def drift(d_param, x):
evaluated_basis = np.zeros((prm.dim, x.shape[0], prm.dof))
out = np.zeros((x.shape[0], prm.dim))
# one dimension at a time, each row of x gets mapped to the hermite basis.
# both dimensions of x are passed to the hermite function since the hermite
# functions depend on all dimensions of x.
for i in range(prm.dim):
evaluated_basis[i, :, :] = hermite_basis(x)
out[:, i] = np.sum(np.dot(evaluated_basis[i, :, :], d_param.theta[:, i]))
return out
def mcmc(allx, allt, d_param, em_param, path_index, step_index):
mmat = np.zeros((prm.dim, prm.dof, prm.dof))
rvec = np.zeros((prm.dim, prm.dof))
gammavec = np.zeros((prm.dim))
# one time series, one interval, all dimensions at a time
x = allx[path_index, step_index:(step_index + 2), :]
t = allt[path_index, step_index:(step_index + 2)]
tdiff = (t[1] - t[0]) / em_param.numsubintervals
samples = np.zeros((em_param.numsubintervals, prm.dim))
_, xcur = brownianbridge(d_param, em_param, x, t)
oldlik = girsanov(d_param, em_param, xcur, tdiff)
arburn = np.zeros(em_param.burninpaths)
for jj in range(em_param.burninpaths):
_, prop = brownianbridge(d_param, em_param, x, t)
proplik = girsanov(d_param, em_param, prop, tdiff)
rho = proplik - oldlik
if (rho > np.log(np.random.uniform())):
xcur = prop
oldlik = proplik
arburn[jj] = 1
meanBurnin = np.mean(arburn)
# for each path being sampled (r = 0 to r = R)
arsamp = np.zeros(em_param.mcmcpaths)
for jj in range(em_param.mcmcpaths):
_, prop = brownianbridge(d_param, em_param, x, t)
proplik = girsanov(d_param, em_param, prop, tdiff)
rho = proplik - oldlik
if (rho > np.log(np.random.uniform())):
xcur = prop
oldlik = proplik
arsamp[jj] = 1
samples = xcur
pp = hermite_basis(samples[:(-1)])
mmat += tdiff * np.matmul(pp.T, pp) / em_param.mcmcpaths
rvec += np.matmul(
(np.diff(samples, axis=0)).T, pp) / em_param.mcmcpaths
gammavec += np.sum(np.square(
np.diff(samples, axis=0) - tdiff * np.matmul(pp, d_param.theta)),
axis=0) / (tdiff * em_param.mcmcpaths *
(em_param.numsubintervals *
(allx.shape[1] - 1) + 1))
meanSample = np.mean(arsamp)
return (mmat, rvec, gammavec, meanBurnin, meanSample, path_index,
step_index)
def comparison(x, threshold, method_type = 'lasso'):
y = np.diff(x, axis = 0)
M = hermite_basis(x[:(-1)])
clf = linear_model.Lasso(alpha = threshold)
clf.fit(M, y)
return theta