def create_shared_params(self,
trace=None,
size=None,
jitter=1,
start=None):
if trace is None:
if size is None:
raise opvi.ParametrizationError(
"Need `trace` or `size` to initialize")
else:
ipfn = make_initial_point_fn(
model=self.model,
overrides=start,
jitter_rvs={},
return_transformed=True,
)
start = ipfn(
self.model.rng_seeder.randint(2**30, dtype=np.int64))
start = pm.floatX(DictToArrayBijection.map(start))
# Initialize particles
histogram = np.tile(start, (size, 1))
histogram += pm.floatX(
np.random.normal(0, jitter, histogram.shape))
else:
histogram = np.empty((len(trace) * len(trace.chains), self.ddim))
i = 0
for t in trace.chains:
for j in range(len(trace)):
histogram[i] = DictToArrayBijection.map(trace.point(j, t))
i += 1
return dict(histogram=aesara.shared(pm.floatX(histogram), "histogram"))
def create_shared_params(self, start=None):
start = self._prepare_start(start)
rho = np.zeros((self.ddim,))
return {
"mu": aesara.shared(pm.floatX(start), "mu"),
"rho": aesara.shared(pm.floatX(rho), "rho"),
}
def __call__(self, x):
neg_value = np.float64(self.logp_func(pm.floatX(x)))
value = -1.0 * nan_to_high(neg_value)
if self.use_gradient:
neg_grad = self.dlogp_func(pm.floatX(x))
if np.all(np.isfinite(neg_grad)):
self.previous_x = x
grad = nan_to_num(-1.0 * neg_grad)
grad = grad.astype(np.float64)
else:
self.previous_x = x
grad = None
if self.n_eval % 10 == 0:
self.update_progress_desc(neg_value, grad)
if self.n_eval > self.maxeval:
self.update_progress_desc(neg_value, grad)
raise StopIteration
self.n_eval += 1
if self.progressbar:
assert isinstance(self.progress, ProgressBar)
self.progress.update_bar(self.n_eval)
if self.use_gradient:
return value, grad
else:
return value
def test_vae():
minibatch_size = 10
data = pm.floatX(np.random.rand(100))
x_mini = pm.Minibatch(data, minibatch_size)
x_inp = at.vector()
x_inp.tag.test_value = data[:minibatch_size]
ae = aesara.shared(pm.floatX([0.1, 0.1]))
be = aesara.shared(pm.floatX(1.0))
ad = aesara.shared(pm.floatX(1.0))
bd = aesara.shared(pm.floatX(1.0))
enc = x_inp.dimshuffle(0, "x") * ae.dimshuffle("x", 0) + be
mu, rho = enc[:, 0], enc[:, 1]
with pm.Model():
# Hidden variables
zs = pm.Normal("zs", mu=0, sigma=1, size=minibatch_size)
dec = zs * ad + bd
# Observation model
pm.Normal("xs_", mu=dec, sigma=0.1, observed=x_inp)
pm.fit(
1,
local_rv={zs: dict(mu=mu, rho=rho)},
more_replacements={x_inp: x_mini},
more_obj_params=[ae, be, ad, bd],
)
def create_shared_params(self,
trace=None,
size=None,
jitter=1,
start=None):
if trace is None:
if size is None:
raise opvi.ParametrizationError(
"Need `trace` or `size` to initialize")
else:
start = self._prepare_start(start)
# Initialize particles
histogram = np.tile(start, (size, 1))
histogram += pm.floatX(
np.random.normal(0, jitter, histogram.shape))
else:
histogram = np.empty((len(trace) * len(trace.chains), self.ddim))
i = 0
for t in trace.chains:
for j in range(len(trace)):
histogram[i] = DictToArrayBijection.map(trace.point(
j, t)).data
i += 1
return dict(histogram=aesara.shared(pm.floatX(histogram), "histogram"))
def test_observed_type(self):
X_ = pm.floatX(np.random.randn(100, 5))
X = pm.floatX(aesara.shared(X_))
with pm.Model():
x1 = pm.Normal("x1", observed=X_)
x2 = pm.Normal("x2", observed=X)
assert x1.type == X.type
assert x2.type == X.type
def test_free_rv(self):
with pm.Model() as model4:
Normal("n", observed=[[1, 1], [1, 1]], total_size=[2, 2])
p4 = aesara.function([], model4.logp())
with pm.Model() as model5:
n = Normal("n", total_size=[2, Ellipsis, 2], size=(2, 2))
p5 = aesara.function([n.tag.value_var], model5.logp())
assert p4() == p5(pm.floatX([[1]]))
assert p4() == p5(pm.floatX([[1, 1], [1, 1]]))
def test_fit_with_nans(score):
X_mean = pm.floatX(np.linspace(0, 10, 10))
y = pm.floatX(np.random.normal(X_mean * 4, 0.05))
with pm.Model():
