_reads)
# sample from the distribution
# uses the BFGS optimization algorithm to find the maximum of the log-posterior
logger.info("Searching the maximum of the log-posterior ..")
start = pm.find_MAP(model=isomer_model)
# trace = pm.sample_smc(n_generations, parallel=False)
# In an upcoming release,
# pm.sample will return an `arviz.InferenceData` object instead of a `MultiTrace` by default
logger.info("Using NUTS sampler ..")
self.trace = pm.sample(n_generations,
tune=n_burn,
discard_tuned_samples=True,
cores=1,
init='adapt_diag',
start=start,
return_inferencedata=True)
logger.info("Summarizing the MCMC traces ..")
summary = az.summary(self.trace)
logger.info("\n{}".format(summary))
axes = az.plot_trace(self.trace)
fig = axes.ravel()[0].figure
fig.savefig(
os.path.join(self.traversome.outdir, "mcmc.trace_plot.pdf"))
return OrderedDict([(_go, _prop)
for _go, _prop in enumerate(summary["mean"])])
def test_multivariate2(self):
# Added test for issue #3271
mn_data = np.random.multinomial(n=100, pvals=[1 / 6.0] * 6, size=10)
with pm.Model() as dm_model:
probs = pm.Dirichlet("probs", a=np.ones(6), shape=6)
obs = pm.Multinomial("obs", n=100, p=probs, observed=mn_data)
burned_trace = pm.sample(20, tune=10, cores=1)
sim_priors = pm.sample_prior_predictive(samples=20, model=dm_model)
sim_ppc = pm.sample_posterior_predictive(burned_trace,
samples=20,
model=dm_model)
assert sim_priors["probs"].shape == (20, 6)
assert sim_priors["obs"].shape == (20, ) + obs.distribution.shape
assert sim_ppc["obs"].shape == (20, ) + obs.distribution.shape
sim_ppc = pm.fast_sample_posterior_predictive(burned_trace,
samples=20,
model=dm_model)
assert sim_ppc["obs"].shape == (20, ) + obs.distribution.shape
def csp_modeling(
obs,
templates,
dbname,
redo=False,
):
""" Model a CSP with bayesian model. """
if os.path.exists(dbname) and not redo:
return dbname
with pm.Model() as model:
w = pm.Dirichlet("w", np.ones(len(templates)))
bestfit = pm.math.dot(w.T, templates)
sigma = pm.Exponential("sigma", lam=1)
likelihood = pm.Normal('like', mu=bestfit, sd=sigma, observed=obs)
with model:
trace = pm.sample(1000, tune=1000)
results = {'model': model, "trace": trace}
with open(dbname, 'wb') as buff:
pickle.dump(results, buff)
return
def test_DiscreteMarkovChain_point():
test_Gammas = at.as_tensor_variable(np.array([[[1.0, 0.0], [0.0, 1.0]]]))
with pm.Model():
