def test_smooth_1D_l2(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, 15
shape = (1, 1, p)
l = 0.0
k = 0.1 # Must have some regularisation for all variables.
g = 0.9
start_vector = weights.RandomUniformWeights(normalise=True)
beta = start_vector.get_weights(p)
rects = [[(0, 5)], [(4, 10)], [(13, 15)]]
# 0 [ 5 ] 0
# 1 [ 5 ] 0
# 2 [ 5 ] 0
# 3 [ 5 ] 0
# 4 [ 4 ] 0 / 1
beta[:5, :] = 5.0 # 5 [ 3 ] 1
beta[4, :] = 4.0 # 6 [ 3 ] 1
beta[5:10, :] = 3.0 # 7 [ 3 ] 1
beta[13:15, :] = 7.0 # 8 [ 3 ] 1
# 9 [ 3 ] 1
# 0 [ x ] -
# 1 [ x ] -
# 2 [ x ] -
# 3 [ 7 ] 2
# 4 [ 7 ] 2
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 = 12000
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_penalty(functions.penalties.L2Squared(l=k,
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_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_overlapping_smooth(self):
import numpy as np
from parsimony.functions import CombinedFunction
import parsimony.functions as functions
import parsimony.functions.nesterov.gl as gl
import parsimony.datasets.simulate.l1_l2_glmu as l1_l2_glmu
import parsimony.utils.weights as weights
np.random.seed(314)
# 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 = 0.0
k = 0.0
g = 0.9
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
mu_min = 5e-8
X, y, beta_star = l1_l2_glmu.load(l,
k,
g,
beta,
M,
e,
A,
mu=mu_min,
snr=snr)
eps = 1e-8
max_iter = 15000
beta_start = start_vector.get_weights(p)
mus = [5e-0, 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 = 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(
gl.GroupLassoOverlap(l=g, A=A, mu=mu, penalty_start=0))
beta_parsimony = fista.run(function, beta_parsimony)
berr = np.linalg.norm(beta_parsimony - beta_star)
# print berr
assert berr < 5e-2
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_overlapping_smooth(self):
import numpy as np
from parsimony.functions import CombinedFunction
import parsimony.functions as functions
import parsimony.functions.nesterov.gl as gl
import parsimony.datasets.simulate.l1_l2_glmu as l1_l2_glmu
import parsimony.utils.start_vectors as start_vectors
np.random.seed(314)
# 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 = 0.0
k = 0.0
g = 0.9
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_min = 5e-8
X, y, beta_star = l1_l2_glmu.load(l, k, g, beta, M, e, A,
mu=mu_min, snr=snr)
eps = 1e-8
max_iter = 15000
beta_start = start_vector.get_vector(p)
mus = [5e-0, 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 = 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(gl.GroupLassoOverlap(l=g, A=A, mu=mu,
penalty_start=0))
beta_parsimony = fista.run(function, beta_parsimony)
berr = np.linalg.norm(beta_parsimony - beta_star)
# print berr
assert berr < 5e-2
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-7
class MultiblockFISTA(bases.ExplicitAlgorithm,
bases.IterativeAlgorithm,
bases.InformationAlgorithm):
""" The projected gradient algorithm with alternating minimisations in a
multiblock setting.
Parameters
----------
info : List or tuple of utils.consts.Info. What, if any, extra run
information should be stored. Default is an empty list, which means
that no run information is computed nor returned.
eps : Positive float. Tolerance for the stopping criterion.
outer_iter : Non-negative integer. Maximum allowed number of outer loop
iterations.
max_iter : Non-negative integer. Maximum allowed number of iterations.
min_iter : Non-negative integer less than or equal to max_iter. Minimum
number of iterations that must be performed. Default is 1.
