outputs=[s, P, ll],
mode=theano.Mode(optimizer="unsafe"))
s, P, ll = kf(Y, 2 * np.ones(m))
import pymc3 as pm
with pm.Model() as model:
# Phi, Q, L, c, H, Sv, d, s0, P0, n, m, g
phi = pm.Normal("phi", shape=(1, 1))
q = pm.HalfStudentT("q", nu=1.0, sd=2.0, shape=(1, 1))
K = KalmanFilter("kf",
phi,
q,
np.array([[1.]]),
np.array([0.]),
np.array([[1.]]),
np.array([[0.0]]),
np.array([0.]),
np.array([0.]),
np.array([[10.]]),
1,
1,
1,
observed=y)
with model:
# approx = pm.fit(n=100, method="advi")
trace = pm.sample_approx(approx, draws=500)
def train_pymc3(docs_te, docs_tr, n_samples_te, n_samples_tr, n_words,
n_topics, n_tokens):
"""
Return:
Pymc3 LDA results
Parameters:
docs_tr: training documents (processed)
docs_te: testing documents (processed)
n_samples_te: number of testing docs
n_samples_tr: number of training docs
n_words: size of vocabulary
n_topics: number of topics to learn
n_tokens: number of non-zero datapoints in processed training tf matrix
"""
# Log-likelihood of documents for LDA
def logp_lda_doc(beta, theta):
"""
Returns the log-likelihood function for given documents.
K : number of topics in the model
V : number of words (size of vocabulary)
D : number of documents (in a mini-batch)
Parameters
----------
beta : tensor (K x V)
Word distribution.
theta : tensor (D x K)
Topic distributions for the documents.
"""
def ll_docs_f(docs):
dixs, vixs = docs.nonzero()
vfreqs = docs[dixs, vixs]
ll_docs = vfreqs * pmmath.logsumexp(
tt.log(theta[dixs]) + tt.log(beta.T[vixs]),
axis=1).ravel()
# Per-word log-likelihood times no. of tokens in the whole dataset
return tt.sum(ll_docs) / (tt.sum(vfreqs) + 1e-9) * n_tokens
return ll_docs_f
# fit the pymc3 LDA
# we have sparse dataset. It's better to have dence batch so that all words accure there
minibatch_size = 128
# defining minibatch
doc_t_minibatch = pm.Minibatch(docs_tr.toarray(), minibatch_size)
doc_t = shared(docs_tr.toarray()[:minibatch_size])
with pm.Model() as model:
theta = Dirichlet(
'theta',
a=pm.floatX((1.0 / n_topics) * np.ones(
(minibatch_size, n_topics))),
shape=(minibatch_size, n_topics),
transform=t_stick_breaking(1e-9),
# do not forget scaling
total_size=n_samples_tr)
beta = Dirichlet('beta',
a=pm.floatX((1.0 / n_topics) * np.ones(
(n_topics, n_words))),
shape=(n_topics, n_words),
transform=t_stick_breaking(1e-9))
# Note, that we defined likelihood with scaling, so here we need no additional `total_size` kwarg
doc = pm.DensityDist('doc',
logp_lda_doc(beta, theta),
observed=doc_t)
# Encoder
class LDAEncoder:
"""Encode (term-frequency) document vectors to variational means and (log-transformed) stds.