# XXX: `draw_values` won't use the `Deterministic`s values in the `point` map!
# Also, `Constant` is only for integer types (?!), so we can't use that.
test_gamma_0 = pm.Dirichlet("gamma_0", np.r_[1.0, 1000.0], shape=2)
test_point = {"gamma_0": np.r_[1.0, 0.0]}
assert np.all(
DiscreteMarkovChain.dist(test_Gammas, test_gamma_0, shape=10).random(
point=test_point
)
== 0
)
assert np.all(
DiscreteMarkovChain.dist(test_Gammas, 1.0 - test_gamma_0, shape=10).random(
point=test_point
)
== 1
)
def run_factorization(self):
rat = self.allelic_counts/self.total_counts
nans = np.isnan(rat)
# Run bb-mf
with pm.Model() as bb_glm:
CONC = pm.HalfCauchy('CONC', beta=5, shape=(1,self.S), testval=self.conc_init)
ALPHA = pm.HalfCauchy('ALPHA', beta=5, shape=(1, self.S), testval=self.alpha_init)
BETA = pm.Normal('BETA', mu=0, tau=(1.0/10.0), shape=(self.S, self.num_cov), testval=self.beta_init)
gamma = pm.HalfCauchy('GAMMA', beta=5, shape=(self.N, self.K), testval=np.ones((self.N, self.K)))
U = pm.Normal('U', mu=0, sigma=1.0/gamma, shape=(self.N, self.K), testval=self.U_init)
V = pm.Normal('V', mu=0, tau=(1.0/1.0), shape=(self.S, self.K), testval=self.V_init)
MU_A = pm.Normal("MU_A", mu=0., sd=100**2, shape=(1,self.S), testval=self.mu_a_init)
SIGMA_A = pm.HalfCauchy("SIGMA_A", beta=5.0, shape=(1,self.S), testval=self.sigma_a_init)
mu_a_mat = pm.math.dot(np.ones((self.I,1)), MU_A)
sigma_a_mat = pm.math.dot(np.ones((self.I,1)), SIGMA_A)
A = pm.Normal('A', mu=mu_a_mat, sigma=sigma_a_mat, shape=(self.I,self.S), testval=self.A_init)
p = pm.math.invlogit(pm.math.dot(self.cov, BETA.T) + pm.math.dot(U,V.T) + A[self.Z,:])
conc_mat = pm.math.dot(np.ones((self.N,1)), CONC)
w = pm.Dirichlet('w', a=np.ones((self.S,2)), testval=self.w_init)
beta_null_mat = pm.math.dot(np.ones((self.N,1)), ALPHA)
BB_GLM = pm.BetaBinomial.dist(alpha=(p*conc_mat), beta=((1.0-p)*conc_mat), n=self.total_counts)
BB_NULL = pm.BetaBinomial.dist(alpha=(np.ones((self.N,self.S))), beta=7.0+beta_null_mat, n=self.total_counts)
mixmod = pm.Mixture('mixmodel', w=w, comp_dists=[BB_GLM, BB_NULL], observed=self.allelic_counts, shape=2)
approx = pm.fit(method='advi', n=30000)
#pickle.dump(approx, open(self.output_root + '_model', 'wb'))
#approx = pickle.load( open(self.output_root + '_model', "rb" ) )
means_dict = approx.bij.rmap(approx.params[0].eval())
np.savetxt(self.output_root + '_temper_U.txt', (means_dict['U']), fmt="%s", delimiter='\t')
np.savetxt(self.output_root + '_temper_V.txt', (means_dict['V'].T), fmt="%s", delimiter='\t')
np.savetxt(self.output_root + '_temper_BETA.txt', (means_dict['BETA'].T), fmt="%s", delimiter='\t')
np.savetxt(self.output_root + '_temper_ALPHA.txt', (np.exp(means_dict['ALPHA_log__'])), fmt="%s", delimiter='\t')
np.savetxt(self.output_root + '_temper_GAMMA.txt', (np.exp(means_dict['GAMMA_log__'])), fmt="%s", delimiter='\t')
np.savetxt(self.output_root + '_temper_CONC.txt', (np.exp(means_dict['CONC_log__'])), fmt="%s", delimiter='\t')
