elif method == 4:
inf_method = approx_inf.GHEP(power=1, damping=0.5)
elif method == 5:
inf_method = approx_inf.GHKS(damping=0.5)
elif method == 6:
inf_method = approx_inf.EP(power=0.01, intmethod='UT', damping=0.5)
elif method == 7:
inf_method = approx_inf.EP(power=0.01, intmethod='GH', damping=0.5)
elif method == 8:
inf_method = approx_inf.VI(intmethod='UT', damping=0.5)
elif method == 9:
inf_method = approx_inf.VI(intmethod='GH', damping=0.5)
model = SDEGP(prior=prior, likelihood=lik, t=X, y=Y, t_test=XT, y_test=YT, approx_inf=inf_method)
neg_log_marg_lik, gradients = model.run()
print(gradients)
neg_log_marg_lik, gradients = model.run()
print(gradients)
neg_log_marg_lik, gradients = model.run()
print(gradients)
print('optimising the hyperparameters ...')
time_taken = np.zeros([10, 1])
for j in range(10):
t0 = time.time()
neg_log_marg_lik, gradients = model.run()
print(gradients)
t1 = time.time()
# inf_method = approx_inf.ExpectationPropagation(power=0.9, intmethod='UT', damping=0.1)
# inf_method = approx_inf.ExpectationPropagation(power=0.1, intmethod='GH', damping=0.5)
# inf_method = approx_inf.VariationalInference(intmethod='GH', damping=0.5)
# inf_method = approx_inf.VariationalInference(intmethod='UT', damping=0.5)
# inf_method = approx_inf.ExtendedEP(power=0, damping=0.5)
# inf_method = approx_inf.ExtendedKalmanSmoother(damping=0.5)
# inf_method = approx_inf.GaussHermiteKalmanSmoother(damping=0.5)
inf_method = approx_inf.StatisticallyLinearisedEP(power=0.1,
intmethod='GH',
damping=0.5)
# inf_method = approx_inf.UnscentedKalmanSmoother(damping=0.5)
model = SDEGP(prior=prior,
likelihood=lik,
t=Xall,
y=Yall,
t_test=XT,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=5e-2)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
var_y = 0.1
theta_prior = jnp.array([var_f, len_f])
theta_lik = jnp.array([])
prior_ = priors.Matern52(theta_prior)
lik_ = likelihoods.SumOfGaussians(theta_lik)
approx_inf_ = EP(power=1.)
# approx_inf_ = PL()
# approx_inf_ = CL(power=0.5)
# approx_inf_ = IKS()
# approx_inf_ = EKEP()
sde_gp_model = SDEGP(prior=prior_,
likelihood=lik_,
t=x,
y=dummy_y,
t_test=x_test,
approx_inf=approx_inf_)
print('generating some data by sampling from the prior ...')
ground_truth = sde_gp_model.prior_sample(1, t=x)
y = sde_gp_model.likelihood.sample(ground_truth)[:, 0, 0]
# plt.figure(1, figsize=(12, 5))
# plt.clf()
# plt.plot(x, ground_truth[:, 0, 0])
# plt.plot(x, y, '.')
# plt.show()
sde_gp_model = SDEGP(prior=prior_,
likelihood=lik_,
elif method == 12:
inf_method = approx_inf.EP(power=1, intmethod='GH', damping=0.05)
elif method == 13:
inf_method = approx_inf.EP(power=0.5, intmethod='GH', damping=0.05)
elif method == 14:
inf_method = approx_inf.EP(power=0.01, intmethod='GH', damping=0.05)
elif method == 15:
inf_method = approx_inf.VI(intmethod='UT', damping=0.05)
elif method == 16:
inf_method = approx_inf.VI(intmethod='GH', damping=0.05)
model = SDEGP(prior=prior,
likelihood=lik,
t=x_train,
y=y_train,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=5e-2)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
# neg_log_marg_lik, gradients = mod.run()
elif method == 11:
inf_method = approx_inf.EP(power=0.01, intmethod='UT', damping=damping)
elif method == 12:
inf_method = approx_inf.EP(power=1, intmethod='GH', damping=damping)
elif method == 13:
inf_method = approx_inf.EP(power=0.5, intmethod='GH', damping=damping)
elif method == 14:
inf_method = approx_inf.EP(power=0.01, intmethod='GH', damping=damping)
elif method == 15:
inf_method = approx_inf.VI(intmethod='UT', damping=damping)
elif method == 16:
inf_method = approx_inf.VI(intmethod='GH', damping=damping)
model = SDEGP(prior=prior, likelihood=lik, t=x_train, y=y_train, approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=1e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
