def test_trace_1():
B = np.ones((3, 3))
X = np.random.randn(100, 9)
y = np.dot(X, B.ravel('F')) + .1 * np.random.randn(100)
alpha = 10.
B_, _ = mt.trace(X, y, alpha, 0., (3, 3), rtol=1e-10)
# KKT conditions
grad = - np.dot(X.T, y - np.dot(X, B_.ravel('F')))
M = (grad / alpha).reshape(B.shape, order='F')
assert np.all(linalg.svdvals(M) < 1. + 1e-3)
testing.assert_allclose(np.dot(M.ravel('F'), B_.ravel('F')),
- linalg.svdvals(B_).sum())
import numpy as np
import multitask as mt
from scipy import linalg
import pylab as pl
n_samples, n_features = 1000, 100
X = np.random.randn(n_samples, n_features)
y = np.random.randn(n_samples)
res = []
for alpha in np.logspace(-1, 3, 100):
print('alpha: %s' % alpha)
B_, gap_ = mt.trace(X, y, alpha, 0., (10, 10), rtol=1e-10, verbose=True, max_iter=1000)
s = linalg.svdvals(B_)
pl.scatter(alpha * np.ones_like(s), s)
ax = pl.gca()
ax.set_xscale('log')
pl.show()
loss.append(.5 * (linalg.norm(Y_train - X.dot(w)) ** 2))
timings.append((datetime.now() - start).total_seconds())
u0 = np.repeat(canonical, n_task).reshape((-1, n_task))
start = datetime.now()
u = np.zeros((size_u, n_task))
for j in range(n_task):
alpha_max = linalg.norm(
X.T.dot(Y_train[:, j]).reshape((size_u, size_v)), 2)
alpha = alpha_max / 2
print('Voxel %s' % j)
while True:
print('alpha: %s' % alpha)
out = mt.trace(
X, Y_train[:, j], alpha, 0., (size_u, size_v),
rtol=1e-6, verbose=True)
ss = linalg.svdvals(out[0])
print(ss[1:].sum())
if ss[1:].sum() < 1e-3:
_u, _s, _vt = splinalg.svds(out[0], 1)
break
else:
alpha_old = alpha
alpha = (alpha_max + alpha) / 2.
u[:, j] = _u.ravel()
tmp = (u.T - u.mean(0)[:, None]).T
sgn = np.sign(tmp.T.dot(u0.ravel('F')[:size_u] - u0.mean()))