def get_step_for_trace(
self,
trace=None,
model=None,
regular_window=0,
regular_variance=1e-3,
**kwargs,
):
"""Get a PyMC3 NUTS step tuned for a given burn-in trace
Args:
trace: The ``MultiTrace`` output from a previous run of
``pymc3.sample``.
regular_window: The weight (in units of number of steps) to use
when regularizing the mass matrix estimate.
regular_variance: The amplitude of the regularization for the mass
matrix. This will be added to the diagonal of the covariance
matrix with weight given by ``regular_window``.
"""
model = pm.modelcontext(model)
# If not given, use the trivial metric
if trace is None or model.ndim == 1:
potential = quad.QuadPotentialDiag(np.ones(model.ndim))
else:
# Loop over samples and convert to the relevant parameter space;
# I'm sure that there's an easier way to do this, but I don't know
# how to make something work in general...
N = len(trace) * trace.nchains
samples = np.empty((N, model.ndim))
i = 0
for chain in trace._straces.values():
for p in chain:
samples[i] = model.bijection.map(p)
i += 1
if self.dense:
# Compute the regularized sample covariance
cov = np.cov(samples, rowvar=0)
if regular_window > 0:
cov = cov * N / (N + regular_window)
cov[np.diag_indices_from(cov)] += (regular_variance *
regular_window /
(N + regular_window))
potential = quad.QuadPotentialFull(cov)
else:
var = np.var(samples, axis=0)
if regular_window > 0:
var = var * N / (N + regular_window)
var += (regular_variance * regular_window /
(N + regular_window))
potential = quad.QuadPotentialDiag(var)
return pm.NUTS(potential=potential, **kwargs)
def test_random_dense():
np.random.seed(42)
for _ in range(3):
cov = np.random.rand(5, 5)
cov += cov.T
cov += 10 * np.eye(5)
inv = np.linalg.inv(cov)
assert np.allclose(inv.dot(cov), np.eye(5))
pots = [
quadpotential.QuadPotentialFull(cov),
quadpotential.QuadPotentialFullInv(inv),
]
if quadpotential.chol_available:
pot = quadpotential.QuadPotential_Sparse(scipy.sparse.csc_matrix(cov))
pots.append(pot)
for pot in pots:
cov_ = np.cov(np.array([pot.random() for _ in range(1000)]).T)
assert np.allclose(cov_, inv, atol=0.1)
times_consumed = []
N = 100
alphas = norm.rvs(size=N)
betas = halfnorm.rvs(size=(N, 2))
sigmas = halfnorm.rvs(size=N)
print("=========================================")
print(f"Tuning NUTS")
print("=========================================")
n_chains = 4
init_trace = pm.sample(draws=1000, tune=1000, cores=n_chains)
cov = np.atleast_1d(pm.trace_cov(init_trace))
start = list(np.random.choice(init_trace, n_chains))
potential = quadpotential.QuadPotentialFull(cov)
step_size = init_trace.get_sampler_stats("step_size_bar")[-1]
size = m.bijection.ordering.size
step_scale = step_size * (size**0.25)
# with pm.Model() as model_new: # reset model. If you use theano.shared you can also update the value of model1 above
for i in range(N):
# No-U-Turn Sampler NUTS
print("=========================================")
print(f"Turn {i}")
print("=========================================")
# start = {"alpha": alphas[i], "beta": betas[i], "sigma": sigmas[i]}
time_zero = default_timer()
step = pm.NUTS(potential=potential,
adapt_step_size=False,
step_scale=step_scale)
def init_nuts(init='auto',
chains=1,
n_init=500000,
model=None,
random_seed=None,
progressbar=True,
**kwargs):
"""Set up the mass matrix initialization for NUTS.
NUTS convergence and sampling speed is extremely dependent on the
choice of mass/scaling matrix. This function implements different
methods for choosing or adapting the mass matrix.
Parameters
----------
init : str
Initialization method to use.
* auto : Choose a default initialization method automatically.
Currently, this is `'jitter+adapt_diag'`, but this can change in
the future. If you depend on the exact behaviour, choose an
initialization method explicitly.
* adapt_diag : Start with a identity mass matrix and then adapt
a diagonal based on the variance of the tuning samples. All
chains use the test value (usually the prior mean) as starting
point.
* jitter+adapt_diag : Same as `adapt_diag`, but add uniform jitter
in [-1, 1] to the starting point in each chain.
* advi+adapt_diag : Run ADVI and then adapt the resulting diagonal
mass matrix based on the sample variance of the tuning samples.