if ~np.any(np.isnan(params[0])):
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
# neg_log_marg_lik, gradients = mod.run_two_stage()
# inf_method = approx_inf.ExpectationPropagation(power=0.9, intmethod='UT', damping=0.1)
inf_method = approx_inf.ExpectationPropagation(power=0.01,
intmethod='GH',
damping=0.5)
# inf_method = approx_inf.VariationalInference(intmethod='GH', damping=0.5)
# inf_method = approx_inf.VariationalInference(intmethod='UT', damping=0.5)
# inf_method = approx_inf.ExtendedEP(power=0, damping=0.5)
# inf_method = approx_inf.ExtendedKalmanSmoother(damping=0.5)
# inf_method = approx_inf.GaussHermiteKalmanSmoother(damping=0.5)
# inf_method = approx_inf.StatisticallyLinearisedEP(intmethod='UT', damping=0.5)
# inf_method = approx_inf.UnscentedKalmanSmoother(damping=0.5)
model = SDEGP(prior=prior,
likelihood=lik,
t=X,
y=Y,
t_test=XT,
y_test=YT,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=5e-2)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
N = nr * nt # number of data points
var_f = 1 # GP variance
len_f = 10 # lengthscale
prior = priors.SpatialMatern32(variance=var_f,
lengthscale=len_f,
z=r[0, ...],
fixed_grid=True)
lik = likelihoods.Poisson()
inf_method = approx_inf.ExtendedKalmanSmoother(damping=0.5)
# inf_method = approx_inf.ExtendedEP()
model = SDEGP(prior=prior,
likelihood=lik,
t=t,
y=Y,
r=r,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod, plot_num_, mu_prev_):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
var_f = 1. # GP variance
len_f = 5.0 # GP lengthscale
prior = priors.Matern52(variance=var_f, lengthscale=len_f)
lik = likelihoods.Bernoulli(link='logit')
inf_method = approx_inf.ExpectationPropagation(power=0.9, intmethod='UT')
# inf_method = approx_inf.VariationalInference(intmethod='GH')
# inf_method = approx_inf.VariationalInference(intmethod='UT')
# inf_method = approx_inf.ExtendedEP(power=0)
# inf_method = approx_inf.ExtendedKalmanSmoother()
# inf_method = approx_inf.GaussHermiteKalmanSmoother()
# inf_method = approx_inf.StatisticallyLinearisedEP(intmethod='UT')
# inf_method = approx_inf.UnscentedKalmanSmoother()
model = SDEGP(prior=prior, likelihood=lik, t=x, y=y, approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
# neg_log_marg_lik, gradients = mod.run_two_stage() # <-- less elegant but reduces compile time
inf_method = approx_inf.VI(intmethod='GH')
# plot_2d_classification(None, 0)
np.random.seed(99)
N = X.shape[0] # number of training points
var_f = 1. # GP variance
len_time = 1. # temporal lengthscale
len_space = 1. # spacial lengthscale
prior = priors.SpatioTemporalMatern52(variance=var_f, lengthscale_time=len_time, lengthscale_space=len_space)
lik = likelihoods.Bernoulli(link='logit')
model = SDEGP(prior=prior, likelihood=lik, t=X, y=Y, r=R, t_test=XT, y_test=YT, r_test=RT, approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod, plot_num_, mu_prev_):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
# neg_log_marg_lik, gradients = mod.run_two_stage()
var_f = 0.3 # GP variance
len_time = 0.3 # temporal lengthscale
len_space = 0.3 # spacial lengthscale
prior = priors.SpatioTemporalMatern52(variance=var_f,
lengthscale_time=len_time,
lengthscale_space=len_space)
lik = likelihoods.Probit()
inf_method = approx_inf.ExpectationPropagation(power=0.5)
# inf_method = approx_inf.StatisticallyLinearisedEP()
# inf_method = approx_inf.ExtendedKalmanSmoother()
# inf_method = approx_inf.VariationalInference()
model = SDEGP(prior=prior,
likelihood=lik,
t=X,
y=Y,
r=R,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod, plot_num_, mu_prev_):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
prior = priors.SpatialMatern32(variance=var_f,
lengthscale=len_f,
z=r[0, ...],
fixed_grid=True)
lik = likelihoods.Poisson()
inf_method = approx_inf.ExtendedKalmanSmoother(damping=1.)
