def test_nonsmooth(self): import numpy as np import parsimony.utils.consts as consts from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions.losses as losses import parsimony.functions.penalties as penalties import parsimony.functions.nesterov as nesterov import parsimony.utils.start_vectors as start_vectors import parsimony.datasets.simulate.l1_l2_tv as l1_l2_tv start_vector = start_vectors.RandomStartVector(normalise=True) np.random.seed(42) n, p = 75, 100 penalty_start = 0 alpha = 0.9 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) beta = start_vector.get_vector(p) beta[np.abs(beta) < 0.1] = 0.0 l = 0.618 k = 0.0 g = 0.0 A = np.eye(p) A = [A, A, A] snr = 100.0 X, y, beta_star = l1_l2_tv.load(l, k, g, beta, M, e, A, snr=snr) function = CombinedFunction() function.add_function(losses.LinearRegression(X, y, # penalty_start=penalty_start, mean=False)) # A = nesterov.l1.A_from_variables(p, penalty_start=penalty_start) # function.add_penalty(nesterov.l1.L1(l, A=A, mu=mu_min, # penalty_start=penalty_start)) function.add_prox(penalties.L1(l, penalty_start=penalty_start)) fista = proximal.FISTA(eps=consts.TOLERANCE, max_iter=7800) beta = fista.run(function, beta) assert np.linalg.norm(beta - beta_star) < 5e-2
def test_smooth_2D_l1(self): from parsimony.functions import CombinedFunction import parsimony.functions as functions import parsimony.functions.nesterov.grouptv as grouptv import parsimony.datasets.simulate.l1_l2_grouptvmu as l1_l2_grouptvmu import parsimony.utils.weights as weights np.random.seed(1337) n, p = 10, 18 shape = (1, 3, 6) l = 0.618 k = 0.0 g = 1.618 start_vector = weights.ZerosWeights() beta = start_vector.get_weights(p) rects = [[(0, 1), (0, 3)], [(1, 2), (3, 6)]] beta = np.reshape(beta, shape[1:]) beta[0:2, 0:4] = 1.0 beta[1:3, 3:6] = 2.0 beta[1, 3] = 1.5 beta = np.reshape(beta, (p, 1)) alpha = 1.0 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) snr = 100.0 A = grouptv.linear_operator_from_rects(rects, shape) mu_min = 5e-8 X, y, beta_star = l1_l2_grouptvmu.load(l=l, k=k, g=g, beta=beta, M=M, e=e, A=A, mu=mu_min, snr=snr) eps = 1e-5 max_iter = 10000 beta_start = start_vector.get_weights(p) mus = [5e-2, 5e-4, 5e-6, 5e-8] fista = FISTA(eps=eps, max_iter=max_iter / len(mus)) beta_parsimony = beta_start for mu in mus: function = CombinedFunction() function.add_loss(functions.losses.LinearRegression(X, y, mean=False)) function.add_penalty(grouptv.GroupTotalVariation(l=g, A=A, mu=mu, penalty_start=0)) function.add_prox(functions.penalties.L1(l=l, penalty_start=0)) beta_parsimony = fista.run(function, beta_parsimony) berr = np.linalg.norm(beta_parsimony - beta_star) # print "berr:", berr assert berr < 5e-2 f_parsimony = function.f(beta_parsimony) f_star = function.f(beta_star) ferr = abs(f_parsimony - f_star) # print "ferr:", ferr assert ferr < 5e-5
def test_combo_overlapping_nonsmooth(self): import numpy as np from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions as functions import parsimony.functions.nesterov.gl as gl import parsimony.datasets.simulate.l1_l2_gl as l1_l2_gl import parsimony.utils.start_vectors as start_vectors np.random.seed(42) # Note that p must be even! n, p = 25, 30 groups = [range(0, 2 * p / 3), range(p / 3, p)] weights = [1.5, 0.5] A = gl.A_from_groups(p, groups=groups, weights=weights) l = 0.618 k = 1.0 - l g = 2.718 start_vector = start_vectors.RandomStartVector(normalise=True) beta = start_vector.get_vector(p) alpha = 1.0 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) snr = 100.0 X, y, beta_star = l1_l2_gl.load(l, k, g, beta, M, e, A, snr=snr) eps = 1e-8 max_iter = 10000 beta_start = start_vector.get_vector(p) mus = [5e-0, 5e-2, 5e-4, 5e-6, 5e-8] fista = proximal.FISTA(eps=eps, max_iter=max_iter / len(mus)) beta_parsimony = beta_start for mu in mus: # function = functions.LinearRegressionL1L2GL(X, y, l, k, g, # A=A, mu=mu, # penalty_start=0) function = CombinedFunction() function.add_function(functions.losses.LinearRegression(X, y, mean=False)) function.add_penalty(functions.penalties.L2Squared(l=k)) function.add_penalty(gl.GroupLassoOverlap(l=g, A=A, mu=mu, penalty_start=0)) function.add_prox(functions.penalties.L1(l=l)) beta_parsimony = fista.run(function, beta_parsimony) berr = np.linalg.norm(beta_parsimony - beta_star) # print berr assert berr < 5e-3 f_parsimony = function.f(beta_parsimony) f_star = function.f(beta_star) # print abs(f_parsimony - f_star) assert abs(f_parsimony - f_star) < 5e-6
def test_combo_smooth(self): from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions as functions import parsimony.functions.nesterov.tv as tv import parsimony.datasets.simulate.l1_l2_tvmu as l1_l2_tvmu import parsimony.utils.start_vectors as start_vectors np.random.seed(42) px = 4 py = 4 pz = 4 shape = (pz, py, px) n, p = 50, np.prod(shape) l = 0.618 k = 1.0 - l g = 1.1 start_vector = start_vectors.RandomStartVector(normalise=True) beta = start_vector.get_vector(p) alpha = 1.0 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) snr = 100.0 A = tv.linear_operator_from_shape(shape) mu_min = 5e-8 X, y, beta_star = l1_l2_tvmu.load(l=l, k=k, g=g, beta=beta, M=M, e=e, A=A, mu=mu_min, snr=snr) eps = 1e-8 max_iter = 5300 beta_start = start_vector.get_vector(p) mus = [5e-2, 5e-4, 5e-6, 5e-8] fista = proximal.FISTA(eps=eps, max_iter=max_iter / len(mus)) beta_parsimony = beta_start for mu in mus: # function = functions.LinearRegressionL1L2GL(X, y, l, k, g, # A=A, mu=mu, # penalty_start=0) function = CombinedFunction() function.add_function(functions.losses.LinearRegression(X, y, mean=False)) function.add_penalty(tv.TotalVariation(l=g, A=A, mu=mu, penalty_start=0)) function.add_penalty(functions.penalties.L2Squared(l=k)) function.add_prox(functions.penalties.L1(l=l)) beta_parsimony = fista.run(function, beta_parsimony) berr = np.linalg.norm(beta_parsimony - beta_star) # print "berr:", berr assert berr < 5e-3 f_parsimony = function.f(beta_parsimony) f_star = function.f(beta_star) ferr = abs(f_parsimony - f_star) # print "ferr:", ferr assert ferr < 5e-5
def test_combo_overlapping_nonsmooth(self): import numpy as np from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions as functions import parsimony.functions.nesterov.gl as gl import parsimony.datasets.simulate.l1_l2_gl as l1_l2_gl import parsimony.utils.weights as weights np.random.seed(42) # Note that p must be even! n, p = 25, 30 groups = [list(range(0, 2 * int(p / 3))), list(range(int(p / 3), p))] group_weights = [1.5, 0.5] A = gl.linear_operator_from_groups(p, groups=groups, weights=group_weights) l = 0.618 k = 1.0 - l g = 2.718 start_vector = weights.RandomUniformWeights(normalise=True) beta = start_vector.get_weights(p) alpha = 1.0 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) snr = 100.0 X, y, beta_star = l1_l2_gl.load(l, k, g, beta, M, e, A, snr=snr) eps = 1e-8 max_iter = 10000 beta_start = start_vector.get_weights(p) mus = [5e-0, 5e-2, 5e-4, 5e-6, 5e-8] fista = proximal.FISTA(eps=eps, max_iter=max_iter / len(mus)) beta_parsimony = beta_start for mu in mus: # function = functions.LinearRegressionL1L2GL(X, y, l, k, g, # A=A, mu=mu, # penalty_start=0) function = CombinedFunction() function.add_loss( functions.losses.LinearRegression(X, y, mean=False)) function.add_penalty(functions.penalties.L2Squared(l=k)) function.add_penalty( gl.GroupLassoOverlap(l=g, A=A, mu=mu, penalty_start=0)) function.add_prox(functions.penalties.L1(l=l)) beta_parsimony = fista.run(function, beta_parsimony) berr = np.linalg.norm(beta_parsimony - beta_star) # print berr assert berr < 5e-3 f_parsimony = function.f(beta_parsimony) f_star = function.f(beta_star) # print abs(f_parsimony - f_star) assert abs(f_parsimony - f_star) < 5e-6