np.savetxt(self.output_root + '_temper_w_stick_breaking.txt', (np.exp(means_dict['w_stickbreaking__'])), fmt="%s", delimiter='\t')
np.savetxt(self.output_root + '_temper_ELBO.txt', (approx.hist), fmt="%s", delimiter='\t')
def SIR_training(self, sequence, totalpopulation):
self.popu = totalpopulation
self.data = sequence[:]
acc_infect = sequence[:, 0] / totalpopulation
basic_model = pm.Model()
n = len(acc_infect)
I = acc_infect[0]
R = 0
S = 1 - I
with basic_model:
BoundedNormal = pm.Bound(pm.Normal, lower=0.0, upper=1.0)
BoundedNormal2 = pm.Bound(pm.Normal, lower=1.0, upper=10.0)
theta = []
r0 = BoundedNormal2('R_0', mu=self.r0, sigma=0.72)
gamma = BoundedNormal('gamma', mu=self.gamma, sigma=0.02)
beta = pm.Deterministic('beta', r0 * gamma)
ka = pm.Gamma('ka', 2, 0.0001)
Lambda1 = pm.Gamma('Lambda1', 2, 0.0001)
qu = pm.Uniform('qu', lower=0.1, upper=1.0)
theta.append(
pm.Deterministic('theta_' + str(0), pm.math.stack([S, I, R])))
for i in range(1, n):
states = theta[i - 1]
solve_theta = pm.Deterministic(
'solve_theta_' + str(i),
ka * pm.math.stack([
states[0] - qu * beta * states[0] * states[1],
states[1] + qu * beta * states[0] * states[1] -
gamma * states[1], states[2] + gamma * states[1]
]))
theta.append(
pm.Dirichlet('theta_' + str(i), a=solve_theta, shape=(3)))
real_infect = pm.Beta('real_infect_' + str(i),
Lambda1 * theta[i][1],
Lambda1 * (1 - theta[i][1]),
observed=acc_infect[i])
step = pm.Metropolis()
Trace = pm.sample(2000, cores=16, chains=1, init='auto', step=step)
self.trace = Trace
def __init__(self,
wave,
flux,
templates,
adegree=None,
mdegree=None,
reddening=False):
""" Model CSP with bayesian model. """
self.wave = wave
self.flux = flux
self.templates = templates
self.ntemplates = len(templates)
self.adegree = adegree
# Construct additive polynomial
if self.adegree is not None:
_ = np.linspace(-1, 1, len(self.wave))
self.apoly = np.zeros((adegree + 1, len(_)))
for i in range(adegree + 1):
self.apoly[i] = legendre(i)(_)
else:
self.apoly = np.zeros(1)
# Build statistical model
with pm.Model() as self.model:
self.flux0 = pm.Normal("f0", mu=1, sd=5) # Multiplicative constant
self.w = pm.Dirichlet("w",
np.ones(self.ntemplates) / self.ntemplates)
self.wpoly = pm.Deterministic("wpoly",
pm.math.zeros_like(self.flux0)) \
if self.adegree is None else \
pm.Normal("wpoly", mu=0, sd=1, shape=self.adegree)
self.bestfit = pm.Deterministic(
"bestfit",
self.__call__(self.w,
wpoly=self.wpoly,
f0=self.flux0,
math=pm.math))
self.sigma = pm.Exponential("sigma", lam=0.01)
self.like = pm.Normal('like',
mu=self.bestfit,
sd=self.sigma,
observed=flux)
def get_logisticnormal_bernoulli_mixture(X, params):
n_doc, n_feat = X.shape
n_comp = params['n_comp']
with pm.Model() as model:
theta = pm.MvNormal('theta',
mu=np.zeros(n_feat),
cov=np.identity(n_feat),
shape=(n_comp, n_feat))
pkw = pm.Deterministic('pkw',
1 / (1 + tt.exp(-theta)))
p_comp = pm.Dirichlet('p_comp',
a=params['pcomp_dirichlet_dist_alpha'] * np.ones(n_comp))
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 _sample_pymc3(cls, dist, size):
"""Sample from PyMC3."""
