def test_sparse_regression():
"""
Test sparse regression
"""
A, y, x_true = generate_sparse_system()
# least squares solution
xls = np.linalg.lstsq(A, y)[0]
# helper function to test relative error
def test_error(xhat):
test_err = np.linalg.norm(xhat - x_true, 2)
naive_err = np.linalg.norm(xls - x_true, 2)
err_ratio = test_err / naive_err
assert err_ratio <= 0.01
# ProximalConsensus
opt = ProximalConsensus(xls)
opt.add('linsys', A=A, b=y)
opt.add('sparse', 1.)
opt.display = None
opt.storage = None
opt.run(maxiter=100)
# test error
test_error(opt.theta)
# Proximal gradient descent and Accelerated proximal gradient descent
for algorithm in [ProximalGradientDescent, AcceleratedProximalGradient]:
# objective
def f_df(x):
err = A.dot(x) - y
obj = 0.5 * np.linalg.norm(err) ** 2
grad = A.T.dot(err)
return obj, grad
# sparsity penalty
proxop = sparse(1.)
# optimizer
opt = algorithm(f_df, xls, proxop, learning_rate=0.005)
opt.display = None
opt.storage = None
opt.run(maxiter=5000)
# test
test_error(opt.theta)
def test_lowrank_matrix_approx():
"""
Test low rank matrix approximation
"""
Xobs, Xtrue = generate_lowrank_matrix()
# helper function to test relative error of given parameters
def test_error(Xhat):
test_err = np.linalg.norm(Xhat - Xtrue, 'fro')
naive_err = np.linalg.norm(Xobs - Xtrue, 'fro')
err_ratio = test_err / naive_err
assert err_ratio <= 0.5
# proximal algorithm for low rank matrix approximation
opt = ProximalConsensus(Xobs)
opt.add('squared_error', Xobs)
opt.add('nucnorm', 0.2)
opt.display = None
opt.storage = None
opt.run(maxiter=100)
# test error
test_error(opt.theta)
# Proximal gradient descent and Accelerated proximal gradient descent
for algorithm in [ProximalGradientDescent, AcceleratedProximalGradient]:
# objective
def f_df(X):
grad = X - Xtrue
obj = 0.5 * np.linalg.norm(grad.ravel()) ** 2
return obj, grad
# sparsity penalty
proxop = nucnorm(0.2)
# optimizer
opt = algorithm(f_df, Xobs, proxop, learning_rate=0.005)
opt.display = None
opt.storage = None
opt.run(maxiter=5000)
# test
test_error(opt.theta)