def load_globals(config):
import mapreduce as GLOBAL # access to global variables
GLOBAL.DATA = GLOBAL.load_data(config["data"])
IM_SHAPE = config["im_shape"]
A= sparse.vstack(nesterov_tv.linear_operator_from_shape(IM_SHAPE))
N_COMP = config["n_comp"]
GLOBAL.A,GLOBAL.N_COMP = A,N_COMP
def test_tvhelper_linear_operator_from_shape(self):
import parsimony.functions.nesterov.tv as tv
dx = 5 # p should be odd
shape = (dx, dx, dx)
# A_from_shape
p = np.prod(shape)
beta = np.zeros(p)
beta[0:p:2] = 1 # checkerboard of 0 and 1
A = tv.linear_operator_from_shape(shape)
tvfunc = tv.TotalVariation(l=1.0, A=A)
assert tvfunc.f(beta) == self._f_checkerboard_cube(shape)
alpha=alpha / 1000 * n_train,
l1_ratio=.5,
fit_intercept=True)
MODELS["2d_l1l2_inter_fista"] = \
estimators.ElasticNetLogisticRegression(alpha=alpha / 10, l=.5,
penalty_start=1,
algorithm_params=algorithm_params)
## LogisticRegressionL1L2TV, Parsimony only
# Minimize:
# f(beta, X, y) = - loglik/n_train
# + k/2 * ||beta||^2_2
# + l * ||beta||_1
# + g * TV(beta)
A = nesterov_tv.linear_operator_from_shape(beta3d.shape)
l1, l2, tv = alpha * np.array((.05, .75, .2)) # l2, l1, tv penalties
MODELS["2d_l1l2tv_fista"] = \
estimators.LogisticRegressionL1L2TV(
l1, l2, tv, A,
algorithm=algorithms.proximal.FISTA(),
algorithm_params=algorithm_params)
MODELS["2d_l1l2tv_inter_fista"] = \
estimators.LogisticRegressionL1L2TV(
l1, l2, tv, A, penalty_start=1,
algorithm=algorithms.proximal.FISTA(),
algorithm_params=algorithm_params)
X = X3d.reshape((n_samples, np.prod(shape)))
###############################################################################
from sklearn.decomposition import PCA
pca = PCA(n_components=3)
pca.fit(X)
print(pca.explained_variance_ratio_)
###############################################################################
# PCA-TV
l1max = PCAL1L2TV.l1_max(X)
alpha = l1max
l1, l2, tv = alpha * np.array((.05, 1, .1)) # l1, l2, tv penalties
Atv = nesterov_tv.linear_operator_from_shape(shape)
pcatv = PCAL1L2TV(l1,
l2,
tv,
Atv,
n_components=3,
eps=1e-6,
max_iter=100,
inner_max_iter=int(1e3),
verbose=True)
pcatv.fit(X)
np.sum(np.abs(pcatv.V) > 1e-6, axis=0)
###############################################################################
# Plot
@license: BSD 3-clause.
"""
#import numpy.random
import numpy as np
import parsimony.datasets
import parsimony.functions.nesterov.tv as tv
from parsimony.functions import PCA_L1_TV
from parsimony.algorithms.multiblock import MultiblockProjectedGradientMethod
import parsimony.utils.weights as weights
n_samples = 500
shape = (30, 30, 1)
X3d, y, beta3d = parsimony.datasets.make_regression_struct(n_samples=n_samples,
shape=shape, r2=.75, random_seed=1)
X = X3d.reshape((n_samples, np.prod(shape)))
A = tv.linear_operator_from_shape(shape)
start_vector = weights.RandomStartVector()
w = start_vector.get_vector(X.shape[1])
alpha = 10.
k, l, g = alpha * np.array((.1, .4, .5)) # l2, l1, tv penalties
# run /home/fh235918/git/pylearn-parsimony/parsimony/functions/functions.py
func = PCA_L1_TV(X, k, l, g, A, mu=0.0001)
#algo = MultiblockProjectedGradientMethod(max_iter=10)
#
## w_x = start_vector_x.get_vector(X.shape[1])
## w_y = start_vector_y.get_vector(Y.shape[1])
#
#algo.run(func, w)
#import numpy.random
import numpy as np
import parsimony.datasets
import parsimony.functions.nesterov.tv as tv
from parsimony.functions import PCA_L1_TV
from parsimony.algorithms.multiblock import MultiblockProjectedGradientMethod
import parsimony.utils.weights as weights
n_samples = 500
shape = (30, 30, 1)
X3d, y, beta3d = parsimony.datasets.make_regression_struct(n_samples=n_samples,
shape=shape,
r2=.75,
random_seed=1)
X = X3d.reshape((n_samples, np.prod(shape)))
A = tv.linear_operator_from_shape(shape)
start_vector = weights.RandomStartVector()
w = start_vector.get_vector(X.shape[1])
alpha = 10.