def test_nonsmooth(self): import numpy as np import parsimony.utils.consts as consts from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions.losses as losses import parsimony.functions.nesterov as nesterov import parsimony.utils.start_vectors as start_vectors import parsimony.datasets.simulate.l1_l2_tv as l1_l2_tv start_vector = start_vectors.RandomStartVector(normalise=True) np.random.seed(42) n, p = 75, 100 alpha = 0.9 V = np.random.randn(p, p) Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.dot(V.T, V) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) beta_start = start_vector.get_vector(p) beta_start[np.abs(beta_start) < 0.1] = 0.0 l = 0.618 k = 0.0 g = 0.0 A = np.eye(p) A = [A, A, A] snr = 100.0 X, y, beta_star = l1_l2_tv.load(l, k, g, beta_start, M, e, A, snr=snr) beta = beta_start for mu in [5e-2, 5e-3, 5e-4, 5e-5]: function = CombinedFunction() function.add_loss(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables(p, penalty_start=0) function.add_penalty(nesterov.l1.L1(l, A=A, mu=mu, penalty_start=0)) fista = proximal.FISTA(eps=consts.TOLERANCE, max_iter=2300) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr # assert berr < 5e-2 assert_less(berr, 5e-2, "The found regression vector is not correct.") # Test proximal operator beta = beta_start function = CombinedFunction() function.add_loss(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables(p, penalty_start=0) # function.add_penalty(nesterov.l1.L1(l, A=A, mu=mu_min, # penalty_start=penalty_start)) function.add_prox(nesterov.l1.L1(l, A=A, mu=5e-5, penalty_start=0)) fista = proximal.FISTA(eps=consts.TOLERANCE, max_iter=2000) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr # assert berr < 5e-0 assert_less(berr, 5e-0, "The found regression vector is not correct.")
def test_smoothed_l1tv(self): import numpy as np from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions as functions import parsimony.functions.penalties as penalties import parsimony.functions.nesterov.tv as tv import parsimony.functions.nesterov.l1tv as l1tv import parsimony.utils.start_vectors as start_vectors import parsimony.datasets.simulate as simulate np.random.seed(42) px = 10 py = 1 pz = 1 shape = (pz, py, px) n, p = 5, np.prod(shape) l = 0.618 k = 0.01 g = 1.1 start_vector = start_vectors.RandomStartVector(normalise=True) beta = start_vector.get_vector(p) alpha = 1.0 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) snr = 100.0 mu = 5e-3 A = tv.linear_operator_from_shape(shape) # X, y, beta_star = l1_l2_tvmu.load(l=l, k=k, g=g, beta=beta, M=M, e=e, # A=A, mu=mu, snr=snr) funs = [simulate.grad.L1(l), simulate.grad.L2Squared(k), simulate.grad.TotalVariation(g, A)] lr = simulate.LinearRegressionData(funs, M, e, snr=snr, intercept=False) X, y, beta_star = lr.load(beta) eps = 1e-8 max_iter = 810 alg = proximal.FISTA(eps=eps, max_iter=max_iter) function = CombinedFunction() function.add_loss(functions.losses.LinearRegression(X, y, mean=False)) function.add_penalty(penalties.L2Squared(l=k)) A = l1tv.linear_operator_from_shape(shape, p) function.add_prox(l1tv.L1TV(l, g, A=A, mu=mu, penalty_start=0)) # A = tv.linear_operator_from_shape(shape) # function.add_penalty(tv.TotalVariation(l=g, A=A, mu=mu, # penalty_start=0)) # function.add_prox(penalties.L1(l=l)) beta_start = start_vector.get_vector(p) beta = alg.run(function, beta_start) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr # assert berr < 5e-1 assert_less(berr, 5e-1, "The found regression vector is not correct.") f_parsimony = function.f(beta) f_star = function.f(beta_star) ferr = abs(f_parsimony - f_star) # print "ferr:", ferr # assert ferr < 5e-3 assert_less(ferr, 5e-3, "The found regression vector is not correct.")