"""
def __init__(self,
n_words,
n_hidden,
n_topics,
p_corruption=0,
random_seed=1):
rng = np.random.RandomState(random_seed)
self.n_words = n_words
self.n_hidden = n_hidden
self.n_topics = n_topics
self.w0 = shared(0.01 * rng.randn(n_words, n_hidden).ravel(),
name='w0')
self.b0 = shared(0.01 * rng.randn(n_hidden), name='b0')
self.w1 = shared(0.01 * rng.randn(n_hidden, 2 *
(n_topics - 1)).ravel(),
name='w1')
self.b1 = shared(0.01 * rng.randn(2 * (n_topics - 1)),
name='b1')
self.rng = MRG_RandomStreams(seed=random_seed)
self.p_corruption = p_corruption
def encode(self, xs):
if 0 < self.p_corruption:
dixs, vixs = xs.nonzero()
mask = tt.set_subtensor(
tt.zeros_like(xs)[dixs, vixs],
self.rng.binomial(size=dixs.shape,
n=1,
p=1 - self.p_corruption))
xs_ = xs * mask
else:
xs_ = xs
w0 = self.w0.reshape((self.n_words, self.n_hidden))
w1 = self.w1.reshape((self.n_hidden, 2 * (self.n_topics - 1)))
hs = tt.tanh(xs_.dot(w0) + self.b0)
zs = hs.dot(w1) + self.b1
zs_mean = zs[:, :(self.n_topics - 1)]
zs_rho = zs[:, (self.n_topics - 1):]
return {'mu': zs_mean, 'rho': zs_rho}
def get_params(self):
return [self.w0, self.b0, self.w1, self.b1]
# call Encoder
encoder = LDAEncoder(n_words=n_words,
n_hidden=100,
n_topics=n_topics,
p_corruption=0.0)
local_RVs = OrderedDict([(theta, encoder.encode(doc_t))])
# get parameters
encoder_params = encoder.get_params()
# Train pymc3 Model
η = .1
s = shared(η)
def reduce_rate(a, h, i):
s.set_value(η / ((i / minibatch_size) + 1)**.7)
with model:
approx = pm.MeanField(local_rv=local_RVs)
approx.scale_cost_to_minibatch = False
inference = pm.KLqp(approx)
inference.fit(10000,
callbacks=[reduce_rate],
obj_optimizer=pm.sgd(learning_rate=s),
more_obj_params=encoder_params,
total_grad_norm_constraint=200,
more_replacements={doc_t: doc_t_minibatch})
# Extracting characteristic words
doc_t.set_value(docs_tr.toarray())
samples = pm.sample_approx(approx, draws=100)
beta_pymc3 = samples['beta'].mean(axis=0)
# Predictive distribution
def calc_pp(ws, thetas, beta, wix):
"""
Parameters
----------
ws: ndarray (N,)
Number of times the held-out word appeared in N documents.
thetas: ndarray, shape=(N, K)
Topic distributions for N documents.
beta: ndarray, shape=(K, V)
Word distributions for K topics.
wix: int
Index of the held-out word
Return
------
Log probability of held-out words.
"""
return ws * np.log(thetas.dot(beta[:, wix]))
def eval_lda(transform, beta, docs_te, wixs):
"""Evaluate LDA model by log predictive probability.
Parameters
----------
transform: Python function
Transform document vectors to posterior mean of topic proportions.
wixs: iterable of int
Word indices to be held-out.
"""
lpss = []
docs_ = deepcopy(docs_te)
thetass = []
wss = []
total_words = 0
for wix in wixs:
ws = docs_te[:, wix].ravel()
if 0 < ws.sum():
# Hold-out
docs_[:, wix] = 0
# Topic distributions
thetas = transform(docs_)
# Predictive log probability
lpss.append(calc_pp(ws, thetas, beta, wix))
docs_[:, wix] = ws
thetass.append(thetas)
wss.append(ws)
total_words += ws.sum()
else:
thetass.append(None)
wss.append(None)
# Log-probability
lp = np.sum(np.hstack(lpss)) / total_words
return {'lp': lp, 'thetass': thetass, 'beta': beta, 'wss': wss}
inp = tt.matrix(dtype='int64')
sample_vi_theta = theano.function([inp],
approx.sample_node(
approx.model.theta,
100,
