# Copyright 2024 - present 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,
# 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 numpy as np
import pytensor.tensor as pt
from pytensor.compile import SharedVariable
from pytensor.graph import ancestors
from pytensor.tensor.variable import TensorConstant
from scipy.cluster.vq import kmeans
from pymc.model.core import modelcontext
from pymc.pytensorf import compile
JITTER_DEFAULT = 1e-6
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 ancestors(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(
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"""
Add 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 * pt.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 "
f"of {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):
"""Validate 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(
f"'{name.lstrip('_')}' not set. Provide as argument "
"to condition, or call 'prior' first"
)
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
[docs]
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,
):
"""Plot 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