def test_nonsmooth(self): import numpy as np import parsimony.utils.consts as consts from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions.losses as losses import parsimony.functions.penalties as penalties import parsimony.functions.nesterov as nesterov import parsimony.utils.start_vectors as start_vectors import parsimony.datasets.simulate.l1_l2_tv as l1_l2_tv start_vector = start_vectors.RandomStartVector(normalise=True) np.random.seed(42) n, p = 75, 100 alpha = 0.9 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) beta_start = start_vector.get_vector(p) beta_start[np.abs(beta_start) < 0.1] = 0.0 l = 0.618 k = 0.0 g = 0.0 A = np.eye(p) A = [A, A, A] snr = 100.0 X, y, beta_star = l1_l2_tv.load(l, k, g, beta_start, M, e, A, snr=snr) beta = beta_start for mu in [5e-2, 5e-3, 5e-4, 5e-5]: function = CombinedFunction() function.add_function(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables(p, penalty_start=0) function.add_penalty(nesterov.l1.L1(l, A=A, mu=mu, penalty_start=0)) fista = proximal.FISTA(eps=consts.TOLERANCE, max_iter=910) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr assert berr < 5e-2 # Test proximal operator beta = beta_start function = CombinedFunction() function.add_function(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables(p, penalty_start=0) # function.add_penalty(nesterov.l1.L1(l, A=A, mu=mu_min, # penalty_start=penalty_start)) function.add_prox(nesterov.l1.L1(l, A=A, mu=5e-5, penalty_start=0)) fista = proximal.FISTA(eps=consts.TOLERANCE, max_iter=800) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr assert berr < 5e-0
def test_smoothed_l1tv(self): import numpy as np from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions as functions import parsimony.functions.penalties as penalties import parsimony.functions.nesterov.tv as tv import parsimony.functions.nesterov.l1tv as l1tv import parsimony.datasets.simulate.l1_l2_tvmu as l1_l2_tvmu import parsimony.utils.start_vectors as start_vectors import parsimony.datasets.simulate as simulate np.random.seed(42) px = 10 py = 1 pz = 1 shape = (pz, py, px) n, p = 5, np.prod(shape) l = 0.618 k = 0.01 g = 1.1 start_vector = start_vectors.RandomStartVector(normalise=True) beta = start_vector.get_vector(p) alpha = 1.0 Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.random.randn(p, p) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) snr = 100.0 mu = 5e-3 A = tv.linear_operator_from_shape(shape) # X, y, beta_star = l1_l2_tvmu.load(l=l, k=k, g=g, beta=beta, M=M, e=e, # A=A, mu=mu, snr=snr) funs = [ simulate.grad.L1(l), simulate.grad.L2Squared(k), simulate.grad.TotalVariation(g, A) ] lr = simulate.LinearRegressionData(funs, M, e, snr=snr, intercept=False) X, y, beta_star = lr.load(beta) eps = 1e-8 max_iter = 810 alg = proximal.FISTA(eps=eps, max_iter=max_iter) function = CombinedFunction() function.add_function( functions.losses.LinearRegression(X, y, mean=False)) function.add_penalty(penalties.L2Squared(l=k)) A = l1tv.linear_operator_from_shape(shape, p) function.add_prox(l1tv.L1TV(l, g, A=A, mu=mu, penalty_start=0)) # A = tv.linear_operator_from_shape(shape) # function.add_penalty(tv.TotalVariation(l=g, A=A, mu=mu, # penalty_start=0)) # function.add_prox(penalties.L1(l=l)) beta_start = start_vector.get_vector(p) beta = alg.run(function, beta_start) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr assert berr < 5e-1 f_parsimony = function.f(beta) f_star = function.f(beta_star) ferr = abs(f_parsimony - f_star) # print "ferr:", ferr assert ferr < 5e-3