k, l, g = alpha * np.array((.1, .4, .5)) # l2, l1, tv penalties
# run /home/fh235918/git/pylearn-parsimony/parsimony/functions/functions.py
func = PCA_L1_TV(X, k, l, g, A, mu=0.0001)
#algo = MultiblockProjectedGradientMethod(max_iter=10)
#
## w_x = start_vector_x.get_vector(X.shape[1])
## w_y = start_vector_y.get_vector(Y.shape[1])
#
#algo.run(func, w)
def test_tvhelper_linear_operator_from_mask(self):
import parsimony.functions.nesterov.tv as tv
## Simple mask with offset
shape = (5, 4)
mask = np.zeros(shape)
mask[1:(shape[0] - 1), 0:(shape[1] - 1)] = 1
Ax_ = np.matrix(
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, -1, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, -1, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, -1, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, -1, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, -1, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, -1, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
Ay_ = np.matrix(
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, -1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, -1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, -1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, -1, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, -1, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
A = tv.linear_operator_from_mask(mask, offset=1)
Ax, Ay, Az = A
assert np.all(Ax.todense() == Ax_)
assert np.all(Ay.todense() == Ay_)
assert np.sum(Az.todense() == 0)
#######################################################################
## GROUP TV
shape = (6, 4)
mask = np.zeros(shape, dtype=int)
mask[:3, :3] = 1
mask[3:6, 1:4] = 2
Ax_ = np.matrix(
[[-1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
Ay_ = np.matrix(
[[-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
A = tv.linear_operator_from_mask(mask)
Ax, Ay, Az = A
assert np.all(Ax.todense() == Ax_)
assert np.all(Ay.todense() == Ay_)
assert np.sum(Az.todense() == 0)
#######################################################################
## test function tv on checkerboard
#######################################################################
dx = 5 # p should be odd
shape = (dx, dx, dx)
# linear_operator_from_masks
mask = np.zeros(shape)
mask[1:(dx - 1), 1:(dx - 1), 1:(dx - 1)] = 1
p = np.prod((dx - 2, dx - 2, dx - 2))
beta = np.zeros(p)
beta[0:p:2] = 1 # checkerboard of 0 and 1
A = tv.linear_operator_from_mask(mask)
tvfunc = tv.TotalVariation(l=1., A=A)
assert tvfunc.f(beta) == self._f_checkerboard_cube((dx - 2,
dx - 2,
dx - 2))
# linear_operator_from_masks with group
mask = np.zeros(shape)
# 4 groups
mask[0:(dx / 2), 0:(dx / 2), :] = 1
mask[0:(dx / 2), (dx / 2):dx, :] = 2
mask[(dx / 2):dx, 0:(dx / 2), :] = 3
mask[(dx / 2):dx, (dx / 2):dx, :] = 4
p = np.prod((dx, dx, dx))
beta = np.zeros(p)
beta[0:p:2] = 1 # checkerboard of 0 and 1
A = tv.linear_operator_from_mask(mask)
tvfunc = tv.TotalVariation(l=1., A=A)
assert np.allclose(tvfunc.f(beta),
self._f_checkerboard_cube((dx / 2, dx / 2, dx)) +
self._f_checkerboard_cube((dx / 2, dx / 2 + 1, dx)) +
self._f_checkerboard_cube((dx / 2 + 1, dx / 2, dx)) +
self._f_checkerboard_cube((dx / 2 + 1, dx / 2 + 1, dx)))
shape = (2, 3)
mask = np.ones(shape)
weights1D = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]
#weights2D = np.reshape(weights1D, shape)
A_shape = tv.linear_operator_from_shape(shape, weights1D)
#A_mask = tv.linear_operator_from_subset_mask(mask, weights2D)
A_true = (np.array([[-1., 1., 0., 0., 0., 0.],
[0., -2., 2., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.],
[0., 0., 0., -4., 4., 0.],
[0., 0., 0., 0., -5., 5.],
[0., 0., 0., 0., 0., 0.]]),
np.array([[-1., 0., 0., 1., 0., 0.],
[0., -2., 0., 0., 2., 0.],
[0., 0., -3., 0., 0., 3.],
[0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.]]),
np.array([[0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0.]]))