import pymc3
pymc3_rv_map = {
'MultivariateNormalDistribution': lambda dist:
pymc3.MvNormal('X', mu=matrix2numpy(dist.mu, float).flatten(),
cov=matrix2numpy(dist.sigma, float), shape=(1, dist.mu.shape[0])),
'MultivariateBetaDistribution': lambda dist:
pymc3.Dirichlet('X', a=list2numpy(dist.alpha, float).flatten()),
'MultinomialDistribution': lambda dist:
pymc3.Multinomial('X', n=int(dist.n),
p=list2numpy(dist.p, float).flatten(), shape=(1, len(dist.p)))
}
dist_list = pymc3_rv_map.keys()
if dist.__class__.__name__ not in dist_list:
return None
with pymc3.Model():
pymc3_rv_map[dist.__class__.__name__](dist)
return pymc3.sample(size, chains=1, progressbar=False)[:]['X']
def create_dirac_zero_hmm(X, mu, xis, observed):
S = 2
z_tt = tt.stack([tt.dot(X, xis[..., s, :]) for s in range(S)], axis=1)
Gammas_tt = pm.Deterministic("Gamma", multilogit_inv(z_tt))
gamma_0_rv = pm.Dirichlet("gamma_0", np.ones((S, )))
if type(observed) == np.ndarray:
T = X.shape[0]
else:
T = X.get_value().shape[0]
V_rv = DiscreteMarkovChain("V_t", Gammas_tt, gamma_0_rv, shape=T)
if type(observed) == np.ndarray:
V_rv.tag.test_value = (observed > 0) * 1
else:
V_rv.tag.test_value = (observed.get_value() > 0) * 1
Y_rv = SwitchingProcess(
"Y_t",
[pm.Constant.dist(0), pm.Constant.dist(mu)],
V_rv,
observed=observed,
)
return Y_rv
def __init__(self, npersons, nitems, nlevels):
super(FourPGRM, self).__init__(npersons, nitems, nlevels)
with self.model:
phi = pm.Dirichlet(name='phi',
a=np.ones(2 * nlevels - 1),
shape=(1, nitems, 2 * nlevels - 1))
# 1. drop the last term, which would make the top term 1 after
# cumsum.
# 2. reshape into a 2 x L matrix for each item, each row
# corresponding to gamma and sigma, respectively
# 3. cumulatively sum across the gamma->sigma, to ensure
# sigma > gamma
# 4. cumulative gammas and sigmas across levels to ensure monotone
phi_star = phi[..., :-1]
phi_star = phi_star.reshape((1, nitems, 2, nlevels - 1))
phi_star = phi_star.cumsum(axis=-2)
phi_star = phi_star.cumsum(axis=-1)
# first row is gamma, second is sigma
gamma = pm.Deterministic(name='gamma', var=phi_star[..., 0, :])
sigma = pm.Deterministic(name='sigma', var=phi_star[..., 1, :])
param_list = [gamma, sigma]
self.params.update({var.name: var for var in param_list})
def _model_eval(self, X, K, n_samples):
# setup model
with pm.Model() as model:
data_dim = X.shape[1]
# prior of mixture ratio
w = pm.Dirichlet('w', a=np.ones(K))
# setup the likelihood
init_mu = np.zeros(data_dim)
components = [
self._multivariate_normal_dist(init_mu, suffix=k)
for k in range(K)
]
like = pm.Mixture('like', w=w, comp_dists=components, observed=X)
# fit model
with model:
trace = pm.sample(2000,
step=pm.NUTS(),
start=pm.find_MAP(),
tune=1000)
# store the result
self.result['K=' + str(K)] = trace
def run_model(self, **kwargs):
"""Run Bayesian model using prefit Y's for each Gene and Dataset distribution"""
# Importing here since Theano base_compiledir needs to be set prior to import
import pymc3 as pm
# Collect fits
self.fits = self.t_fits()
click.echo("Building model")
with pm.Model() as self.model:
# Convex model priors
b = ([1] if len(self.backgrounds) == 1 else pm.Dirichlet(