def test_smoothed(self): import numpy as np import scipy.sparse from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions.losses as losses import parsimony.functions.nesterov as nesterov import parsimony.utils.weights as weights import parsimony.datasets.simulate.l1_l2_tv as l1_l2_tv start_vector = weights.RandomUniformWeights(normalise=True) np.random.seed(42) n, p = 75, 100 penalty_start = 0 alpha = 0.9 V = np.random.randn(p, p) Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.dot(V.T, V) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) beta = start_vector.get_weights(p) beta[np.abs(beta) < 0.1] = 0.0 l = 0.618 k = 0.0 g = 0.0 mu_min = 0.001 # consts.TOLERANCE A = scipy.sparse.eye(p) # A = np.eye(p) A = [A, A, A] snr = 100.0 X, y, beta_star = l1_l2_tv.load(l, k, g, beta, M, e, A, snr=snr) function = CombinedFunction() function.add_loss(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables(p, penalty_start=penalty_start) function.add_penalty(nesterov.l1.L1(l, A=A, mu=mu_min, penalty_start=penalty_start)) # function.add_prox(penalties.L1(l, penalty_start=penalty_start)) fista = proximal.FISTA(eps=mu_min, max_iter=23500) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr # assert berr < 5 assert_less(berr, 5.0, "The found regression vector is not correct.") # Test proximal operator function = CombinedFunction() function.add_loss(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables(p, penalty_start=penalty_start) function.add_prox(nesterov.l1.L1(l, A=A, mu=mu_min, penalty_start=penalty_start)) fista = proximal.FISTA(eps=mu_min, max_iter=20000) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr # assert berr < 0.1 assert_less(berr, 0.1, "The found regression vector is not correct.")
def test_smoothed(self): import numpy as np from parsimony.functions import CombinedFunction import parsimony.algorithms.proximal as proximal import parsimony.functions.losses as losses import parsimony.functions.nesterov as nesterov import parsimony.utils.start_vectors as start_vectors import parsimony.datasets.simulate.l1_l2_tv as l1_l2_tv start_vector = start_vectors.RandomStartVector(normalise=True) np.random.seed(42) n, p = 75, 100 penalty_start = 0 alpha = 0.9 V = np.random.randn(p, p) Sigma = alpha * np.eye(p, p) \ + (1.0 - alpha) * np.dot(V.T, V) mean = np.zeros(p) M = np.random.multivariate_normal(mean, Sigma, n) e = np.random.randn(n, 1) beta = start_vector.get_vector(p) beta[np.abs(beta) < 0.1] = 0.0 l = 0.618 k = 0.0 g = 0.0 mu_min = 0.001 # consts.TOLERANCE A = np.eye(p) A = [A, A, A] snr = 100.0 X, y, beta_star = l1_l2_tv.load(l, k, g, beta, M, e, A, snr=snr) function = CombinedFunction() function.add_loss(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables( p, penalty_start=penalty_start) function.add_penalty( nesterov.l1.L1(l, A=A, mu=mu_min, penalty_start=penalty_start)) # function.add_prox(penalties.L1(l, penalty_start=penalty_start)) fista = proximal.FISTA(eps=mu_min, max_iter=23500) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr # assert berr < 5 assert_less(berr, 5.0, "The found regression vector is not correct.") # Test proximal operator function = CombinedFunction() function.add_loss(losses.LinearRegression(X, y, mean=False)) A = nesterov.l1.linear_operator_from_variables( p, penalty_start=penalty_start) function.add_prox( nesterov.l1.L1(l, A=A, mu=mu_min, penalty_start=penalty_start)) fista = proximal.FISTA(eps=mu_min, max_iter=20000) beta = fista.run(function, beta) berr = np.linalg.norm(beta - beta_star) # print "berr:", berr # assert berr < 0.1 assert_less(berr, 0.1, "The found regression vector is not correct.")