"""
INTERFACES = [multiblock_properties.MultiblockFunction,
multiblock_properties.MultiblockGradient,
multiblock_properties.MultiblockProjectionOperator,
multiblock_properties.MultiblockStepSize]
INFO_PROVIDED = [Info.ok,
Info.num_iter,
Info.time,
Info.fvalue,
Info.converged]
def __init__(self, info=[], outer_iter=20,
eps=consts.TOLERANCE,
max_iter=consts.MAX_ITER, min_iter=1):
super(MultiblockFISTA, self).__init__(info=info,
max_iter=max_iter,
min_iter=min_iter)
self.outer_iter = outer_iter
self.eps = float(eps)
# from parsimony.algorithms.primaldual import NaiveCONESTA
# Copy the allowed info keys for FISTA.
self.fista_info = list()
for nfo in self.info_copy():
if nfo in FISTA.INFO_PROVIDED:
self.fista_info.append(nfo)
# if not self.fista_info.allows(Info.num_iter):
# self.fista_info.add_key(Info.num_iter)
if Info.converged not in self.fista_info:
self.fista_info.append(Info.converged)
# self.algorithm = FISTA(info=self.fista_info,
# eps=self.eps,
# max_iter=self.max_iter,
# min_iter=self.min_iter)
# self.algorithm = algorithms.StaticCONESTA(mu_start=1.0,
# info=self.info,
# eps=self.eps,
# max_iter=self.max_iter,
# min_iter=self.min_iter)
@bases.force_reset
@bases.check_compatibility
def run(self, function, w):
if self.info_requested(Info.ok):
self.info_set(Info.ok, False)
if self.info_requested(Info.time):
t = [0.0]
if self.info_requested(Info.fvalue):
f = [function.f(w)]
if self.info_requested(Info.converged):
self.info_set(Info.converged, False)
self.algorithm = FISTA(info=self.fista_info,
eps=self.eps,
max_iter=self.max_iter,
min_iter=self.min_iter)
print "len(w):", len(w)
print "max_iter:", self.algorithm.max_iter
num_iter = [0] * len(w)
# w_old = [0] * len(w)
# it = 0
# while True:
for it in xrange(1, self.outer_iter + 1):
all_converged = True
for i in xrange(len(w)):
print "it: %d, i: %d" % (it, i)
# for j in xrange(len(w)):
# w_old[j] = w[j]
if i == 0:
pass
if i == 1:
pass
if i == 2:
pass
func = mb_losses.MultiblockFunctionWrapper(function, w, i)
# self.fista_info.clear()
# self.algorithm.set_params(max_iter=self.max_iter - num_iter[i])
# w[i] = self.algorithm.run(func, w_old[i])
w[i] = self.algorithm.run(func, w[i])
num_iter[i] += self.algorithm.num_iter
if self.algorithm.info_requested(Info.time):
tval = self.algorithm.info_get(Info.time)
if self.algorithm.info_requested(Info.fvalue):
fval = self.algorithm.info_get(Info.fvalue)
# if Info.converged in self.fista_info:
# if not self.fista_info[Info.converged] \
# or self.fista_info[Info.num_iter] > 1:
# all_converged = False
# if maths.norm(w_old[i] - w[i]) < self.eps:
# converged = True
# break
if self.info_requested(Info.time):
t = t + tval
if self.info_requested(Info.fvalue):
f = f + fval
print "l0 :", maths.norm0(w[i]), \
", l1 :", maths.norm1(w[i]), \
", l2²:", maths.norm(w[i]) ** 2.0
if self.algorithm.info_requested(Info.fvalue):
print "f:", fval[-1]
for i in xrange(len(w)):
# Take one ISTA step for use in the stopping criterion.
step = function.step(w, i)
w_tilde = function.prox(w[:i] +
[w[i] - step * function.grad(w, i)] +
w[i + 1:], i, step)
# func = mb_losses.MultiblockFunctionWrapper(function, w, i)
# step2 = func.step(w[i])
# w_tilde2 = func.prox(w[i] - step2 * func.grad(w[i]), step2)
#
# print "diff:", maths.norm(w_tilde - w_tilde2)
# print "err:", maths.norm(w[i] - w_tilde) * (1.0 / step)
if maths.norm(w[i] - w_tilde) > step * self.eps:
all_converged = False
break
if all_converged:
print "All converged!"
if self.info_requested(Info.converged):
self.info_set(Info.converged, True)
break
# # If all blocks have used max_iter iterations, stop.
# if np.all(np.asarray(num_iter) >= self.max_iter):
# break
# it += 1
if self.info_requested(Info.num_iter):
self.info_set(Info.num_iter, num_iter)
if self.info_requested(Info.time):
self.info_set(Info.time, t)
if self.info_requested(Info.fvalue):
self.info_set(Info.fvalue, f)
if self.info_requested(Info.ok):
self.info_set(Info.ok, True)
return w