inp = pm.Normal("X", X_mean, size=X_mean.shape)
coef = pm.Normal("b", 4.0)
mean = inp * coef
pm.Normal("y", mean, 0.1, observed=y)
with pytest.raises(FloatingPointError) as e:
advi = pm.fit(100, score=score, obj_optimizer=pm.adam(learning_rate=float("nan")))
def test_var_replacement():
X_mean = pm.floatX(np.linspace(0, 10, 10))
y = pm.floatX(np.random.normal(X_mean * 4, 0.05))
with pm.Model():
inp = pm.Normal("X", X_mean, size=X_mean.shape)
coef = pm.Normal("b", 4.0)
mean = inp * coef
pm.Normal("y", mean, 0.1, observed=y)
advi = pm.fit(100)
assert advi.sample_node(mean).eval().shape == (10,)
x_new = pm.floatX(np.linspace(0, 10, 11))
assert advi.sample_node(mean, more_replacements={inp: x_new}).eval().shape == (11,)
def randidx(self, size=None):
if size is None:
size = (1,)
elif isinstance(size, TensorVariable):
if size.ndim < 1:
size = size[None]
elif size.ndim > 1:
raise ValueError("size ndim should be no more than 1d")
else:
pass
else:
size = tuple(np.atleast_1d(size))
return self._rng.uniform(
size=size, low=pm.floatX(0), high=pm.floatX(self.histogram.shape[0]) - pm.floatX(1e-16)
).astype("int32")
def test_aesara_switch_broadcast_edge_cases_1(self):
# Tests against two subtle issues related to a previous bug in Theano
# where `tt.switch` would not always broadcast tensors with single
# values https://github.com/pymc-devs/aesara/issues/270
# Known issue 1: https://github.com/pymc-devs/pymc/issues/4389
data = pm.floatX(np.zeros(10))
with pm.Model() as m:
p = pm.Beta("p", 1, 1)
obs = pm.Bernoulli("obs", p=p, observed=data)
npt.assert_allclose(
logpt_sum(obs).eval({p.tag.value_var: pm.floatX(np.array(0.0))}),
np.log(0.5) * 10,
)
def test_cloning_available(self):
gop = generator(integers())
res = gop**2
shared = aesara.shared(floatX(10))
res1 = aesara.clone_replace(res, {gop: shared})
f = aesara.function([], res1)
assert f() == np.float32(100)
def apply(self, f):
# f: kernel function for KSD f(histogram) -> (k(x,.), \nabla_x k(x,.))
stein = Stein(
approx=self.approx,
kernel=f,
use_histogram=self.approx.all_histograms,
temperature=self.temperature,
)
return pm.floatX(-1) * stein.grad
def rslice(self, total, size, seed):
if size is None:
return slice(None)
elif isinstance(size, int):
rng = pm.at_rng(seed)
Minibatch.RNG[id(self)].append(rng)
return rng.uniform(size=(size,), low=0.0, high=pm.floatX(total) - 1e-16).astype("int64")
else:
raise TypeError("Unrecognized size type, %r" % size)
def build_model(self, distfam, params, size, transform, initval=None):
if initval is not None:
initval = pm.floatX(initval)
with pm.Model() as m:
distfam("x",
size=size,
transform=transform,
initval=initval,
**params)
return m
def create_shared_params(self, start=None):
ipfn = make_initial_point_fn(
model=self.model,
overrides=start,
jitter_rvs={},
return_transformed=True,
)
start = ipfn(self.model.rng_seeder.randint(2**30, dtype=np.int64))
if self.batched:
start = start[self.group[0].name][0]
else:
start = DictToArrayBijection.map(start)
rho = np.zeros((self.ddim, ))
if self.batched:
start = np.tile(start, (self.bdim, 1))
rho = np.tile(rho, (self.bdim, 1))
return {
"mu": aesara.shared(pm.floatX(start), "mu"),
"rho": aesara.shared(pm.floatX(rho), "rho"),
}
def adagrad_window(loss_or_grads=None,
params=None,
learning_rate=0.001,
epsilon=0.1,
n_win=10):
"""Returns a function that returns parameter updates.
Instead of accumulated estimate, uses running window
Parameters
----------
loss_or_grads: symbolic expression or list of expressions
A scalar loss expression, or a list of gradient expressions
params: list of shared variables
The variables to generate update expressions for
learning_rate: float
Learning rate.
epsilon: float
Offset to avoid zero-division in the normalizer of adagrad.
n_win: int
Number of past steps to calculate scales of parameter gradients.
