def run_irl(world, car, reward, theta, data):
def gen():
for point in data:
for c, x0, u in zip(world.cars, point['x0'], point['u']):
c.traj.x0.set_value(x0)
for cu, uu in zip(c.traj.u, u):
cu.set_value(uu)
yield
r = car.traj.reward(reward)
g = utils.grad(r, car.traj.u)
H = utils.hessian(r, car.traj.u)
I = tt.eye(utils.shape(H)[0])
reg = utils.vector(1)
reg.set_value([1e-1])
H = H - reg[0] * I
L = tt.dot(g, tt.dot(tn.MatrixInverse()(H), g)) + tt.log(tn.Det()(-H))
for _ in gen():
pass
optimizer = utils.Maximizer(L, [theta],
gen=gen,
method='gd',
eps=0.1,
debug=True,
iters=1000,
inf_ignore=10)
optimizer.maximize()
print theta.get_value()
def minus_two_log_gauss_likelihood_2D(residuals, covariance_values):
"""computes the -2 log gaussian likelihood (ignoring the constant term)
from the given residuals and covariance values in the form of a
1D array: [variance1, covariance, variance2]"""
cov = covariance_matrix_2D(covariance_values)
det = L.Det()(cov)
precis = L.MatrixInverse()(cov)
term1 = T.dot(T.transpose(residuals), T.dot(precis, residuals))
term2 = T.log(det)
return term1 + term2
def dima(x):
return -T.log(nlinalg.Det()(T.dot(x.T, x)))
residual = rtransform - routput
# For covariance, we want to subtract out the means...
sigmean = rtransform.mean(axis=(0, 2), keepdims=True)
epsmean = residual.mean(axis=(0, 2), keepdims=True)
rtdelta = rtransform - sigmean
epsdelta = residual - epsmean
# Covariance matrices
sig_cov = T.tensordot(rtdelta, rtdelta, axes=(
(0, 2), (0, 2))) / (rtransform.shape[0] * rtransform.shape[2])
eps_cov = T.tensordot(epsdelta, epsdelta, axes=(
(0, 2), (0, 2))) / (residual.shape[0] * residual.shape[2])
det_sig = TNL.Det()(sig_cov) + 1e-48
det_eps = TNL.Det()(eps_cov) + 1e-48
entropy = T.log(det_sig)
info = T.log(det_eps)
# First two terms gives the entropy contrast, but we'd also like the predictions to be correct (as opposed to constant offset), so we add a third term to encourage the mean residual to be zero.
loss = info - entropy + 1e-2 * (epsmean**2).mean()
else:
# Entropy term measures the entropy of the average transformed signal. We want to make this large
entropy = -1 * (rtransform.mean(axis=(0, 2)) *
T.log(rtransform.mean(axis=(0, 2)) + 1e-6)).sum()
# Info term measures the error of the predictor (standard cross-entropy error between the prediction and true distribution). We want to make this small
info = -1 * ((rtransform * T.log(routput + 1e-6)).mean(axis=(0, 2))).sum()