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import theano
import cascade_creation
from theano import tensor, function
import numpy as np
import timeout
import cvxopt
@timeout.timeout(10)
def sparse_recovery(M_val, w_val, lbda):
"""
Solves:
min lbda * |theta|_1 - 1/n_cascades*(
sum w log(e^[M*theta]) + (1-w) log(1-e^[M*theta])
)
s.t theta_j <= 0
The objective must be re-normalized:
-> log(e^x - 1) = (1-k)x + log(e^[kx] - 1)
with k chosen as : n_nodes*n_cascades
"""
assert len(M_val) == len(w_val)
if M_val.dtype == bool:
M_val = M_val.astype('float32')
if type(lbda) == int:
lbda = np.array(lbda)
m, n = M_val.shape
theta = tensor.row().T
theta_ = theta.flatten()
M = theano.shared(M_val.astype(theano.config.floatX))
w = theano.shared(w_val.astype(theano.config.floatX))
lbda = theano.shared(lbda.astype(theano.config.floatX))
#Objective
y = lbda * (theta_).norm(1) - 1./m*(
tensor.dot(1-w, tensor.log(1-tensor.exp(M.dot(theta_ *1./(n*m)))))\
+ (1 - 1./(n*m)) * tensor.dot(1 - w, tensor.dot(M, theta_)) \
+ tensor.dot(w, tensor.dot(M, theta_)))
return diff_and_opt(theta, theta_, M, M_val, w, lbda, y)
@timeout.timeout(20)
def type_lasso(M_val, w_val, lbda):
"""
Solves:
min - sum_j theta_j + lbda*|e^{M*theta} - (1 - w)|_2
s.t theta_j <= 0
"""
assert len(M_val) == len(w_val)
if M_val.dtype == bool:
M_val = M_val.astype('float32')
if type(lbda) == int:
lbda = np.array(lbda)
theta = tensor.row().T
theta_ = theta.flatten()
M = theano.shared(M_val.astype(theano.config.floatX))
w = theano.shared(w_val.astype(theano.config.floatX))
lbda = theano.shared(lbda.astype(theano.config.floatX))
y = lbda * (theta_).norm(1) + (
tensor.exp(M.dot(theta_)) - (1 - w)).norm(2)
return diff_and_opt(theta, theta_, M, M_val, w, lbda, y)
def diff_and_opt(theta, theta_, M, M_val, w, lbda, y):
z = tensor.row().T
z_ = z.flatten()
m, n = M_val.shape
y_diff = tensor.grad(y, theta_)
y_hess = z[0] * theano.gradient.hessian(y, theta_)
f_x = theano.function([theta], [y, y_diff], allow_input_downcast=True)
f_xz = theano.function([theta, z], [y, y_diff, y_hess],
allow_input_downcast=True)
def F(x=None, z=None):
if x is None:
return 0, cvxopt.matrix(-.001, (n,1))
elif z is None:
y, y_diff = f_x(x)
return cvxopt.matrix(float(y), (1, 1)),\
cvxopt.matrix(y_diff.astype("float64")).T
else:
y, y_diff, y_hess = f_xz(x, z)
return cvxopt.matrix(float(y), (1, 1)), \
cvxopt.matrix(y_diff.astype("float64")).T, \
cvxopt.matrix(y_hess.astype("float64"))
G = cvxopt.spdiag([1 for i in range(n)])
h = cvxopt.matrix(0.0, (n,1))
#Relaxing precision constraints
cvxopt.solvers.options['feastol'] = 2e-5
cvxopt.solvers.options['abstol'] = 2e-5
#cvxopt.solvers.options['maxiters'] = 100
cvxopt.solvers.options['show_progress'] = True
try:
theta = cvxopt.solvers.cp(F, G, h)['x']
except ArithmeticError:
print("ArithmeticError thrown, change initial point"+\
" given to the solver")
except
return 1 - np.exp(theta), theta
def test():
"""
unit test
"""
lbda = 1
G = cascade_creation.InfluenceGraph(max_proba=.8)
G.erdos_init(n=100, p = .1)
A = cascade_creation.generate_cascades(G, .1, 100)
M_val, w_val = cascade_creation.icc_matrixvector_for_node(A, 0)
#Type lasso
if 0:
p_vec, theta = type_lasso(M_val, w_val, lbda)
print(p_vec)
#Sparse recovery
if 1:
p_vec, theta = sparse_recovery(M_val, w_val, lbda)
print(p_vec)
if __name__=="__main__":
test()
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