Returns
-------
OrderedDict
A dictionary mapping each parameter to its update expression
"""
if loss_or_grads is None and params is None:
return partial(adagrad_window, **_get_call_kwargs(locals()))
elif loss_or_grads is None or params is None:
raise ValueError(
"Please provide both `loss_or_grads` and `params` to get updates")
grads = get_or_compute_grads(loss_or_grads, params)
updates = OrderedDict()
for param, grad in zip(params, grads):
i = aesara.shared(pm.floatX(0))
i_int = i.astype("int32")
value = param.get_value(borrow=True)
accu = aesara.shared(
np.zeros(value.shape + (n_win, ), dtype=value.dtype))
# Append squared gradient vector to accu_new
accu_new = at.set_subtensor(accu[..., i_int], grad**2)
i_new = at.switch((i + 1) < n_win, i + 1, 0)
updates[accu] = accu_new
updates[i] = i_new
accu_sum = accu_new.sum(axis=-1)
updates[param] = param - (learning_rate * grad /
at.sqrt(accu_sum + epsilon))
return updates
def test_scale_cost_to_minibatch_works(aux_total_size):
mu0 = 1.5
sigma = 1.0
y_obs = np.array([1.6, 1.4])
beta = len(y_obs) / float(aux_total_size)
# TODO: aesara_config
# with pm.Model(aesara_config=dict(floatX='float64')):
# did not not work as expected
# there were some numeric problems, so float64 is forced
with aesara.config.change_flags(floatX="float64", warn_float64="ignore"):
assert aesara.config.floatX == "float64"
assert aesara.config.warn_float64 == "ignore"
post_mu = np.array([1.88], dtype=aesara.config.floatX)
post_sigma = np.array([1], dtype=aesara.config.floatX)
with pm.Model():
mu = pm.Normal("mu", mu=mu0, sigma=sigma)
pm.Normal("y", mu=mu, sigma=1, observed=y_obs, total_size=aux_total_size)
# Create variational gradient tensor
mean_field_1 = MeanField()
assert mean_field_1.scale_cost_to_minibatch
mean_field_1.shared_params["mu"].set_value(post_mu)
mean_field_1.shared_params["rho"].set_value(np.log(np.exp(post_sigma) - 1))
with aesara.config.change_flags(compute_test_value="off"):
elbo_via_total_size_scaled = -pm.operators.KL(mean_field_1)()(10000)
with pm.Model():
mu = pm.Normal("mu", mu=mu0, sigma=sigma)
pm.Normal("y", mu=mu, sigma=1, observed=y_obs, total_size=aux_total_size)
# Create variational gradient tensor
mean_field_2 = MeanField()
assert mean_field_1.scale_cost_to_minibatch
mean_field_2.scale_cost_to_minibatch = False
assert not mean_field_2.scale_cost_to_minibatch
mean_field_2.shared_params["mu"].set_value(post_mu)
mean_field_2.shared_params["rho"].set_value(np.log(np.exp(post_sigma) - 1))
with aesara.config.change_flags(compute_test_value="off"):
elbo_via_total_size_unscaled = -pm.operators.KL(mean_field_2)()(10000)
np.testing.assert_allclose(
elbo_via_total_size_unscaled.eval(),
elbo_via_total_size_scaled.eval() * pm.floatX(1 / beta),
rtol=0.02,
atol=1e-1,
)
def __call__(self, nmc, **kwargs):
op = self.op # type: KSD
grad = op.apply(self.tf)
if self.approx.all_histograms:
z = self.approx.joint_histogram
else:
z = self.approx.symbolic_random
if "more_obj_params" in kwargs:
params = self.obj_params + kwargs["more_obj_params"]
else:
params = self.test_params + kwargs["more_tf_params"]
grad *= pm.floatX(-1)
grads = at.grad(None, params, known_grads={z: grad})
return self.approx.set_size_and_deterministic(
grads, nmc, 0, kwargs.get("more_replacements"))
class TestElementWiseLogp(SeededTest):
def build_model(self, distfam, params, size, transform, initval=None):
if initval is not None:
initval = pm.floatX(initval)
with pm.Model() as m:
distfam("x",
size=size,
transform=transform,
initval=initval,
**params)
return m
def check_transform_elementwise_logp(self, model):
x = model.free_RVs[0]
x_val_transf = x.tag.value_var
pt = model.initial_point(0)
test_array_transf = floatX(
np.random.randn(*pt[x_val_transf.name].shape))
transform = x_val_transf.tag.transform
test_array_untransf = transform.backward(test_array_transf,
*x.owner.inputs).eval()
# Create input variable with same dimensionality as untransformed test_array
x_val_untransf = at.constant(test_array_untransf).type()
jacob_det = transform.log_jac_det(test_array_transf, *x.owner.inputs)
assert joint_logpt(x, sum=False)[0].ndim == x.ndim == jacob_det.ndim