more_replacements={
doc_t: inp
}).mean(0))
def transform_pymc3(docs):
return sample_vi_theta(docs)
result_pymc3 = eval_lda(transform_pymc3, beta_pymc3, docs_te.toarray(),
np.arange(100))
print('Predictive log prob (pm3) = {}'.format(result_pymc3['lp']))
return result_pymc3
def variational_inference(X_train, Y_train, X_test, Y_test, m, k):
import numpy as np
import pymc3 as pm
from sklearn.preprocessing import MinMaxScaler
import theano
import matplotlib.pyplot as plt
import numpy
import random
#输入数据并进行标准化
n, p = np.shape(X_train)
Y_train = np.reshape(Y_train, (len(Y_train), 1))
Y_test = np.reshape(Y_test, (len(Y_test), 1))
scaler_x = MinMaxScaler(feature_range=(-1, 1))
X_train = scaler_x.fit_transform(X_train)
X_test = scaler_x.transform(X_test)
scaler_y = MinMaxScaler(feature_range=(0, 1))
Y_train = scaler_y.fit_transform(Y_train)
Y_test = scaler_y.transform(Y_test)
X_train = theano.shared(X_train)
#添加噪音
#sigma=0.1
#rd_num=int(sigma*len(Y_train))
#rd=random.sample(range(len(Y_train)),rd_num)
#sm=np.random.uniform(-0.1,0,size=rd_num)
#Y_train=np.ravel(Y_train)
#Y_train[rd]=sm
#定义模型
basic_model = pm.Model()
with basic_model:
b = pm.Normal('b', mu=0, tau=1)
A = pm.Normal('A', mu=0, tau=1, shape=(p, m))
gamma_0 = pm.Gamma('gamma_0', alpha=10**(-5), beta=10**(-5))
gamma_1 = pm.Gamma('gamma_1', alpha=10**(-5), beta=10**(-5))
beta = pm.Normal('beta', mu=0, tau=gamma_0, shape=(m, 1))
Y_obs = pm.Normal('Y_obs',
mu=sigmoid_kernel(X_train, beta, A, b),
tau=gamma_1,
observed=Y_train)
start = pm.find_MAP()
#approx=pm.fit(k,start=start,obj_optimizer=pm.adam(),callbacks=[tracker])
approx = pm.fit(k, start=start, obj_optimizer=pm.adam())
#在拟合好的模型中，对参数z={beta,A,b,gamma_0,gamma_1}进行抽样
trace = pm.sample_approx(approx=approx, draws=5000)
#pm.traceplot(trace)
#pm.summary(trace)
#取5000次后验预测的均值为最终结果。
post_pred = pm.sample_ppc(trace, samples=5000, model=basic_model)
y_train_pred = np.mean(post_pred['Y_obs'], axis=0)
#对预测结果与实际结果进行比较。
mse_train = (((y_train_pred - Y_train)**2).sum()) / np.size(Y_train, 0)
X_train.set_value(X_test)
post_pred = pm.sample_ppc(trace, samples=5000, model=basic_model)
y_test_pred = np.mean(post_pred['Y_obs'], axis=0)
mse_test = (((y_test_pred - Y_test)**2).sum()) / np.size(Y_test, 0) #
Y_mean = np.ones_like(Y_test) * np.mean(Y_test)
r2 = 1 - (((y_test_pred - Y_test)**2).sum()) / (
((Y_test - Y_mean)**2).sum()) #
n = len(Y_test)
err = Y_test - y_test_pred
err_mean = np.ones_like(err) * np.mean(err)
err_var = (((err - err_mean)**2).sum()) / (n - 1)
y_var = (((Y_test - Y_mean)**2).sum()) / (n - 1)
Evar = 1 - err_var / y_var
#print('mse_train=',mse_train,'\n mse_test=',mse_test,'\n r2=',r2,'\n Evar=',Evar,'\n m=',m)
return mse_train, mse_test, r2, Evar, m
def run_lda(args):
tf_vectorizer, docs_tr, docs_te = prepare_sparse_matrix_nonlabel(args.n_tr, args.n_te, args.n_word)
feature_names = tf_vectorizer.get_feature_names()
doc_tr_minibatch = pm.Minibatch(docs_tr.toarray(), args.bsz)
doc_tr = shared(docs_tr.toarray()[:args.bsz])
def log_prob(beta, theta):
"""Returns the log-likelihood function for given documents.
K : number of topics in the model
V : number of words (size of vocabulary)
D : number of documents (in a mini-batch)
Parameters
----------
beta : tensor (K x V)
Word distributions.
theta : tensor (D x K)
Topic distributions for documents.
