def test_hessian_2():
n = 3
seqs = [[
1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2,
2, 1, 1, 1, 1, 2, 3, 3, 3, 3
]]
model = ContinuousTimeMSM().fit(seqs)
print(model.timescales_)
print(model.uncertainty_timescales())
theta = model.theta_
C = model.countsmat_
print(C)
C_flat = (C + C.T)[np.triu_indices_from(C, k=1)]
print(C_flat)
print('theta', theta, '\n')
inds = np.where(theta != 0)[0]
hessian1 = _ratematrix.hessian(theta, C, inds=inds)
hessian2 = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C)[1])(theta)
hessian3 = nd.Hessian(lambda x: _ratematrix.loglikelihood(x, C)[0])(theta)
np.set_printoptions(precision=3)
# H1 = hessian1[np.ix_(active, active)]
# H2 = hessian2[np.ix_(active, active)]
# H3 = hessian2[np.ix_(active, active)]
print(hessian1, '\n')
print(hessian2, '\n')
# print(hessian3)
print('\n')
info1 = np.zeros((len(theta), len(theta)))
info2 = np.zeros((len(theta), len(theta)))
info1[np.ix_(inds, inds)] = scipy.linalg.pinv(-hessian1)
info2[np.ix_(inds,
inds)] = scipy.linalg.pinv(-hessian2[np.ix_(inds, inds)])
print('Inverse Hessian')
print(info1)
print(info2)
# print(scipy.linalg.pinv(hessian2))
# print(scipy.linalg.pinv(hessian1)[np.ix_(last, last)])
# print(scipy.linalg.pinv(hessian2)[np.ix_(last, last)])
print(_ratematrix.sigma_pi(info1, theta, n))
print(_ratematrix.sigma_pi(info2, theta, n))
def test_hessian_1():
n = 5
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(use_sparse=False).fit(seqs)
theta = model.theta_
C = model.countsmat_
hessian1 = _ratematrix.hessian(theta, C, n)
Hfun = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C, n)[1])
hessian2 = Hfun(theta)
# not sure what the cutoff here should be (see plot_test_hessian)
assert np.linalg.norm(hessian1-hessian2) < 1
def test_hessian_1():
n = 3
seqs = [[1,1,1,1,1,2,2,2,2,1,1,1,1,3,3,3,3,3,2,2,2,2,2,2,1,1,1,1,2,3,3,3,3]]
model = ContinuousTimeMSM().fit(seqs)
theta = model.theta_
C = model.countsmat_
hessian1 = _ratematrix.hessian(theta, C)
Hfun = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C)[1])
hessian2 = Hfun(theta)
# not sure what the cutoff here should be (see plot_test_hessian)
assert np.linalg.norm(hessian1-hessian2) < 1e-6
print(_ratematrix.sigma_pi(-scipy.linalg.pinv(hessian1), theta, n))
def test_hessian_2():
n = 3
seqs = [
[1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2,
2, 1, 1, 1, 1, 2, 3, 3, 3, 3]]
model = ContinuousTimeMSM().fit(seqs)
print(model.timescales_)
print(model.uncertainty_timescales())
theta = model.theta_
C = model.countsmat_
print(C)
C_flat = (C + C.T)[np.triu_indices_from(C, k=1)]
print(C_flat)
print('theta', theta, '\n')
inds = np.where(theta != 0)[0]
hessian1 = _ratematrix.hessian(theta, C, inds=inds)
hessian2 = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C)[1])(theta)
hessian3 = nd.Hessian(lambda x: _ratematrix.loglikelihood(x, C)[0])(theta)
np.set_printoptions(precision=3)
# H1 = hessian1[np.ix_(active, active)]
# H2 = hessian2[np.ix_(active, active)]
# H3 = hessian2[np.ix_(active, active)]
print(hessian1, '\n')
print(hessian2, '\n')
# print(hessian3)
print('\n')
info1 = np.zeros((len(theta), len(theta)))
info2 = np.zeros((len(theta), len(theta)))
info1[np.ix_(inds, inds)] = scipy.linalg.pinv(-hessian1)
info2[np.ix_(inds, inds)] = scipy.linalg.pinv(-hessian2[np.ix_(inds, inds)])
print('Inverse Hessian')
print(info1)
print(info2)
# print(scipy.linalg.pinv(hessian2))
# print(scipy.linalg.pinv(hessian1)[np.ix_(last, last)])
# print(scipy.linalg.pinv(hessian2)[np.ix_(last, last)])
print(_ratematrix.sigma_pi(info1, theta, n))
print(_ratematrix.sigma_pi(info2, theta, n))
def test_hessian_1():
n = 3
seqs = [[
1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2,
1, 1, 1, 1, 2, 3, 3, 3, 3
]]
model = ContinuousTimeMSM().fit(seqs)
theta = model.theta_
C = model.countsmat_
hessian1 = _ratematrix.hessian(theta, C)
Hfun = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C)[1])
hessian2 = Hfun(theta)
# not sure what the cutoff here should be (see plot_test_hessian)
assert np.linalg.norm(hessian1 - hessian2) < 1e-6
print(_ratematrix.sigma_pi(-scipy.linalg.pinv(hessian1), theta, n))
def _plot_test_hessian():
# plot the difference between the numerical hessian and the analytic
# approximate hessian (opens Matplotlib window)
n = 5
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(use_sparse=False).fit(seqs)
theta = model.theta_
C = model.countsmat_
hessian1 = _ratematrix.hessian(theta, C, n)
Hfun = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C, n)[1])
hessian2 = Hfun(theta)
import matplotlib.pyplot as pp
pp.scatter(hessian1.flat, hessian2.flat, marker='x')
pp.plot(pp.xlim(), pp.xlim(), 'k')
print('Plotting...', file=sys.stderr)
pp.show()