v1 = joint_logpt(x, x_val_transf, jacobian=False).eval(
{x_val_transf: test_array_transf})
v2 = joint_logpt(x, x_val_untransf, transformed=False).eval(
{x_val_untransf: test_array_untransf})
close_to(v1, v2, tol)
def check_vectortransform_elementwise_logp(self, model):
x = model.free_RVs[0]
x_val_transf = x.tag.value_var
pt = model.initial_point(0)
test_array_transf = floatX(
np.random.randn(*pt[x_val_transf.name].shape))
transform = x_val_transf.tag.transform
test_array_untransf = transform.backward(test_array_transf,
*x.owner.inputs).eval()
# Create input variable with same dimensionality as untransformed test_array
x_val_untransf = at.constant(test_array_untransf).type()
jacob_det = transform.log_jac_det(test_array_transf, *x.owner.inputs)
# Original distribution is univariate
if x.owner.op.ndim_supp == 0:
assert joint_logpt(
x, sum=False)[0].ndim == x.ndim == (jacob_det.ndim + 1)
# Original distribution is multivariate
else:
assert joint_logpt(
x, sum=False)[0].ndim == (x.ndim - 1) == jacob_det.ndim
a = joint_logpt(x, x_val_transf,
jacobian=False).eval({x_val_transf: test_array_transf})
b = joint_logpt(x, x_val_untransf, transformed=False).eval(
{x_val_untransf: test_array_untransf})
# Hack to get relative tolerance
close_to(a, b, np.abs(0.5 * (a + b) * tol))
@pytest.mark.parametrize(
"sigma,size",
[
(2.5, 2),
(5.0, (2, 3)),
(np.ones(3) * 10.0, (4, 3)),
],
)
def test_half_normal(self, sigma, size):
model = self.build_model(pm.HalfNormal, {"sigma": sigma},
size=size,
transform=tr.log)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize("lam,size", [(2.5, 2), (5.0, (2, 3)),
(np.ones(3), (4, 3))])
def test_exponential(self, lam, size):
model = self.build_model(pm.Exponential, {"lam": lam},
size=size,
transform=tr.log)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize(
"a,b,size",
[
(1.0, 1.0, 2),
(0.5, 0.5, (2, 3)),
(np.ones(3), np.ones(3), (4, 3)),
],
)
def test_beta(self, a, b, size):
model = self.build_model(pm.Beta, {
"alpha": a,
"beta": b
},
size=size,
transform=tr.logodds)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize(
"lower,upper,size",
[
(0.0, 1.0, 2),
(0.5, 5.5, (2, 3)),
(pm.floatX(np.zeros(3)), pm.floatX(np.ones(3)), (4, 3)),
],
)
def test_uniform(self, lower, upper, size):
def transform_params(*inputs):
_, _, _, lower, upper = inputs
lower = at.as_tensor_variable(lower) if lower is not None else None
upper = at.as_tensor_variable(upper) if upper is not None else None
return lower, upper
interval = tr.Interval(bounds_fn=transform_params)
model = self.build_model(pm.Uniform, {
"lower": lower,
"upper": upper
},
size=size,
transform=interval)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize(
"lower, c, upper, size",
[
(0.0, 1.0, 2.0, 2),
(-10, 0, 200, (2, 3)),
(np.zeros(3), np.ones(3), np.ones(3), (4, 3)),
],
)
def test_triangular(self, lower, c, upper, size):
def transform_params(*inputs):
_, _, _, lower, _, upper = inputs
lower = at.as_tensor_variable(lower) if lower is not None else None
upper = at.as_tensor_variable(upper) if upper is not None else None
return lower, upper
interval = tr.Interval(bounds_fn=transform_params)
model = self.build_model(pm.Triangular, {
"lower": lower,
"c": c,
"upper": upper
},
size=size,
transform=interval)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize("mu,kappa,size",
[(0.0, 1.0, 2), (-0.5, 5.5, (2, 3)),
(np.zeros(3), np.ones(3), (4, 3))])
def test_vonmises(self, mu, kappa, size):
model = self.build_model(pm.VonMises, {
"mu": mu,
"kappa": kappa
},
size=size,
transform=tr.circular)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize("a,size", [(np.ones(2), None),
(np.ones((2, 3)) * 0.5, None),
(np.ones(3), (4, ))])
def test_dirichlet(self, a, size):
model = self.build_model(pm.Dirichlet, {"a": a},
size=size,
transform=tr.simplex)
self.check_vectortransform_elementwise_logp(model)
def test_normal_ordered(self):
model = self.build_model(
pm.Normal,
{
"mu": 0.0,
"sigma": 1.0
},
size=3,
initval=np.asarray([-1.0, 1.0, 4.0]),
transform=tr.ordered,
)
self.check_vectortransform_elementwise_logp(model)
@pytest.mark.parametrize(
"sigma,size",
[
(2.5, (2, )),
(np.ones(3), (4, 3)),
],
)