assert np.array_equal(A_true[0], A_shape[0].todense())
assert np.array_equal(A_shape[0].todense(), A_shape[0].todense())
assert np.array_equal(A_true[1], A_shape[1].todense())
assert np.array_equal(A_shape[1].todense(), A_shape[1].todense())
assert np.array_equal(A_true[2], A_shape[2].todense())
assert np.array_equal(A_shape[2].todense(), A_shape[2].todense())
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
ridge_prsmy = estimators.RidgeLogisticRegression(alpha)
yte_pred_ridge_prsmy = ridge_prsmy.fit(Xtr, ytr).predict(Xte)
_, recall_ridge_prsmy, _, _ = \
precision_recall_fscore_support(yte, yte_pred_ridge_prsmy, average=None)
# EldasticNet
enet = estimators.ElasticNetLogisticRegression(l=0.5, alpha=alpha)
yte_pred_enet = enet.fit(Xtr, ytr).predict(Xte)
_, recall_enet, _, _ = \
precision_recall_fscore_support(yte, yte_pred_enet, average=None)
# GraphNet
# l1, l2, gn = alpha * np.array((.05, .75, .2)) # l1, l2, gn penalties
l1, l2, gn = alpha * np.array((.33, .33, 33)) # l1, l2, gn penalties
A = sparse.vstack(nesterov_tv.linear_operator_from_shape(shape))
enetgn = estimators.LogisticRegressionL1L2GraphNet(l1, l2, gn, A)
yte_pred_enetgn = enetgn.fit(Xtr, ytr).predict(Xte)
_, recall_enetgn, _, _ = \
precision_recall_fscore_support(yte, yte_pred_enetgn, average=None)
# LogisticRegressionL1L2TV
l1, l2, tv = alpha * np.array((.05, .75, .2)) # l1, l2, tv penalties
# l1, l2, tv = alpha * np.array((.33, .33, 33)) # l1, l2, gn penalties
A = nesterov_tv.linear_operator_from_shape(beta3d.shape)
enettv = estimators.LogisticRegressionL1L2TV(l1,
l2,
tv,
A,
algorithm_params=dict(eps=1e-5))
yte_pred_enettv = enettv.fit(Xtr, ytr).predict(Xte)
ridge_prsmy = estimators.RidgeLogisticRegression(alpha)
yte_pred_ridge_prsmy = ridge_prsmy.fit(Xtr, ytr).predict(Xte)
_, recall_ridge_prsmy, _, _ = precision_recall_fscore_support(yte, yte_pred_ridge_prsmy, average=None)
###########################################################################
## LogisticRegressionL1L2TV
# Minimize:
# f(beta, X, y) = - loglik/n_train
# + l2/2 * ||beta||^2_2
# + l1 * ||beta||_1
# + tv * TV(beta)
l1, l2, tv = alpha * np.array((.05, .75, .2)) # l1, l2, tv penalties
## Limit the precison to 1e-3
A = nesterov_tv.linear_operator_from_shape(beta3d.shape)
enettv = estimators.LogisticRegressionL1L2TV(l1, l2, tv, A, algorithm_params = dict(eps=1e-3))
yte_pred_enettv = enettv.fit(Xtr, ytr).predict(Xte)
_, recall_enettv, _, _ = precision_recall_fscore_support(yte, yte_pred_enettv, average=None)
###########################################################################
## Plot
plot = plt.subplot(221)
limits = None #np.array((beta3d.min(), beta3d.max())) / 2.
