from regreg.algorithms import FISTA from regreg.smooth import l2normsq from regreg.atoms import l1norm, maxnorm from regreg.seminorm import seminorm sparsity = l1norm(500, l=1.3) D = (np.identity(500) + np.diag([-1]*499,k=1))[:-1] D = scipy.sparse.csr_matrix(D) fused = l1norm(D, l=20) penalty = seminorm(sparsity,fused) Y = np.random.standard_normal(500); Y[100:150] += 7; Y[250:300] += 14 loss = l2normsq.shift(-Y, l=0.5) problem = loss.add_seminorm(penalty) solver = FISTA(problem) solver.fit(max_its=100, tol=1e-10) solution = solver.problem.coefs import pylab pylab.scatter(np.arange(Y.shape[0]), Y, c='r') pylab.plot(solution, color='yellow', linewidth=5) l1_fused = np.fabs(D * solution).sum() l1_sparsity = np.fabs(solution).sum() new_fused = l1norm(D, l=l1_fused) new_sparsity = l1norm(500, l=l1_sparsity) conjugate = l2normsq.shift(Y, l=0.5)
import pylab from scipy import sparse from regreg.algorithms import FISTA from regreg.atoms import positive_part from regreg.container import container from regreg.smooth import l2normsq n = 100 Y = np.random.standard_normal(n) Y[:-30] += np.arange(n - 30) * 0.2 D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:] nisotonic = positive_part.linear(-sparse.csr_matrix(D), l=3) loss = l2normsq.shift(-Y, l=0.5) p = container(loss, nisotonic) solver = FISTA(p.problem()) vals = solver.fit(max_its=25000, tol=1e-05) soln = solver.problem.coefs.copy() nisotonic.atoms[0].l = 100. solver.fit(max_its=25000, tol=1e-05) soln2 = solver.problem.coefs.copy() nisotonic.atoms[0].l = 1000. solver.fit(max_its=25000, tol=1e-05) soln3 = solver.problem.coefs.copy() X = np.arange(n)
import numpy as np import pylab from scipy import sparse from regreg.algorithms import FISTA from regreg.atoms import l1norm from regreg.container import container from regreg.smooth import l2normsq Y = np.random.standard_normal(500); Y[100:150] += 7; Y[250:300] += 14 loss = l2normsq.shift(-Y, coef=0.5) sparsity = l1norm(len(Y), 1.4) # TODO should make a module to compute typical Ds D = sparse.csr_matrix((np.identity(500) + np.diag([-1]*499,k=1))[:-1]) fused = l1norm.linear(D, 25.5) problem = container(loss, sparsity, fused) solver = FISTA(problem.composite()) solver.fit(max_its=100, tol=1e-10) solution = solver.composite.coefs delta1 = np.fabs(D * solution).sum() delta2 = np.fabs(solution).sum() fused_constraint = l1norm.linear(D, bound=delta1) sparsity_constraint = l1norm(500, bound=delta2) constrained_problem = container(loss, fused_constraint, sparsity_constraint) constrained_solver = FISTA(constrained_problem.composite()) constrained_solver.composite.lipshitz = 1.01
from regreg.algorithms import FISTA from regreg.atoms import positive_part from regreg.container import container from regreg.smooth import l2normsq n = 100 Y = np.random.standard_normal(n) Y[:-30] += np.arange(n-30) * 0.2 D = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:] nisotonic = positive_part.linear(-sparse.csr_matrix(D), l=3) loss = l2normsq.shift(-Y,l=0.5) p = container(loss, nisotonic) solver=FISTA(p.problem()) vals = solver.fit(max_its=25000, tol=1e-05) soln = solver.problem.coefs.copy() nisotonic.atoms[0].l = 100. solver.fit(max_its=25000, tol=1e-05) soln2 = solver.problem.coefs.copy() nisotonic.atoms[0].l = 1000. solver.fit(max_its=25000, tol=1e-05) soln3 = solver.problem.coefs.copy() X = np.arange(n)
import numpy as np import pylab from scipy import sparse from regreg.algorithms import FISTA from regreg.atoms import l1norm from regreg.container import container from regreg.smooth import l2normsq Y = np.random.standard_normal(500) Y[100:150] += 7 Y[250:300] += 14 loss = l2normsq.shift(-Y, coef=0.5) sparsity = l1norm(len(Y), 1.4) # TODO should make a module to compute typical Ds D = sparse.csr_matrix((np.identity(500) + np.diag([-1] * 499, k=1))[:-1]) fused = l1norm.linear(D, 25.5) problem = container(loss, sparsity, fused) solver = FISTA(problem.composite()) solver.fit(max_its=100, tol=1e-10) solution = solver.composite.coefs delta1 = np.fabs(D * solution).sum() delta2 = np.fabs(solution).sum() fused_constraint = l1norm.linear(D, bound=delta1) sparsity_constraint = l1norm(500, bound=delta2) constrained_problem = container(loss, fused_constraint, sparsity_constraint)