def test_changepoint_scaled():
p = 150
M = multiscale(p)
M.minsize = 10
X = ra.adjoint(M)
Y = np.random.standard_normal(p)
Y[20:50] += 8
Y += 2
meanY = Y.mean()
lammax = np.fabs(np.sqrt(M.sizes) * X.adjoint_map(Y) / (1 + np.sqrt(np.log(M.sizes)))).max()
penalty = rr.weighted_l1norm((1 + np.sqrt(np.log(M.sizes))) / np.sqrt(M.sizes), lagrange=0.5*lammax)
loss = rr.squared_error(X, Y - meanY)
problem = rr.simple_problem(loss, penalty)
soln = problem.solve()
Yhat = X.linear_map(soln)
Yhat += meanY
if INTERACTIVE:
plt.scatter(np.arange(p), Y)
plt.plot(np.arange(p), Yhat)
plt.show()
def test_multiscale():
M = _multiscale_matrix(200)
Mtrans = multiscale(200)
V = np.random.standard_normal(M.shape[1])
W = np.random.standard_normal(M.shape[0])
np.testing.assert_allclose(np.dot(M, V), Mtrans.linear_map(V))
np.testing.assert_allclose(np.dot(M.T, W), Mtrans.adjoint_map(W))
def test_multiscale():
M = _multiscale_matrix(200)
Mtrans = multiscale(200)
V = np.random.standard_normal(M.shape[1])
W = np.random.standard_normal(M.shape[0])
np.testing.assert_allclose(np.dot(M, V), Mtrans.linear_map(V))
np.testing.assert_allclose(np.dot(M.T, W), Mtrans.adjoint_map(W))
Mtrans.update_slices([(s,e) for s, e in Mtrans.slices])
np.testing.assert_allclose(np.dot(M, V), Mtrans.linear_map(V))
np.testing.assert_allclose(np.dot(M.T, W), Mtrans.adjoint_map(W))
Mtrans = multiscale(200, slices=[(s,e) for s, e in Mtrans.slices])
Mtrans.update_slices(Mtrans.slices)
Mtrans = multiscale(200, slices=[(s,e) for s, e in Mtrans.slices], scaling=2)
Mtrans.linear_map(V)
Mtrans.affine_map(V)
Mtrans.adjoint_map(W)
def __init__(self, Y, minsize=None):
self.Y = Y
self.p = p = Y.shape[0]
self.M = multiscale(p)
self.M.scaling = np.sqrt(self.M.sizes)
self.tuning_param = choose_tuning_parameter(self.M,
ndraw=self.ndraw,
quantile=self.quantile,
sigma=self.sigma)
self.feature_weights = (self.tuning_param + np.sqrt(
2 * np.log(p / self.M.sizes))) / np.sqrt(p)
def test_choose_parameter(delta=2, p=60):
signal = np.zeros(p)
signal[(p//2):] += delta
Z = np.random.standard_normal(p) + signal
p = Z.shape[0]
M = multiscale(p)
M.scaling = np.sqrt(M.sizes)
lam = choose_tuning_parameter(M)
weights = (lam + np.sqrt(2 * np.log(p / M.sizes))) / np.sqrt(p)
Z0 = Z - Z.mean()
loss = rr.squared_error(ra.adjoint(M), Z0)
penalty = rr.weighted_l1norm(weights, lagrange=1.)
problem = rr.simple_problem(loss, penalty)
coef = problem.solve()
active = coef != 0
if active.sum():
X = M.form_matrix(M.slices[active])[0]
def test_changepoint():
p = 150
M = multiscale(p)
M.minsize = 10
X = ra.adjoint(M)
Y = np.random.standard_normal(p)
Y[20:50] += 8
Y += 2
meanY = Y.mean()
lammax = np.fabs(X.adjoint_map(Y)).max()
penalty = rr.l1norm(X.input_shape, lagrange=0.5*lammax)
loss = rr.squared_error(X, Y - meanY)
problem = rr.simple_problem(loss, penalty)
soln = problem.solve()
Yhat = X.linear_map(soln)
Yhat += meanY
plt.scatter(np.arange(p), Y)
plt.plot(np.arange(p), Yhat)
def test_changepoint():
p = 150
M = multiscale(p)
M.minsize = 10
X = ra.adjoint(M)
Y = np.random.standard_normal(p)
Y[20:50] += 8
Y += 2
meanY = Y.mean()
lammax = np.fabs(X.adjoint_map(Y)).max()
penalty = rr.l1norm(X.input_shape, lagrange=0.5*lammax)
loss = rr.squared_error(X, Y - meanY)
problem = rr.simple_problem(loss, penalty)
soln = problem.solve()
Yhat = X.linear_map(soln)
Yhat += meanY
plt.scatter(np.arange(p), Y)
plt.plot(np.arange(p), Yhat)
plt.show()