#limits = None
utils.plot_map2d(beta3d.reshape(shape), plot, title="beta star")
plot = plt.subplot(222)
utils.plot_map2d(enettv.beta.reshape(shape), plot, limits=limits,
title="L1+L2+TV (%.2f, %.2f)" % tuple(recall_enettv))
plot = plt.subplot(223)
utils.plot_map2d(ridge_sklrn.coef_.reshape(shape), plot, limits=limits,
ytr = y[:n_train]
Xte = X[n_train:, :]
yte = y[n_train:]
alpha = 1. # global penalty
###############################################################################
# Estimators
# Fit RidgeRegression
rr = estimators.RidgeRegression(l=alpha)
rr.fit(Xtr, ytr)
yte_pred_rr = rr.fit(Xtr, ytr).predict(Xte)
# Fit GraphNet
l1, l2, gn = alpha * np.array((.33, .33, 33)) # l1, l2, gn penalties
A = sparse.vstack(nesterov_tv.linear_operator_from_shape(shape))
enetgn = estimators.LinearRegressionL1L2GraphNet(l1, l2, gn, A)
yte_pred_enetgn = enetgn.fit(Xtr, ytr).predict(Xte)
# Fit LinearRegressionL1L2TV
l1, l2, tv = alpha * np.array((.33, .33, .33)) # l1, l2, tv penalties
Atv = nesterov_tv.linear_operator_from_shape(shape)
enettv = estimators.LinearRegressionL1L2TV(l1,
l2,
tv,
Atv,
algorithm_params=dict(max_iter=500))
yte_pred_enettv = enettv.fit(Xtr, ytr).predict(Xte)
###############################################################################
# Plot
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_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
#
# Empirically set the global penalty, based on maximum l1 penaly
alpha = l1_max_logistic_loss(X, y)
###############################################################################
# Penalization parameters are now vectors of equal length
l1 = alpha * np.array([0.5, 0.5, 0.5])
l2 = alpha * np.array([0.5, 0.5, 0.5])
tv = alpha * np.array([0.01, 0.2, 0.8])
max_iter = 1000
###############################################################################
# Build linear operator and fit the model:
A = nesterov_tv.linear_operator_from_shape(beta3d.shape, calc_lambda_max=True)
enettv = estimators.LogisticRegressionL1L2TV(
l1=l1,
l2=l2,
tv=tv,
A = A,
algorithm_params=dict(max_iter=max_iter))
enettv.fit(X, y)
###############################################################################
# Plot coeffitients maps
plt.clf()
plot = plt.subplot(221)
utils.plots.map2d(beta3d, plot, title="beta star")
# Create data
n = 20
natural_shape = px, py, pz = (10, 10, 10)
p = np.prod(natural_shape)
data_shape = n, p
# Uniform data
X = np.random.rand(n, p)
# Multiply some variables to increase variance along them
X[:, 0] = 3 * X[:, 0]
X[:, 1] = 5 * X[:, 1]
# Scale
X = sklearn.preprocessing.scale(X, with_mean=True, with_std=False)
# A matrices
Atv = nesterov_tv.linear_operator_from_shape(natural_shape)
# Test function
l1 = 1
l2 = 1
ltv = 1
u = np.random.rand(n, 1)
u /= np.linalg.norm(u)
f = pca_tv.RightSingularL1L2SmoothedTV_CONESTA(X, u, l1, l2, ltv, Atv)
# Fit an estimator without l1 and TV constraints and compare to PCA
e_con = pca_tv.PCAL1L2TV(l1=0.0,
l2=1.0,
ltv=6e-8,
Atv=Atv,
n_components=2,
# + alpha * l * ||beta||_1
# + alpha * ((1.0 - l) / 2) * ||beta||²_2
# Parsimony Elasticnet is based on FISTA, is then slower that scikit-learn one
l1_ratio = .5
enet = estimators.ElasticNet(alpha=alpha, l=.5)
yte_pred_enet = enet.fit(Xtr, ytr).predict(Xte)
###########################################################################
## Fit LinearRegressionL1L2TV
# Min: (1 / (2 * n)) * ||Xbeta - y||^2_2
# + l1 * ||beta||_1
# + (l2 / 2) * ||beta||^2_2
# + tv * TV(beta)
#
l1, l2, tv = alpha * np.array((.33, .33, .33)) # l1, l2, tv penalties
A = nesterov_tv.linear_operator_from_shape(shape)
algo = algorithms.proximal.CONESTA(max_iter=500)
enettv = estimators.LinearRegressionL1L2TV(l1, l2, tv, A, algorithm=algo)
yte_pred_enettv = enettv.fit(Xtr, ytr).predict(Xte)
###########################################################################
## Plot
# TODO: Please remove dependence on scikit-learn. Add required functionality
# to parsimony instead.
plot = plt.subplot(131)
utils.plot_map2d(beta3d.reshape(shape), plot, title="beta star")
plot = plt.subplot(132)
utils.plot_map2d(enet.beta.reshape(shape), plot, title="beta enet (R2=%.2f)" %
r2_score(yte, yte_pred_enet))
#utils.plot_map2d(enet.coef_.reshape(shape), plot, title="beta enet (R2=%.2f)" %