# inf_method = approx_inf.ExtendedEP()
# t_spacetime = np.block([t[..., 0][..., None], r])
model = SDEGP(prior=prior,
likelihood=lik,
t=t,
y=Y,
r=r,
t_test=t,
y_test=Y,
r_test=r,
approx_inf=inf_method)
neg_log_marg_lik, gradients = model.run_two_stage()
print(gradients)
neg_log_marg_lik, gradients = model.run_two_stage()
print(gradients)
neg_log_marg_lik, gradients = model.run_two_stage()
print(gradients)
print('optimising the hyperparameters ...')
time_taken = np.zeros([10, 1])
for j in range(10):
y_ = f + np.math.sqrt(0.05) * np.random.randn(x.shape[0])
y = np.maximum(np.sign(y_), 0.)
x_test = np.linspace(np.min(x) - 10.0, np.max(x) + 10.0, num=500)
var_f = 1.0 # GP variance
len_f = 5.0 # GP lengthscale
prior = priors.Matern52(variance=var_f, lengthscale=len_f)
lik = likelihoods.Probit()
approx_inf_1 = approx_inf.EP()
approx_inf_2 = approx_inf.VI()
model_1 = SDEGP(prior=prior,
likelihood=lik,
t=x,
y=y,
t_test=x_test,
approx_inf=approx_inf_1)
model_2 = SDEGP(prior=prior,
likelihood=lik,
t=x,
y=y,
t_test=x_test,
approx_inf=approx_inf_2)
opt_init, opt_update, get_params = optimizers.adam(step_size=5e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model_1.prior.hyp, model_1.likelihood.hyp])
def gradient_step(i, state, mod):
meanval = np.log(len(disaster_timings) /
num_time_bins) # TODO: incorporate mean
var_f = 1.0 # GP variance
len_f = 1.0 # GP lengthscale
prior = priors.Matern52(variance=var_f, lengthscale=len_f)
lik = likelihoods.Poisson()
# inf_method = approx_inf.EP(power=0.5)
# inf_method = approx_inf.SLEP()
inf_method = approx_inf.EKS()
# inf_method = approx_inf.EEP()
# inf_method = approx_inf.VI()
model = SDEGP(prior=prior, likelihood=lik, t=x, y=y, approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=1e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
# neg_log_marg_lik, gradients = mod.run_two_stage() # <-- less elegant but reduces compile time
inf_method = approx_inf.GHKS()
elif method == 6:
inf_method = approx_inf.EP(power=0.01, intmethod='UT')
elif method == 7:
inf_method = approx_inf.EP(power=0.01, intmethod='GH')
elif method == 8:
inf_method = approx_inf.VI(intmethod='UT')
elif method == 9:
inf_method = approx_inf.VI(intmethod='GH')
model = SDEGP(prior=prior,
likelihood=lik,
t=x_train,
y=y_train,
t_test=x_test,
y_test=y_test,
approx_inf=inf_method)
neg_log_marg_lik, gradients = model.run()
print(gradients)
neg_log_marg_lik, gradients = model.run()
print(gradients)
neg_log_marg_lik, gradients = model.run()
print(gradients)
print('optimising the hyperparameters ...')