"b", a=np.ones(len(self.backgrounds))))
# Model error
eps = pm.InverseGamma("eps", 1, 1)
# Convex model declaration
for gene in tqdm(self.training_genes):
y, norm_term = 0, 0
for i, dataset in enumerate(self.backgrounds):
name = f"{gene}={dataset}"
fit = self.fits.loc[name]
x = pm.StudentT(name, nu=fit.nu, mu=fit.mu, lam=fit.lam)
y += (b[i] / fit.sd) * x
norm_term += b[i] / fit.sd
# y_g = \frac{\sum_d \frac{\beta * x}{\sigma} + \epsilon}{\sum_d\frac{\beta}{\sigma}}
# Embed mu in laplacian distribution
pm.Laplace(
gene,
mu=y / norm_term,
b=eps / norm_term,
observed=self.sample[gene],
)
# Sample
self.trace = pm.sample(**kwargs)
def trend_model(y_old, y_new):
# PyMC3 trend changepoint model
# trend is modeled by Normal RVs
# y_old: older data points since the last changepoint
# y_new: last win(10) datapoints
g_new = np.gradient(y_new) # observed trend
g_old = np.gradient(y_old) if len(y_old) > 1 else g_new
mu_new = g_new.mean() if len(g_new) > 0 else None
mu_old = g_old.mean() if len(g_old) > 0 else mu_new
sigma_new = max(1.0, g_new.std()) if len(g_new) > 0 else None
sigma_old = max(1.0, g_old.std()) if len(g_old) > 0 else sigma_new
y_ = np.concatenate((y_old, y_new))
y_obs = theano.shared(y_)
ts = np.array(range(1, 1 + len(y_))) # start from 1 to deal with intercept
t_arr = np.array([ts, ts]).T
with pm.Model() as model:
w = pm.Dirichlet('w', a=np.ones(2))
mu = pm.Normal('mu', np.array([mu_old, mu_new]), np.array([sigma_old, sigma_new]), shape=(2,))
mu_t = pm.Deterministic('mu_t', t_arr * mu)
tau = pm.Gamma('tau', 1.0, 1.0, shape=2)
diff = pm.Deterministic('diff', mu[1] - mu[0]) # needed for PyMC3 model
obs = pm.NormalMixture('obs', w, mu_t, tau=tau, observed=y_obs) # needed for PyMC3 model
return model
(D, W) = data.shape
def log_lda(theta, phi):
def ll_lda(value):
dixs, vixs = value.nonzero()
vfreqs = value[dixs, vixs]
ll = vfreqs * pm.math.logsumexp(
t.log(theta[dixs]) + t.log(phi.T[vixs]), axis=1).ravel()
return t.sum(ll)
return ll_lda
with model1:
theta = pm.Dirichlet("theta", a=alpha, shape=(D, K))
phi = pm.Dirichlet("phi", a=beta, shape=(K, V))
doc = pm.DensityDist('doc', log_lda(theta, phi), observed=data)
with model1:
inference = pm.ADVI()
approx = pm.fit(
n=10000,
method=inference,
callbacks=[pm.callbacks.CheckParametersConvergence(diff='absolute')])
#inference
tr1 = approx.sample(draws=1000)
pm.plots.traceplot(tr1)
pm.plot_posterior(tr1, color='LightSeaGreen')
plt.plot(approx.hist)
data = data[0:1000]
truth = truth[0:1000]
data[np.where(data>=1)]=1
np.random.seed(12345)
alphaprime=10
nclusters = 10
ncells = data.shape[0]
nsites = data.shape[1]
#without scaling
model = pm.Model()
with model:
pi = pm.Dirichlet('pi', a=np.array([alphaprime]*nclusters),shape=nclusters)
# Define priors
pk = pm.Beta('pk', 1,1,shape=(nclusters,nsites))
z = pm.Categorical("z",p=pi,shape=ncells)
# Define likelihood
likelihood = pm.Bernoulli('likelihood',p=pk[z],observed=data,shape=(ncells))
with model:
step1 = pm.Metropolis(vars=[pk, pi, alpha])
step2 = pm.ElemwiseCategorical(vars=[category], values=[0, 1, 2])
tr = pm.sample(100, step=[step1, step2])
traceplot(trace)