def test_proximal_fast_gm_nonsmooth():
# Minimize ||x||_1.
oracle = oracles.create_lasso_prox_oracle(np.zeros([2, 2]),
np.zeros(2),
regcoef=1.0)
x_0 = np.array([2.0, -1.0])
[x_star, status,
hist] = optimization.proximal_fast_gradient_method(oracle,
x_0,
trace=True)
eq_(status, 'success')
ok_(np.allclose(x_star, np.array([7.64497775e-06, 0.0])))
ok_(
np.allclose(
np.array(hist['func']),
np.array([[
3.0, 1.0, 0.2679491924311227, 0.099179721203666166,
0.041815858679730096, 0.018850854415891891,
0.0088302704548977509, 0.0042337678350286671,
0.0020598280587097542, 0.0010116006643634953,
0.00049984569823222113, 0.00024797029202045391,
0.00012334133663333596, 6.1457610088328345e-05,
3.0658125993932962e-05, 1.5305578515886715e-05,
7.6449777454652732e-06
]])))
def experiment_3(parameter='n', method='subgradient', seed=31415):
# n, m and lambda
n, m, reg_coef = 500, 500, 1.0
np.random.seed(seed)
grids = dict()
grids['n'] = [10, 100, 1000]
grids['m'] = [10, 100, 1000]
grids['reg_coef'] = [0.01, 0.1, 1.0, 10.0]
fig1, ax1 = plt.subplots()
fig2, ax2 = plt.subplots()
ax1.set_xlabel('Номер итерации')
ax1.set_ylabel('Гарантированная точность по зазору двойственности')
ax1.grid()
ax1.set_yscale('log')
ax2.set_xlabel('Время от начала эксперимента')
ax2.set_ylabel('Гарантированная точность по зазору двойственности')
ax2.grid()
ax2.set_yscale('log')
os.makedirs("report/pics/3", exist_ok=True)
experiment_parameters = {'n': n, 'm': m, 'reg_coef': 1.0}
for value in grids[parameter]:
experiment_parameters[parameter] = value
A = np.random.randn(experiment_parameters['m'], experiment_parameters['n'])
b = np.random.randn(experiment_parameters['m'])
x_0 = np.ones(experiment_parameters['n'])
reg_coef = experiment_parameters['reg_coef']
if method == 'subgradient':
oracle = create_lasso_nonsmooth_oracle(A, b, reg_coef)
x_opt, message, history = subgradient_method(oracle, x_0, trace=True, max_iter=10000)
if method == 'proximal':
oracle = create_lasso_prox_oracle(A, b, reg_coef)
x_opt, message, history = proximal_gradient_method(oracle, x_0, trace=True, max_iter=10000)
if method == 'proximal_fast':
oracle = create_lasso_prox_oracle(A, b, reg_coef)
x_opt, message, history = proximal_fast_gradient_method(oracle, x_0, trace=True, max_iter=10000)
ax1.plot(history['duality_gap'], label=f'{parameter}={value}')
ax2.plot(history['time'], history['duality_gap'], label=f'{parameter}={value}')
ax1.legend()
ax2.legend()
os.makedirs(f"report/pics/3/{method}", exist_ok=True)
fig1.savefig(f"report/pics/3/{method}/lasso_gap_vs_iter_{parameter}.pdf", bbox_inches='tight')
fig2.savefig(f"report/pics/3/{method}/lasso_gap_vs_time_{parameter}.pdf", bbox_inches='tight')
def proximal_fast_gm_one_step():
# Simple smooth quadratic task.
A = np.eye(2)
b = np.array([1.0, 0.0])
oracle = oracles.create_lasso_prox_oracle(A, b, regcoef=0.0)
x_0 = np.zeros(2)
x_star, status, hist = optimization.proximal_fast_gradient_method(
oracle, x_0, trace=True)
eq_(status, 'success')
ok_(np.allclose(x_star, np.array([1.0, 0.0])))
ok_(np.allclose(np.array(hist['func']), np.array([0.5, 0.0])))
def test_proximal_fast_gm_nonsmooth2():
oracle = oracles.create_lasso_prox_oracle(np.array([[1, 2, 3], [4, 5, 6]]),
np.array([1, 4]),
regcoef=1.0)
x_0 = np.array([1, 1, -1])
x_star, status, hist = optimization.proximal_fast_gradient_method(
oracle, x_0, trace=True, max_iter=3)
eq_(status, 'iterations_exceeded')
ok_(np.allclose(x_star, np.array([[1.01714486, 1.04658812, -0.85594606]])))
ok_(
np.allclose(
np.array(hist['func']),
np.array(
[4.0, 3.219970703125, 3.0946475565433502,
3.0380920410969945])))
def experiment_2():
np.random.seed(31415)
data_path = "data"
datasets = ["bodyfat", "housing"]
for dataset in datasets:
print("___________________________")
logging.info(f"{dataset} is in process...")
A, b = load_svmlight_file(os.path.join(data_path, dataset))
fig, ax = plt.subplots(figsize=(12, 8))
ax.set_xlabel('Номер итерации')
ax.set_ylabel('Суммарное число шагов подбора L')
ax.grid()
oracle = create_lasso_prox_oracle(A, b, 1.0)
print(A.shape, 1 - A.size / (A.shape[0] * A.shape[1]), np.linalg.matrix_rank(A.toarray()))
n = A.shape[1]
x0 = np.random.randn(n)
x_opt, message, history_usual = proximal_gradient_method(oracle, x0, trace=True, max_iter=10000)
x_opt, message, history_fast = proximal_fast_gradient_method(oracle, x0, trace=True, max_iter=10000)
sum_int_steps_usual = list(accumulate(history_usual['int_steps']))
sum_int_steps_fast = list(accumulate(history_fast['int_steps']))
ax.plot(sum_int_steps_usual, label="Usual proximal method")
ax.plot(sum_int_steps_fast, label=f'Fast proximal method')
ax.legend()
os.makedirs("report/pics/2", exist_ok=True)
fig.savefig(f"report/pics/2/prox_methods_steps_{dataset}.pdf", bbox_inches='tight')