def test_half_normal_ordered(self, sigma, size):
initval = np.sort(np.abs(np.random.randn(*size)))
model = self.build_model(
pm.HalfNormal,
{"sigma": sigma},
size=size,
initval=initval,
transform=tr.Chain([tr.log, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model)
@pytest.mark.parametrize("lam,size", [(2.5, (2, )), (np.ones(3), (4, 3))])
def test_exponential_ordered(self, lam, size):
initval = np.sort(np.abs(np.random.randn(*size)))
model = self.build_model(
pm.Exponential,
{"lam": lam},
size=size,
initval=initval,
transform=tr.Chain([tr.log, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model)
@pytest.mark.parametrize(
"a,b,size",
[
(
1.0,
1.0,
(2, ),
),
(np.ones(3), np.ones(3), (4, 3)),
],
)
def test_beta_ordered(self, a, b, size):
initval = np.sort(np.abs(np.random.rand(*size)))
model = self.build_model(
pm.Beta,
{
"alpha": a,
"beta": b
},
size=size,
initval=initval,
transform=tr.Chain([tr.logodds, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model)
@pytest.mark.parametrize(
"lower,upper,size",
[(0.0, 1.0, (2, )),
(pm.floatX(np.zeros(3)), pm.floatX(np.ones(3)), (4, 3))],
)
def test_uniform_ordered(self, lower, upper, size):
def transform_params(*inputs):
_, _, _, lower, upper = inputs
lower = at.as_tensor_variable(lower) if lower is not None else None
upper = at.as_tensor_variable(upper) if upper is not None else None
return lower, upper
interval = tr.Interval(bounds_fn=transform_params)
initval = np.sort(np.abs(np.random.rand(*size)))
model = self.build_model(
pm.Uniform,
{
"lower": lower,
"upper": upper
},
size=size,
initval=initval,
transform=tr.Chain([interval, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model)
@pytest.mark.parametrize("mu,kappa,size",
[(0.0, 1.0, (2, )),
(np.zeros(3), np.ones(3), (4, 3))])
def test_vonmises_ordered(self, mu, kappa, size):
initval = np.sort(np.abs(np.random.rand(*size)))
model = self.build_model(
pm.VonMises,
{
"mu": mu,
"kappa": kappa
},
size=size,
initval=initval,
transform=tr.Chain([tr.circular, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model)
@pytest.mark.parametrize(
"lower,upper,size,transform",
[
(0.0, 1.0, (2, ), tr.simplex),
(0.5, 5.5, (2, 3), tr.simplex),
(np.zeros(3), np.ones(3),
(4, 3), tr.Chain([tr.sum_to_1, tr.logodds])),
],
)
def test_uniform_other(self, lower, upper, size, transform):
initval = np.ones(size) / size[-1]
model = self.build_model(
pm.Uniform,
{
"lower": lower,
"upper": upper
},
size=size,
initval=initval,
transform=transform,
)
self.check_vectortransform_elementwise_logp(model)
@pytest.mark.parametrize(
"mu,cov,size,shape",
[
(np.zeros(2), np.diag(np.ones(2)), None, (2, )),
(np.zeros(3), np.diag(np.ones(3)), (4, ), (4, 3)),
],
)
def test_mvnormal_ordered(self, mu, cov, size, shape):
initval = np.sort(np.random.randn(*shape))
model = self.build_model(pm.MvNormal, {
"mu": mu,
"cov": cov
},
size=size,
initval=initval,
transform=tr.ordered)
self.check_vectortransform_elementwise_logp(model)
def __init__(self, approx, beta=1.0):
super().__init__(approx)
self.beta = pm.floatX(beta)
def integers():
i = 0
while True:
yield pm.floatX(i)
i += 1
def gen():
for i in range(2):
yield floatX(np.ones((10, 10)) * i)
def cov(self):
x = self.histogram - self.mean
return x.T.dot(x) / pm.floatX(self.histogram.shape[0])
class TestElementWiseLogp(SeededTest):
def build_model(self, distfam, params, size, transform, initval=None):
if initval is not None:
initval = pm.floatX(initval)
with pm.Model() as m:
distfam("x",
size=size,
transform=transform,
initval=initval,
**params)
return m
def check_transform_elementwise_logp(self, model):
x = model.free_RVs[0]
x0 = x.tag.value_var
assert x.ndim == logpt(x, sum=False).ndim
pt = model.initial_point
array = np.random.randn(*pt[x0.name].shape)
transform = x0.tag.transform
logp_notrans = logpt(x,
transform.backward(array, *x.owner.inputs),
transformed=False)
jacob_det = transform.log_jac_det(aesara.shared(array),
*x.owner.inputs)
assert logpt(x, sum=False).ndim == jacob_det.ndim
v1 = logpt(x, array, jacobian=False).eval()
v2 = logp_notrans.eval()
close_to(v1, v2, tol)
def check_vectortransform_elementwise_logp(self, model, vect_opt=0):
x = model.free_RVs[0]
