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248 lines (206 loc) · 7.55 KB
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# Copyright 2020 The PyMC Developers
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS
10BC8
,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import warnings
import aesara.tensor as at
import numpy as np
from aesara.compile import SharedVariable
from aesara.tensor.slinalg import ( # noqa: W0611; pylint: disable=unused-import
SolveTriangular,
cholesky,
solve,
)
from aesara.tensor.var import TensorConstant
from scipy.cluster.vq import kmeans
from pymc.aesaraf import compile_pymc, walk_model
# Avoid circular dependency when importing modelcontext
from pymc.distributions.distribution import Distribution
_ = Distribution # keep both pylint and black happy
from pymc.model import modelcontext
JITTER_DEFAULT = 1e-6
solve_lower = SolveTriangular(lower=True)
solve_upper = SolveTriangular(lower=False)
def replace_with_values(vars_needed, replacements=None, model=None):
R"""
Replace random variable nodes in the graph with values given by the replacements dict.
Uses untransformed versions of the inputs, performs some basic input validation.
Parameters
----------
vars_needed: list of TensorVariables
A list of variable outputs
replacements: dict with string keys, numeric values
The variable name and values to be replaced in the model graph.
model: Model
A PyMC model object
"""
model = modelcontext(model)
inputs, input_names = [], []
for rv in walk_model(vars_needed):
if rv in model.named_vars.values() and not isinstance(rv, SharedVariable):
inputs.append(rv)
input_names.append(rv.name)
# Then it's deterministic, no inputs are required, can eval and return
if len(inputs) == 0:
return tuple(v.eval() for v in vars_needed)
fn = compile_pymc(
inputs,
vars_needed,
allow_input_downcast=True,
accept_inplace=True,
on_unused_input="ignore",
)
# Remove unneeded inputs
replacements = {name: val for name, val in replacements.items() if name in input_names}
missing = set(input_names) - set(replacements.keys())
# Error if more inputs are needed
if len(missing) > 0:
missing_str = ", ".join(missing)
raise ValueError(f"Values for {missing_str} must be included in `replacements`.")
return fn(**replacements)
def stabilize(K, jitter=JITTER_DEFAULT):
R"""
Adds small diagonal to a covariance matrix.
Often the matrices calculated from covariance functions, `K = cov_func(X)`
do not appear numerically to be positive semi-definite. Adding a small
correction, `jitter`, to the diagonal is usually enough to fix this.
Parameters
----------
K: array-like
A square covariance or kernel matrix.
jitter: float
A small constant.
"""
return K + jitter * at.identity_like(K)
def kmeans_inducing_points(n_inducing, X, **kmeans_kwargs):
R"""
Use the K-means algorithm to initialize the locations `X` for the inducing
points `fu`.
Parameters
----------
n_inducing: int
The number of inducing points (or k, the number of clusters)
X: array-like
Gaussian process input matrix.
**kmeans_kwargs:
Extra keyword arguments that are passed to `scipy.cluster.vq.kmeans`
"""
# first whiten X
if isinstance(X, TensorConstant):
X = X.value
elif isinstance(X, (np.ndarray, tuple, list)):
X = np.asarray(X)
else:
raise TypeError(
"To use K-means initialization, "
"please provide X as a type that "
"can be cast to np.ndarray, instead "
"of {}".format(type(X))
)
scaling = np.std(X, 0)
# if std of a column is very small (zero), don't normalize that column
scaling[scaling <= 1e-6] = 1.0
Xw = X / scaling
if "k_or_guess" in kmeans_kwargs:
warnings.warn("Use `n_inducing` to set the `k_or_guess` parameter instead.")
Xu, distortion = kmeans(Xw, k_or_guess=n_inducing, **kmeans_kwargs)
return Xu * scaling
def conditioned_vars(varnames):
"""Decorator for validating attrs that are conditioned on."""
def gp_wrapper(cls):
def make_getter(name):
def getter(self):
value = getattr(self, name, None)
if value is None:
raise AttributeError(
"'{}' not set. Provide as argument "
"to condition, or call 'prior' "
"first".format(name.lstrip("_"))
)
else:
return value
return getattr(self, name)
return getter
def make_setter(name):
def setter(self, val):
setattr(self, name, val)
return setter
for name in varnames:
getter = make_getter("_" + name)
setter = make_setter("_" + name)
setattr(cls, name, property(getter, setter))
return cls
return gp_wrapper
def plot_gp_dist(
ax,
samples: np.ndarray,
x: np.ndarray,
plot_samples=True,
palette="Reds",
fill_alpha=0.8,
samples_alpha=0.1,
fill_kwargs=None,
samples_kwargs=None,
):
"""A helper function for plotting 1D GP posteriors from trace
Parameters
----------
ax: axes
Matplotlib axes.
samples: numpy.ndarray
Array of S posterior predictive sample from a GP.
Expected shape: (S, X)
x: numpy.ndarray
Grid of X values corresponding to the samples.
Expected shape: (X,) or (X, 1), or (1, X)
plot_samples: bool
Plot the GP samples along with posterior (defaults True).
palette: str
Palette for coloring output (defaults to "Reds").
fill_alpha: float
Alpha value for the posterior interval fill (defaults to 0.8).
samples_alpha: float
Alpha value for the sample lines (defaults to 0.1).
fill_kwargs: dict
Additional arguments for posterior interval fill (fill_between).
samples_kwargs: dict
Additional keyword arguments for samples plot.
Returns
-------
ax: Matplotlib axes
"""
import matplotlib.pyplot as plt
if fill_kwargs is None:
fill_kwargs = {}
if samples_kwargs is None:
samples_kwargs = {}
if np.any(np.isnan(samples)):
warnings.warn(
"There are `nan` entries in the [samples] arguments. "
"The plot will not contain a band!",
UserWarning,
)
cmap = plt.get_cmap(palette)
percs = np.linspace(51, 99, 40)
colors = (percs - np.min(percs)) / (np.max(percs) - np.min(percs))
samples = samples.T
x = x.flatten()
for i, p in enumerate(percs[::-1]):
upper = np.percentile(samples, p, axis=1)
lower = np.percentile(samples, 100 - p, axis=1)
color_val = colors[i]
ax.fill_between(x, upper, lower, color=cmap(color_val), alpha=fill_alpha, **fill_kwargs)
if plot_samples:
# plot a few samples
idx = np.random.randint(0, samples.shape[1], 30)
ax.plot(x, samples[:, idx], color=cmap(0.9), lw=1, alpha=samples_alpha, **samples_kwargs)
return ax