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sparse_tensor.py
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sparse_tensor.py
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"""
Poisson Tensor Factorization using sparse representation of input tensor by: 2017-11-24 Eliezer de Souza da Silva <eliezer.souza.silva@ntnu.no>
Modification of a code created in: 2014-03-25 02:06:52 by Dawen Liang <dliang@ee.columbia.edu>
"""
import sys
import numpy as np
from scipy import special
import numpy_indexed as npi
from sklearn.base import BaseEstimator, TransformerMixin
class PoissonTF(BaseEstimator, TransformerMixin):
""" Poisson tensor factorization with batch inference """
def __init__(self, n_components=100, max_iter=100, tol=0.0005,
smoothness=100, random_state=None, verbose=False,
**kwargs):
""" Poisson tensor factorization
Arguments
---------
n_components : int
Number of latent components
max_iter : int
Maximal number of iterations to perform
tol : float
The threshold on the increase of the objective to stop the
iteration
smoothness : int
Smoothness on the initialization variational parameters
random_state : int or RandomState
Pseudo random number generator used for sampling
verbose : bool
Whether to show progress during model fitting
**kwargs: dict
Model hyperparameters
"""
self.n_components = n_components
self.max_iter = max_iter
self.tol = tol
self.smoothness = smoothness
self.random_state = random_state
self.verbose = verbose
if type(self.random_state) is int:
np.random.seed(self.random_state)
elif self.random_state is not None:
np.random.setstate(self.random_state)
self._parse_args(**kwargs)
def _parse_args(self, **kwargs):
self.a = float(kwargs.get('a', 0.1))
self.b = float(kwargs.get('b', 0.1))
def _init_components(self, n_rows):
# variational parameters modes
self.mode_sizes = n_rows
self.gamma_b=[]
self.rho_b=[]
self.Eb=[]
self.Elogb=[]
self.partial_sums=[]
self.gamma_lambda=np.random.gamma(self.smoothness, 1. / self.smoothness,
size=(1, self.n_components))
self.rho_lambda=np.random.gamma(self.smoothness, 1. / self.smoothness,
size=(1, self.n_components))
self.Elambda,self.Eloglambda=_compute_expectations(self.gamma_lambda, self.rho_lambda)
for mode_n in n_rows:
gamma_b=self.smoothness \
* np.random.gamma(self.smoothness, 1. / self.smoothness,
size=(mode_n, self.n_components))
rho_b = self.smoothness \
* np.random.gamma(self.smoothness, 1. / self.smoothness,
size=(mode_n, self.n_components))
self.gamma_b.append(gamma_b)
self.rho_b.append(rho_b)
tempE, tempElog = _compute_expectations(gamma_b, rho_b)
self.partial_sums.append(np.sum(tempE,axis=0,keepdims=True)) ### shape=(1,self.n_components)
self.Eb.append(tempE)
self.Elogb.append(tempElog)
def set_components(self, shape, rate):
'''Set the latent components from variational parameters.
Parameters
----------
shape : list of numpy-array, shape (n_items_mode, n_components)
Shape parameters for the variational distribution
rate : list of numpy-array, shape (n_items_mode, n_components)
Rate parameters for the variational distribution
Returns
-------
self : object
Return the instance itself.
'''
self.gamma_b, self.rho_b = shape, rate
self.Eb, self.Elogb = shape,rate
for s,r,i in zip(shape,rate,range(len(shape))):
self.Eb[i], self.Elogb[i] = _compute_expectations(s, r)
return self
def fit(self, X):
'''Fit the model to the data in X.
Parameters
----------
X : sparse tensor array-like, shape (n_examples, n_modes+1)
Training data.
[[X_mode_1,...,X_mode_n,V],
....]
V[X_mode_1,...,X_mode]] is the value indexed by [X_mode_1,...,X_mode_n] in a dense tensor array
Returns
-------
self: object
Returns the instance itself.
'''
self.n_ids_mode = []
self.unique_id_mode=[]
X_new=np.zeros(shape=X.shape,dtype=int)
X_new[:, -1]=X[:,-1] ## copy the last column
for mode in range(X.shape[1]-1): ## the last column is the value, is not a mode
unique_ids= np.unique(X[:,mode])
self.unique_id_mode.append(unique_ids)
d_ids = dict(zip(unique_ids,range(len(unique_ids))))
X_new[:, mode] = np.array([d_ids[x] for x in X[:, mode]])
self.n_ids_mode.append( np.max(X_new[:,mode])+1 )
if self.verbose:
print("n_ids in mode "+str(mode)+"= "+str(self.n_ids_mode[mode]))
self._init_components(self.n_ids_mode)
self._update(X_new)
return self
def transform(self, X, attr=None):
'''Encode the data as a linear combination of the latent components.
Parameters
----------
X : array-like, shape (n_samples, n_feats)
attr: string
The name of attribute, default 'Eb'. Can be changed to Elogb to
obtain E_q[log beta] as transformed data.
Returns
-------
X_new : array-like, shape(n_samples, n_filters)
Transformed data, as specified by attr.