x0 = x.tag.value_var
# TODO: For some reason the ndim relations
# dont hold up here. But final log-probablity
# values are what we expected.
# assert (x.ndim - 1) == logpt(x, sum=False).ndim
pt = model.initial_point
array = np.random.randn(*pt[x0.name].shape)
transform = x0.tag.transform
logp_nojac = logpt(x,
transform.backward(array, *x.owner.inputs),
transformed=False)
jacob_det = transform.log_jac_det(aesara.shared(array),
*x.owner.inputs)
# assert logpt(x).ndim == jacob_det.ndim
# Hack to get relative tolerance
a = logpt(x, array.astype(aesara.config.floatX), jacobian=False).eval()
b = logp_nojac.eval()
close_to(a, b, np.abs(0.5 * (a + b) * tol))
@pytest.mark.parametrize(
"sd,size",
[
(2.5, 2),
(5.0, (2, 3)),
(np.ones(3) * 10.0, (4, 3)),
],
)
def test_half_normal(self, sd, size):
model = self.build_model(pm.HalfNormal, {"sd": sd},
size=size,
transform=tr.log)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize("lam,size", [(2.5, 2), (5.0, (2, 3)),
(np.ones(3), (4, 3))])
def test_exponential(self, lam, size):
model = self.build_model(pm.Exponential, {"lam": lam},
size=size,
transform=tr.log)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize(
"a,b,size",
[
(1.0, 1.0, 2),
(0.5, 0.5, (2, 3)),
(np.ones(3), np.ones(3), (4, 3)),
],
)
def test_beta(self, a, b, size):
model = self.build_model(pm.Beta, {
"alpha": a,
"beta": b
},
size=size,
transform=tr.logodds)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize(
"lower,upper,size",
[
(0.0, 1.0, 2),
(0.5, 5.5, (2, 3)),
(pm.floatX(np.zeros(3)), pm.floatX(np.ones(3)), (4, 3)),
],
)
def test_uniform(self, lower, upper, size):
def transform_params(*inputs):
_, _, _, lower, upper = inputs
lower = at.as_tensor_variable(lower) if lower is not None else None
upper = at.as_tensor_variable(upper) if upper is not None else None
return lower, upper
interval = tr.interval(transform_params)
model = self.build_model(pm.Uniform, {
"lower": lower,
"upper": upper
},
size=size,
transform=interval)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize(
"lower, c, upper, size",
[
(0.0, 1.0, 2.0, 2),
(-10, 0, 200, (2, 3)),
(np.zeros(3), np.ones(3), np.ones(3), (4, 3)),
],
)
def test_triangular(self, lower, c, upper, size):
def transform_params(*inputs):
_, _, _, lower, _, upper = inputs
lower = at.as_tensor_variable(lower) if lower is not None else None
upper = at.as_tensor_variable(upper) if upper is not None else None
return lower, upper
interval = tr.interval(transform_params)
model = self.build_model(pm.Triangular, {
"lower": lower,
"c": c,
"upper": upper
},
size=size,
transform=interval)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize("mu,kappa,size",
[(0.0, 1.0, 2), (-0.5, 5.5, (2, 3)),
(np.zeros(3), np.ones(3), (4, 3))])
def test_vonmises(self, mu, kappa, size):
model = self.build_model(pm.VonMises, {
"mu": mu,
"kappa": kappa
},
size=size,
transform=tr.circular)
self.check_transform_elementwise_logp(model)
@pytest.mark.parametrize("a,size", [(np.ones(2), None),
(np.ones((2, 3)) * 0.5, None),
(np.ones(3), (4, ))])
def test_dirichlet(self, a, size):
model = self.build_model(pm.Dirichlet, {"a": a},
size=size,
transform=tr.simplex)
self.check_vectortransform_elementwise_logp(model, vect_opt=1)
def test_normal_ordered(self):
model = self.build_model(
pm.Normal,
{
"mu": 0.0,
"sd": 1.0
},
size=3,
initval=np.asarray([-1.0, 1.0, 4.0]),
transform=tr.ordered,
)
self.check_vectortransform_elementwise_logp(model, vect_opt=0)
