def estimate_precision(XX):
p = XX.shape[1]
# Find neighbors (or non-zero elements in precision matrix) iterating
# through columns of the data matrix (whose dimension is n \times p)
A = np.zeros([p,p])
for i in range(p):
# i-th column is a response variable
X = np.delete(XX, i, 1)
b = XX[:,i]
b.shape = (b.size, 1)
grad = lasso_problem(X, b)
theta0 = np.zeros([p-1, 1]) # initial point
theta = subgradient_steepest_descent(None, grad, theta0,
method = 'diminishing',
max_iter=200)
# putting in regressed values except the diagonal entries
for j in range(theta.size):
if j < i:
A[i,j] = theta[j]
else:
A[i,j+1] = theta[j]
return A
def problem_2():
n_observations, n_variables = 1000, 100
X = generate_well_conditioned(n_observations, n_variables)
for non_zero_count in [10, 25]:
beta = generate_sparse_sample(n_variables, non_zero_count)
penalty1, penalty2 = 0.1, 0.1
func, grad = generate_subgradient_elastic_net(X, beta, penalty1, penalty2)
x0 = np.ones([beta.shape[0], 1])
print "non_zero_count:%d, with penalty1 %f, penalty2 %f" % (
non_zero_count, penalty1, penalty2)
estimated_beta, history = subgradient_steepest_descent(func, grad, x0, beta,
method = 'diminishing', max_iter=1e3)
np.savetxt('problem_2_convergence'
+ '_%d_%.1f_%.1f' % (non_zero_count, penalty1, penalty2), history)
np.savetxt('problem_2_beta'
+ '_%d_%.1f_%.1f' % (non_zero_count, penalty1, penalty2), estimated_beta)