'''
'''
if not hasattr(self, 'Eb'):
raise ValueError('There are no pre-trained components.')
n_samples, n_feats = X.shape
if n_feats != self.Eb.shape[1]:
raise ValueError('The dimension of the transformed data '
'does not match with the existing components.')
if attr is None:
attr = 'Et'
self._init_weights(n_samples)
self._update(X, update_beta=False)
return getattr(self, attr)
'''
def _update(self, X, update_beta=True):
# alternating between update latent components and weights
old_bd = -np.inf
self._update_phi(X)
for i in xrange(self.max_iter):
self._update_lambda(X)
self._update_latent_factors(X)
self._update_phi(X)
bound = self._bound(X)
improvement = (bound - old_bd) / abs(old_bd)
if self.verbose:
sys.stdout.write('\r\tAfter ITERATION: %d\tObjective: %.0f\t'
'Old objective: %.0f\t'
'Improvement: %.5f' % (i, bound, old_bd,
improvement))
sys.stdout.flush()
if np.abs(improvement) < self.tol:
break
old_bd = bound
if self.verbose:
sys.stdout.write('\n')
pass
def _update_lambda(self,X):
self.gamma_lambda = self.a+self.phi_var_data.sum(axis=0,keepdims=True)
self.rho_lambda = self.b
for mode in range(X.shape[1]-1):
self.rho_lambda+=self.Eb[mode].sum(axis=0,keepdims=True)
self.Elambda,self.Eloglambda=_compute_expectations(self.gamma_lambda, self.rho_lambda)
def _update_phi(self,X):
self.phi_var = np.zeros((X.shape[0], self.n_components)) ### start zeroing everything
for mode in range(X.shape[1]-1): ### for each element of the mode, minus the last one, which is the value
# select the non-zero evidence elements of the latent factor of each mode
# [m1, m2, m3, m4, m5, v] => Data[m1,m2,m3,m5]=v, so for each mode i we select m_i = {index non zero}
self.phi_var = np.add(self.phi_var, np.exp(self.Elogb[mode][X[:,mode], :]))
self.phi_var = np.add(self.phi_var, np.exp(self.Eloglambda))
self.phi_var = np.divide(self.phi_var, np.sum(self.phi_var, axis=1)[:, np.newaxis])
self.phi_var_data =X[:,-1,np.newaxis]*self.phi_var ### X[m1, m2, m3, m4, m5, v][-1]=v
def _update_latent_factors(self, X):
# variational parameters modes
for mode in range(X.shape[1]-1):
self.gamma_b[mode]=self.a + npi.group_by(X[:,mode]).sum(self.phi_var_data)[1]
self.rho_b[mode]=self.b + self.Elambda*np.prod(self.partial_sums[:mode]+self.partial_sums[(mode+1):], axis=0)
tempE, tempElog = _compute_expectations(self.gamma_b[mode], self.rho_b[mode])
self.partial_sums[mode]=np.sum(tempE,axis=0,keepdims=True) ### shape=(1,self.n_components)
self.Eb[mode]=tempE
self.Elogb[mode]=tempElog
def _xexplog(self):
'''
sum_k exp(E[log theta_{ik} * beta_{kd}])
'''
return np.dot(np.exp(self.Elogt), np.exp(self.Elogb))
def _bound(self, X):
bound=0
bound+=np.sum(self.phi_var_data*self.Eloglambda)
for mode in range(X.shape[1]-1):
bound+=np.sum(self.phi_var_data*self.Elogb[mode][X[:,mode], :])
bound-=np.sum(self.Elambda*np.prod(self.partial_sums,axis=0))
bound += _gamma_term(self.a, self.a ,
self.gamma_b[mode], self.rho_b[mode],
self.Eb[mode], self.Elogb[mode])
bound += _gamma_term(self.a, self.a ,
self.gamma_lambda, self.rho_lambda,
self.Elambda, self.Eloglambda)
bound -= np.sum(np.log(self.phi_var+0.00000000000001)*self.phi_var_data)
return bound
def _compute_expectations(alpha, beta):
'''
Given x ~ Gam(alpha, beta), compute E[x] and E[log x]
'''
#beta=beta.reshape((beta.shape[0], 1))
# TODO: maybe use 1-dimensional beta and broadcast in the appropriate dimension... save memory if it is a problem
return (alpha / beta, special.psi(alpha) - np.log(beta))
def _gamma_term(a, b, shape, rate, Ex, Elogx):
return np.sum((a - shape) * Elogx - (b - rate) * Ex +
(special.gammaln(shape) - shape * np.log(rate)))
def _sum_product_newaxis1(auxvar, data, axis=1):
return np.sum(auxvar * data[np.newaxis, :, :], axis=axis)
def _compute_entropy(alpha, beta):
'''
Given x ~ Gam(alpha, beta), compute Entropy[x]
'''
#beta=beta.reshape((beta.shape[0], 1))
# TODO: use 1-dimensional beta and broadcast in the appropriate dimension... save memory if it is a problem
return alpha+(1-alpha)*special.psi(alpha) - np.log(beta)+special.gammaln(alpha)