* advi+adapt_diag_grad : Run ADVI and then adapt the resulting
diagonal mass matrix based on the variance of the gradients
during tuning. This is **experimental** and might be removed
in a future release.
* advi : Run ADVI to estimate posterior mean and diagonal mass
matrix.
* advi_map: Initialize ADVI with MAP and use MAP as starting point.
* map : Use the MAP as starting point. This is discouraged.
* nuts : Run NUTS and estimate posterior mean and mass matrix from
the trace.
chains : int
Number of jobs to start.
n_init : int
Number of iterations of initializer
If 'ADVI', number of iterations, if 'nuts', number of draws.
model : Model (optional if in `with` context)
progressbar : bool
Whether or not to display a progressbar for advi sampling.
**kwargs : keyword arguments
Extra keyword arguments are forwarded to pymc3.NUTS.
Returns
-------
start : pymc3.model.Point
Starting point for sampler
nuts_sampler : pymc3.step_methods.NUTS
Instantiated and initialized NUTS sampler object
"""
model = pm.modelcontext(model)
vars = kwargs.get('vars', model.vars)
if set(vars) != set(model.vars):
raise ValueError('Must use init_nuts on all variables of a model.')
if not pm.model.all_continuous(vars):
raise ValueError('init_nuts can only be used for models with only '
'continuous variables.')
if not isinstance(init, str):
raise TypeError('init must be a string.')
if init is not None:
init = init.lower()
if init == 'auto':
init = 'jitter+adapt_diag'
pm._log.info('Initializing NUTS using {}...'.format(init))
if random_seed is not None:
random_seed = int(np.atleast_1d(random_seed)[0])
np.random.seed(random_seed)
cb = [
pm.callbacks.CheckParametersConvergence(tolerance=1e-2,
diff='absolute'),
pm.callbacks.CheckParametersConvergence(tolerance=1e-2,
diff='relative'),
]
if init == 'adapt_diag':
start = [model.test_point] * chains
mean = np.mean([model.dict_to_array(vals) for vals in start], axis=0)
var = np.ones_like(mean)
potential = quadpotential.QuadPotentialDiagAdapt(
model.ndim, mean, var, 10)
elif init == 'jitter+adapt_diag':
start = []
for _ in range(chains):
mean = {var: val.copy() for var, val in model.test_point.items()}
for val in mean.values():
val[...] += 2 * np.random.rand(*val.shape) - 1
start.append(mean)
mean = np.mean([model.dict_to_array(vals) for vals in start], axis=0)
var = np.ones_like(mean)
potential = quadpotential.QuadPotentialDiagAdapt(
model.ndim, mean, var, 10)
elif init == 'advi+adapt_diag_grad':
approx = pm.fit(
random_seed=random_seed,
n=n_init,
method='advi',
model=model,
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window,
) # type: pm.MeanField
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds)**2
mean = approx.bij.rmap(approx.mean.get_value())
mean = model.dict_to_array(mean)
weight = 50
potential = quadpotential.QuadPotentialDiagAdaptGrad(
model.ndim, mean, cov, weight)
elif init == 'advi+adapt_diag':
approx = pm.fit(
random_seed=random_seed,
n=n_init,
method='advi',
model=model,
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window,
) # type: pm.MeanField
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds)**2
mean = approx.bij.rmap(approx.mean.get_value())
mean = model.dict_to_array(mean)
weight = 50
potential = quadpotential.QuadPotentialDiagAdapt(
model.ndim, mean, cov, weight)
elif init == 'advi':
approx = pm.fit(random_seed=random_seed,
n=n_init,
method='advi',
model=model,
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window) # type: pm.MeanField
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds)**2
potential = quadpotential.QuadPotentialDiag(cov)
elif init == 'advi_map':
start = pm.find_MAP(include_transformed=True)
approx = pm.MeanField(model=model, start=start)
pm.fit(random_seed=random_seed,
n=n_init,
method=pm.KLqp(approx),
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window)
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds)**2
potential = quadpotential.QuadPotentialDiag(cov)
elif init == 'map':
start = pm.find_MAP(include_transformed=True)
cov = pm.find_hessian(point=start)
start = [start] * chains
potential = quadpotential.QuadPotentialFull(cov)
elif init == 'nuts':
init_trace = pm.sample(draws=n_init,
step=pm.NUTS(),
tune=n_init // 2,
random_seed=random_seed)
cov = np.atleast_1d(pm.trace_cov(init_trace))
start = list(np.random.choice(init_trace, chains))
potential = quadpotential.QuadPotentialFull(cov)
else:
raise NotImplementedError(
'Initializer {} is not supported.'.format(init))
step = pm.NUTS(potential=potential, **kwargs)
return start, step
