def test_Inference(self):
# ===== Distributions ===== #
dist = Normal(0., 1.)
mvn = Independent(Normal(torch.zeros(2), torch.ones(2)), 1)
# ===== Define model ===== #
linear = AffineProcess((f, g), (1., 0.25), dist, dist)
model = LinearGaussianObservations(linear, scale=0.1)
mv_linear = AffineProcess((fmvn, gmvn), (0.5, 0.25), mvn, mvn)
mvnmodel = LinearGaussianObservations(mv_linear, torch.eye(2), scale=0.1)
# ===== Test for multiple models ===== #
priors = Exponential(1.), LogNormal(0., 1.)
hidden1d = AffineProcess((f, g), priors, dist, dist)
oned = LinearGaussianObservations(hidden1d, 1., scale=0.1)
hidden2d = AffineProcess((fmvn, gmvn), priors, mvn, mvn)
twod = LinearGaussianObservations(hidden2d, torch.eye(2), scale=0.1 * torch.ones(2))
particles = 1000
# ====== Run inference ===== #
for trumod, model in [(model, oned), (mvnmodel, twod)]:
x, y = trumod.sample_path(1000)
algs = [
(NESS, {'particles': particles, 'filter_': APF(model.copy(), 200)}),
(NESS, {'particles': particles, 'filter_': UKF(model.copy())}),
(SMC2, {'particles': particles, 'filter_': APF(model.copy(), 200)}),
(SMC2FW, {'particles': particles, 'filter_': APF(model.copy(), 200)}),
(NESSMC2, {'particles': particles, 'filter_': APF(model.copy(), 200)})
]
for alg, props in algs:
alg = alg(**props).initialize()
alg = alg.fit(y)
w = normalize(alg._w_rec if hasattr(alg, '_w_rec') else torch.ones(particles))
tru_params = trumod.hidden.theta._cont + trumod.observable.theta._cont
inf_params = alg.filter.ssm.hidden.theta._cont + alg.filter.ssm.observable.theta._cont
for trup, p in zip(tru_params, inf_params):
if not p.trainable:
continue
kde = p.get_kde(weights=w)
transed = p.bijection.inv(trup)
densval = kde.logpdf(transed.numpy().reshape(-1, 1))
priorval = p.distr.log_prob(trup)
assert (densval > priorval.numpy()).all()
def test_SequentialAlgorithms(self):
particles = 1000
for true_model, model in [(make_model(False), make_model(True)),
(make_model(False, 2), make_model(True, 2))]:
x, y = true_model.sample_path(1000)
algs = [
(NESS, {
"particles": particles,
"filter_": APF(model.copy(), 200)
}),
(NESS, {
"particles": particles,
"filter_": UKF(model.copy())
}),
(SMC2, {
"particles": particles,
"filter_": APF(model.copy(), 125)
}),
(SMC2FW, {
"particles": particles,
"filter_": APF(model.copy(), 200)
}),
(NESSMC2, {
"particles": particles,
"filter_": APF(model.copy(), 200)
}),
]
for alg_type, props in algs:
alg = alg_type(**props)
state = alg.fit(y)
w = state.normalized_weights()
zipped = zip(true_model.hidden.functional_parameters(),
alg.filter.ssm.parameters_and_priors())
for true_p, (p, prior) in zipped:
kde = gaussian_kde(
prior.get_unconstrained(p).squeeze().numpy(),
weights=w.numpy())
inverse_true_value = prior.bijection.inv(true_p)
posterior_log_prob = kde.logpdf(
inverse_true_value.numpy().reshape(-1, 1))
prior_log_prob = prior.unconstrained_prior.log_prob(
inverse_true_value)
assert (posterior_log_prob > prior_log_prob.numpy()).all()
def test_StateDict(self):
# ===== Define model ===== #
norm = Normal(0., 1.)
linear = AffineProcess((f, g), (1., 1.), norm, norm)
linearobs = AffineObservations((fo, go), (1., 1.), norm)
model = StateSpaceModel(linear, linearobs)
# ===== Define filter ===== #
filt = SISR(model, 100).initialize()
# ===== Get statedict ===== #
sd = filt.state_dict()
# ===== Verify that we don't save multiple instances ===== #
assert '_model' in sd and '_model' not in sd['_proposal']
newfilt = SISR(model, 1000).load_state_dict(sd)
assert newfilt._w_old is not None and newfilt.ssm is newfilt._proposal._model
# ===== Test same with UKF and verify that we save UT ===== #
ukf = UKF(model).initialize()
sd = ukf.state_dict()
assert '_model' in sd and '_model' not in sd['_ut']
def test_SDE(self):
def f(x, a, s):
return -a * x
def g(x, a, s):
return s
em = AffineEulerMaruyama((f, g), (0.02, 0.15), Normal(0., 1.), Normal(0., 1.), dt=1e-2, num_steps=10)
model = LinearGaussianObservations(em, scale=1e-3)
x, y = model.sample_path(500)
with self.assertRaises(NotImplementedError):
SISR(model, 200)
for filt in [SISR(model, 500, proposal=Bootstrap()), UKF(model)]:
filt = filt.initialize().longfilter(y)
means = filt.filtermeans
if isinstance(filt, UKF):
means = means[:, 0]
self.assertLess(torch.std(x - means), 5e-2)
def test_SDE(self):
def f(x, a, s):
return -a * x
def g(x, a, s):
return s
dt = 1e-2
norm = DistributionWrapper(Normal, loc=0.0, scale=sqrt(dt))
em = AffineEulerMaruyama((f, g), (0.02, 0.15), norm, norm, dt=1e-2, num_steps=10)
model = LinearGaussianObservations(em, scale=1e-3)
x, y = model.sample_path(500)
for filt in [SISR(model, 500, proposal=prop.Bootstrap()), UKF(model)]:
result = filt.longfilter(y)
means = result.filter_means
if isinstance(filt, UKF):
means = means[:, 0]
self.assertLess(torch.std(x - means), 5e-2)