@pytest.mark.parametrize(
"sd,size",
[
(2.5, (2, )),
(np.ones(3), (4, 3)),
],
)
def test_half_normal_ordered(self, sd, size):
initval = np.sort(np.abs(np.random.randn(*size)))
model = self.build_model(
pm.HalfNormal,
{"sd": sd},
size=size,
initval=initval,
transform=tr.Chain([tr.log, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model, vect_opt=0)
@pytest.mark.parametrize("lam,size", [(2.5, (2, )), (np.ones(3), (4, 3))])
def test_exponential_ordered(self, lam, size):
initval = np.sort(np.abs(np.random.randn(*size)))
model = self.build_model(
pm.Exponential,
{"lam": lam},
size=size,
initval=initval,
transform=tr.Chain([tr.log, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model, vect_opt=0)
@pytest.mark.parametrize(
"a,b,size",
[
(
1.0,
1.0,
(2, ),
),
(np.ones(3), np.ones(3), (4, 3)),
],
)
def test_beta_ordered(self, a, b, size):
initval = np.sort(np.abs(np.random.rand(*size)))
model = self.build_model(
pm.Beta,
{
"alpha": a,
"beta": b
},
size=size,
initval=initval,
transform=tr.Chain([tr.logodds, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model, vect_opt=0)
@pytest.mark.parametrize(
"lower,upper,size",
[(0.0, 1.0, (2, )),
(pm.floatX(np.zeros(3)), pm.floatX(np.ones(3)), (4, 3))],
)
def test_uniform_ordered(self, lower, upper, size):
def transform_params(*inputs):
_, _, _, lower, upper = inputs
lower = at.as_tensor_variable(lower) if lower is not None else None
upper = at.as_tensor_variable(upper) if upper is not None else None
return lower, upper
interval = tr.interval(transform_params)
initval = np.sort(np.abs(np.random.rand(*size)))
model = self.build_model(
pm.Uniform,
{
"lower": lower,
"upper": upper
},
size=size,
initval=initval,
transform=tr.Chain([interval, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model, vect_opt=1)
@pytest.mark.parametrize("mu,kappa,size",
[(0.0, 1.0, (2, )),
(np.zeros(3), np.ones(3), (4, 3))])
def test_vonmises_ordered(self, mu, kappa, size):
initval = np.sort(np.abs(np.random.rand(*size)))
model = self.build_model(
pm.VonMises,
{
"mu": mu,
"kappa": kappa
},
size=size,
initval=initval,
transform=tr.Chain([tr.circular, tr.ordered]),
)
self.check_vectortransform_elementwise_logp(model, vect_opt=0)
@pytest.mark.parametrize(
"lower,upper,size,transform",
[
(0.0, 1.0, (2, ), tr.simplex),
(0.5, 5.5, (2, 3), tr.simplex),
(np.zeros(3), np.ones(3),
(4, 3), tr.Chain([tr.sum_to_1, tr.logodds])),
],
)
def test_uniform_other(self, lower, upper, size, transform):
initval = np.ones(size) / size[-1]
model = self.build_model(
pm.Uniform,
{
"lower": lower,
"upper": upper
},
size=size,
initval=initval,
transform=transform,
)
self.check_vectortransform_elementwise_logp(model, vect_opt=1)
@pytest.mark.parametrize(
"mu,cov,size,shape",
[
(np.zeros(2), np.diag(np.ones(2)), None, (2, )),
(np.zeros(3), np.diag(np.ones(3)), (4, ), (4, 3)),
],
)
def test_mvnormal_ordered(self, mu, cov, size, shape):
initval = np.sort(np.random.randn(*shape))
model = self.build_model(pm.MvNormal, {
"mu": mu,
"cov": cov
},
size=size,
initval=initval,
transform=tr.ordered)
self.check_vectortransform_elementwise_logp(model, vect_opt=1)
def find_constrained_prior(
distribution: pm.Distribution,
lower: float,
upper: float,
init_guess: Dict[str, float],
mass: float = 0.95,
fixed_params: Optional[Dict[str, float]] = None,
) -> Dict[str, float]:
"""
Find optimal parameters to get `mass` % of probability
of `pm_dist` between `lower` and `upper`.
