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import theano
import cascade_creation
from theano import tensor, function
import numpy as np
import timeout
import cvxopt
import scipy
@timeout.timeout(20)
def sparse_recovery(lbda, n_cascades):
"""
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
"""
if type(lbda) == int or type(lbda) == float:
lbda = np.array(lbda)
lbda = theano.shared(lbda.astype(theano.config.floatX))
theta = tensor.row().T
theta_ = theta.flatten()
M = tensor.matrix(name='M', dtype=theano.config.floatX)
w = tensor.vector(name='w', dtype=theano.config.floatX)
y = lbda * theta_.norm(1) - 1./n_cascades*(
(w).dot(tensor.log(1-tensor.exp(M.dot(theta_))))
+ (1-w).dot(tensor.dot(M, theta_))
)
z = tensor.row().T
z_ = z.flatten()
y_diff = tensor.grad(y, theta_)
y_hess = z[0] * theano.gradient.hessian(y, theta_)
f_x = theano.function([theta, M, w], [y, y_diff],
allow_input_downcast=True)
f_xz = theano.function([theta, z, M, w], [y, y_diff, y_hess],
allow_input_downcast=True)
return f_x, f_xz
def type_lasso(lbda, n_cascades):
"""
Solves:
min - sum_j theta_j + lbda*|e^{M*theta} - (1 - w)|_2
s.t theta_j <= 0
"""
if type(lbda) == int or type(lbda) == float:
lbda = np.array(lbda)
lbda = theano.shared(lbda.astype(theano.config.floatX))
theta = tensor.row().T
theta_ = theta.flatten()
M = tensor.matrix(name='M', dtype=theano.config.floatX)
w = tensor.vector(name='w', dtype=theano.config.floatX)
y = lbda * (theta_).norm(1) + (
tensor.exp(M.dot(theta_)) - (1 - w)).norm(2)
z = tensor.row().T
z_ = z.flatten()
y_diff = tensor.grad(y, theta_)
y_hess = z[0] * theano.gradient.hessian(y, theta_)
f_x = theano.function([theta, M, w], [y, y_diff],
allow_input_downcast=True)
f_xz = theano.function([theta, z, M, w], [y, y_diff, y_hess],
allow_input_downcast=True)
return f_x, f_xz
@timeout.timeout(70)
def diff_and_opt(M_val, w_val, f_x, f_xz):
if M_val.dtype == bool:
M_val = M_val.astype(theano.config.floatX)
m, n = M_val.shape
def F(x=None, z=None):
if x is None:
return 0, cvxopt.matrix(-.1, (n,1))
elif z is None:
y, y_diff = f_x(x, M_val, w_val)
return cvxopt.matrix(float(y), (1, 1)),\
cvxopt.matrix(y_diff.astype("float64")).T
else:
y, y_diff, y_hess = f_xz(x, z, M_val, w_val)
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'] = 50
cvxopt.solvers.options['show_progress'] = False
try:
theta = cvxopt.solvers.cp(F, G, h)['x']
except ArithmeticError:
print("ArithmeticError thrown, change initial point"
" given to the solver")
except ValueError:
print("Domain Error, skipping to next node")
theta = np.zeros(M_val.shape[1])
if cvxopt.solvers.options['show_progress']:
print(1 - np.exp(theta))
return 1 - np.exp(theta), theta
def restrictedEigenvalue(M_val, w_val, theta_val, gramMatrix=False):
"""
returns the smallest restricted eigenvalue of the matrix on the set S
gramMatrix (bool) : If true, use the gram matrix instead of the Hessian
theta_val : true vector of parameters
"""
m, n = M_val.shape
if gramMatrix:
H = 1./m * np.dot(M_val.T,M_val)
else:
#compute the Hessian
#theta = tensor.row().T
#theta_ = theta.flatten()
#M = tensor.matrix(name='M', dtype=theano.config.floatX)
#w = tensor.vector(name='w', dtype=theano.config.floatX)
#y = - 1./n*( (w).dot(tensor.log(1-tensor.exp(M.dot(theta_)))) +
#(1-w).dot(tensor.dot(M, theta_)))
#f = theano.function([theta, M, w], [theano.gradient.hessian(y,
#theta_)], allow_input_downcast=True)
#print(theta_val)
#H = f(np.atleast_2d(theta_val).T, M_val.astype('float64'), w_val)
#print(H)
#evals_small, evecs_small = scipy.sparse.linalg.eigsh(H.astype('float64'), 1,
#which="LM")
#print(evals_small)
theta = tensor.vector()
M = tensor.matrix(name='M', dtype=theano.config.floatX)
w = tensor.vector(name='w', dtype=theano.config.floatX)
y = - 1./n*((w).dot(tensor.log(1-tensor.exp(M.dot(theta)))) +
(1-w).dot(tensor.dot(M, theta)))
f = theano.function([theta, M, w], [theano.gradient.hessian(y,
theta)], allow_input_downcast=True)
H = f(theta_val, M_val.astype('float32'), w_val)
print(H)
evals_small, evecs_small = scipy.sparse.linalg.eigsh(H, 1,
which="LM")
print(evals_small)
def test():
"""
unit test
"""
lbda = .0001
G = cascade_creation.InfluenceGraph(max_proba=.9, min_proba=.2)
G.erdos_init(n=20, p = .3)
A = cascade_creation.generate_cascades(G, .1, 500)
M_val, w_val = cascade_creation.icc_matrixvector_for_node(A, 0)
print(M_val.shape)
print(w_val.shape)
#Type lasso
if 0:
f_x, f_xz = type_lasso(lbda, 500)
p_vec, _ = diff_and_opt(M_val, w_val, f_x, f_xz)
print(G.mat[2])
#Sparse recovery
if 0:
f_x, f_xz = sparse_recovery(lbda, 500)
p_vec, _ = diff_and_opt(M_val, w_val, f_x, f_xz)
print(G.mat[2])
#Restricted Eigenvalue
if 2:
node = 1
parents = np.nonzero(G.mat[:, node])[0]
theta_val = G.logmat[:,node]
restrictedEigenvalue(M_val, w_val, theta_val)
if __name__=="__main__":
test()
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