time_taken = np.zeros([10, 1])
for j in range(10):
t0 = time.time()
len_time = 0.3 # temporal lengthscale
len_space = 0.3 # spacial lengthscale
prior = priors.SpatioTemporalMatern52(variance=var_f,
lengthscale_time=len_time,
lengthscale_space=len_space)
lik = likelihoods.Probit()
inf_method = approx_inf.ExpectationPropagation(power=0.5)
# inf_method = approx_inf.StatisticallyLinearisedEP()
# inf_method = approx_inf.ExtendedKalmanSmoother()
# inf_method = approx_inf.VariationalInference()
model = SDEGP(prior=prior,
likelihood=lik,
t=X,
y=Y,
r=R,
t_test=Xtest,
r_test=Rtest,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod, plot_num_, mu_prev_):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
inf_method = approx_inf.VI(intmethod='GH')
# plot_2d_classification(None, 0)
np.random.seed(99)
N = X.shape[0] # number of training points
var_f = 1. # GP variance
len_time = 1. # temporal lengthscale
len_space = 1. # spacial lengthscale
prior = priors.SpatioTemporalMatern52(variance=var_f, lengthscale_time=len_time, lengthscale_space=len_space)
lik = likelihoods.Bernoulli(link='logit')
model = SDEGP(prior=prior, likelihood=lik, t=X, y=Y, r=R, approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod, plot_num_, mu_prev_):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
# neg_log_marg_lik, gradients = mod.run_two_stage()
elif method == 11:
inf_method = approx_inf.EP(power=0.01, intmethod='UT')
elif method == 12:
inf_method = approx_inf.EP(power=1, intmethod='GH')
elif method == 13:
inf_method = approx_inf.EP(power=0.5, intmethod='GH')
elif method == 14:
inf_method = approx_inf.EP(power=0.01, intmethod='GH')
elif method == 15:
inf_method = approx_inf.VI(intmethod='UT')
elif method == 16:
inf_method = approx_inf.VI(intmethod='GH')
model = SDEGP(prior=prior, likelihood=lik, t=x_train, y=y_train, t_test=x_test, y_test=y_test, approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
# neg_log_marg_lik, gradients = mod.run_two_stage()
if method == 0:
inf_method = approx_inf.EKS(damping=.5)
elif method == 1:
inf_method = approx_inf.UKS(damping=.5)
elif method == 2:
inf_method = approx_inf.GHKS(damping=.5)
elif method == 3:
inf_method = approx_inf.EP(power=1, intmethod='GH', damping=.5)
elif method == 4:
inf_method = approx_inf.EP(power=0.5, intmethod='GH', damping=.5)
elif method == 5:
inf_method = approx_inf.EP(power=0.01, intmethod='GH', damping=.5)
elif method == 6:
inf_method = approx_inf.VI(intmethod='GH', damping=.5)
model = SDEGP(prior=prior, likelihood=lik, t=x_train, y=y_train, t_test=x_test, y_test=y_test,
approx_inf=inf_method, z=z)
opt_init, opt_update, get_params = optimizers.adam(step_size=1e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
batch_ind = np.random.permutation(N)[:N_batch]
# grad(Filter) + Smoother:
var_f = 1.0 # GP variance
len_f = 5.0 # GP lengthscale
var_y = 0.5 # observation noise
prior = priors.Matern52(variance=var_f, lengthscale=len_f)
# prior_ = priors.QuasiPeriodicMatern32([var_f, len_f, 20., 50.])
lik = likelihoods.Gaussian(variance=var_y)
inf_method = approx_inf.EP(power=0.5)
# inf_method = approx_inf.EKS()
# inf_method = approx_inf.EEP()
# inf_method = approx_inf.VI()
model = SDEGP(prior=prior,
likelihood=lik,
t=x,
y=y,
t_test=x_test,
y_test=y_test,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=5e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
elif method == 12:
if fold in [3, 4, 6, 7, 9]:
inf_method = approx_inf.EP(power=1, intmethod='GH', damping=0.1)
else:
inf_method = approx_inf.EP(power=1, intmethod='GH', damping=0.5)
elif method == 13:
inf_method = approx_inf.EP(power=0.5, intmethod='GH', damping=0.5)
elif method == 14:
inf_method = approx_inf.EP(power=0.01, intmethod='GH', damping=0.5)
elif method == 15:
inf_method = approx_inf.VI(intmethod='UT', damping=0.5)
elif method == 16:
inf_method = approx_inf.VI(intmethod='GH', damping=0.5)
model = SDEGP(prior=prior, likelihood=lik, t=X, y=Y, approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=step_size)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
# grad(Filter) + Smoother:
neg_log_marg_lik, gradients = mod.run()
# neg_log_marg_lik, gradients = mod.run_two_stage()
var_f = 1 # GP variance
len_f = 10 # lengthscale
prior = priors.SpatialMatern32(variance=var_f,
lengthscale=len_f,
z=r[0, ...],
fixed_grid=True)
lik = likelihoods.Poisson()
inf_method = approx_inf.ExtendedKalmanSmoother(damping=0.5)
# inf_method = approx_inf.ExtendedEP()
model = SDEGP(prior=prior,
likelihood=lik,
t=t,
y=Y,
r=r,
t_test=t,
y_test=Y,
r_test=r,
approx_inf=inf_method)
opt_init, opt_update, get_params = optimizers.adam(step_size=2e-1)
# parameters should be a 2-element list [param_prior, param_likelihood]
opt_state = opt_init([model.prior.hyp, model.likelihood.hyp])
def gradient_step(i, state, mod, plot_num_, mu_prev_):
params = get_params(state)
mod.prior.hyp = params[0]
mod.likelihood.hyp = params[1]