Note: only works for one- and two-parameter distributions, as there
are exactly two constraints. Fix some combination of parameters
if you want to use it on >=3-parameter distributions.
Parameters
----------
distribution : pm.Distribution
PyMC distribution you want to set a prior on.
Needs to have a ``logcdf`` method implemented in PyMC.
lower : float
Lower bound to get `mass` % of probability of `pm_dist`.
upper : float
Upper bound to get `mass` % of probability of `pm_dist`.
init_guess: Dict[str, float]
Initial guess for ``scipy.optimize.least_squares`` to find the
optimal parameters of `pm_dist` fitting the interval constraint.
Must be a dictionary with the name of the PyMC distribution's
parameter as keys and the initial guess as values.
mass: float, default to 0.95
Share of the probability mass we want between ``lower`` and ``upper``.
Defaults to 95%.
fixed_params: Dict[str, float], Optional, default None
Only used when `pm_dist` has at least three parameters.
Dictionary of fixed parameters, so that there are only 2 to optimize.
For instance, for a StudenT, you fix nu to a constant and get the optimized
mu and sigma.
Returns
-------
The optimized distribution parameters as a dictionary with the parameters'
name as key and the optimized value as value.
Examples
--------
.. code-block:: python
# get parameters obeying constraints
opt_params = pm.find_constrained_prior(
pm.Gamma, lower=0.1, upper=0.4, mass=0.75, init_guess={"alpha": 1, "beta": 10}
)
# use these parameters to draw random samples
samples = pm.Gamma.dist(**opt_params, size=100).eval()
# use these parameters in a model
with pm.Model():
x = pm.Gamma('x', **opt_params)
# specify fixed values before optimization
opt_params = pm.find_constrained_prior(
pm.StudentT,
lower=0,
upper=1,
init_guess={"mu": 5, "sigma": 2},
fixed_params={"nu": 7},
)
"""
assert 0.01 <= mass <= 0.99, (
"This function optimizes the mass of the given distribution +/- "
f"1%, so `mass` has to be between 0.01 and 0.99. You provided {mass}.")
# exit when any parameter is not scalar:
if np.any(np.asarray(distribution.rv_op.ndims_params) != 0):
raise NotImplementedError(
"`pm.find_constrained_prior` does not work with non-scalar parameters yet.\n"
"Feel free to open a pull request on PyMC repo if you really need this feature."
)
dist_params = aet.vector("dist_params")
params_to_optim = {
arg_name: dist_params[i]
for arg_name, i in zip(init_guess.keys(), range(len(init_guess)))
}
if fixed_params is not None:
params_to_optim.update(fixed_params)
dist = distribution.dist(**params_to_optim)
try:
logcdf_lower = pm.logcdf(dist, pm.floatX(lower))
logcdf_upper = pm.logcdf(dist, pm.floatX(upper))
except AttributeError:
raise AttributeError(
f"You cannot use `find_constrained_prior` with {distribution} -- it doesn't have a logcdf "
"method yet.\nOpen an issue or, even better, a pull request on PyMC repo if you really "
"need it.")
cdf_error = (pm.math.exp(logcdf_upper) - pm.math.exp(logcdf_lower)) - mass
cdf_error_fn = pm.aesaraf.compile_pymc([dist_params],
cdf_error,
allow_input_downcast=True)
try:
aesara_jac = pm.gradient(cdf_error, [dist_params])
jac = pm.aesaraf.compile_pymc([dist_params],
aesara_jac,
allow_input_downcast=True)
# when PyMC cannot compute the gradient
except (NotImplementedError, NullTypeGradError):
jac = "2-point"
opt = optimize.least_squares(cdf_error_fn,
x0=list(init_guess.values()),
jac=jac)
if not opt.success:
raise ValueError("Optimization of parameters failed.")
# save optimal parameters
opt_params = {
param_name: param_value
for param_name, param_value in zip(init_guess.keys(), opt.x)
}
if fixed_params is not None:
opt_params.update(fixed_params)
# check mass in interval is not too far from `mass`
opt_dist = distribution.dist(**opt_params)
mass_in_interval = (pm.math.exp(pm.logcdf(opt_dist, upper)) -
pm.math.exp(pm.logcdf(opt_dist, lower))).eval()
if (np.abs(mass_in_interval - mass)) > 0.01:
warnings.warn(
f"Final optimization has {(mass_in_interval if mass_in_interval.ndim < 1 else mass_in_interval[0])* 100:.0f}% of probability mass between "
f"{lower} and {upper} instead of the requested {mass * 100:.0f}%.\n"
"You may need to use a more flexible distribution, change the fixed parameters in the "
"`fixed_params` dictionary, or provide better initial guesses.")
return opt_params