"""
def ll_docs_f(docs):
dixs, vixs = docs.nonzero()
vfreqs = docs[dixs, vixs]
ll_docs = (vfreqs * pmmath.logsumexp(tt.log(theta[dixs]) + tt.log(beta.T[vixs]),
axis=1).ravel())
return tt.sum(ll_docs) / (tt.sum(vfreqs) + 1e-9)
return ll_docs_f
with pm.Model() as model:
beta = Dirichlet("beta",
a=pm.floatX((1. / args.n_topic) * np.ones((args.n_topic, args.n_word))),
shape=(args.n_topic, args.n_word), )
theta = Dirichlet("theta",
a=pm.floatX((10. / args.n_topic) * np.ones((args.bsz, args.n_topic))),
shape=(args.bsz, args.n_topic), total_size=args.n_tr, )
doc = pm.DensityDist("doc", log_prob(beta, theta), observed=doc_tr)
encoder = ThetaEncoder(n_words=args.n_word, n_hidden=100, n_topics=args.n_topic)
local_RVs = OrderedDict([(theta, encoder.encode(doc_tr))])
encoder_params = encoder.get_params()
s = shared(args.lr)
def reduce_rate(a, h, i):
s.set_value(args.lr / ((i / args.bsz) + 1) ** 0.7)
with model:
approx = pm.MeanField(local_rv=local_RVs)
approx.scale_cost_to_minibatch = False
inference = pm.KLqp(approx)
inference.fit(args.n_iter,
callbacks=[reduce_rate, pm.callbacks.CheckParametersConvergence(diff="absolute")],
obj_optimizer=pm.adam(learning_rate=s),
more_obj_params=encoder_params,
total_grad_norm_constraint=200,
more_replacements={ doc_tr: doc_tr_minibatch }, )
doc_tr.set_value(docs_tr.toarray())
inp = tt.matrix(dtype="int64")
sample_vi_theta = theano.function([inp],
approx.sample_node(approx.model.theta, args.n_sample, more_replacements={doc_tr: inp}), )
test = docs_te.toarray()
test_n = test.sum(1)
beta_pymc3 = pm.sample_approx(approx, draws=args.n_sample)['beta']
theta_pymc3 = sample_vi_theta(test)
assert beta_pymc3.shape == (args.n_sample, args.n_topic, args.n_word)
assert theta_pymc3.shape == (args.n_sample, args.n_te, args.n_topic)
beta_mean = beta_pymc3.mean(0)
theta_mean = theta_pymc3.mean(0)
pred_rate = theta_mean.dot(beta_mean)
pp_test = (test * np.log(pred_rate)).sum(1) / test_n
posteriors = { 'theta': theta_pymc3, 'beta': beta_pymc3,}
log_top_words(beta_pymc3.mean(0), feature_names, n_top_words=args.n_top_word)
save_elbo(approx.hist)
save_pp(pp_test)
save_draws(posteriors)
local_RVs = OrderedDict([(theta, encoder.encode(counts_share))])
encoder_params = encoder.get_params()
with lda_model:
approx1 = pm.fit(
6000,
method='advi',
local_rv=local_RVs,
more_obj_params=encoder_params,
# https://arxiv.org/pdf/1705.08292.pdf
# sgd(with/without momentum) seems to be good choice for high dimensional problems
obj_optimizer=pm.sgd,
# but your gradients will explode here
total_grad_norm_constraint=1000)
samples = pm.sample_approx(approx1, draws=100)
beta_pymc3 = samples['beta'].mean(axis=0)
theta_pymc3 = samples['theta'].mean(axis=0)
plt.plot(approx1.hist[10:])
plt.show()
## get label for each cell
z_pymc3 = theta_pymc3.argmax(axis=1)
pd.DataFrame({
"celda": z_celda,
"pymc3": z_pymc3
}).groupby(['celda', 'pymc3']).size()
## 3:21 minutes to run the AEVB with ADVI to get the posterior Dis