# Copyright 2024 The PyMC Labs 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
#
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# distributed under the License is distributed on an "AS IS" BASIS,
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"""Custom PyMC models for causal inference"""
from typing import Any, Dict, Optional
import arviz as az
import numpy as np
import pandas as pd
import pymc as pm
import pytensor.tensor as pt
import xarray as xr
from arviz import r2_score
from causalpy.utils import round_num
[docs]
class PyMCModel(pm.Model):
"""A wraper class for PyMC models. This provides a scikit-learn like interface with
methods like `fit`, `predict`, and `score`. It also provides other methods which are
useful for causal inference.
Example
-------
>>> import causalpy as cp
>>> import numpy as np
>>> import pymc as pm
>>> from causalpy.pymc_models import PyMCModel
>>> class MyToyModel(PyMCModel):
... def build_model(self, X, y, coords):
... with self:
... X_ = pm.Data(name="X", value=X)
... y_ = pm.Data(name="y", value=y)
... beta = pm.Normal("beta", mu=0, sigma=1, shape=X_.shape[1])
... sigma = pm.HalfNormal("sigma", sigma=1)
... mu = pm.Deterministic("mu", pm.math.dot(X_, beta))
... pm.Normal("y_hat", mu=mu, sigma=sigma, observed=y_)
>>> rng = np.random.default_rng(seed=42)
>>> X = rng.normal(loc=0, scale=1, size=(20, 2))
>>> y = rng.normal(loc=0, scale=1, size=(20,))
>>> model = MyToyModel(
... sample_kwargs={
... "chains": 2,
... "draws": 2000,
... "progressbar": False,
... "random_seed": rng,
... }
... )
>>> model.fit(X, y)
Inference data...
>>> X_new = rng.normal(loc=0, scale=1, size=(20,2))
>>> model.predict(X_new)
Inference data...
>>> model.score(X, y)
r2 0.390344
r2_std 0.081135
dtype: float64
"""
[docs]
def __init__(self, sample_kwargs: Optional[Dict[str, Any]] = None):
"""
:param sample_kwargs: A dictionary of kwargs that get unpacked and passed to the
:func:`pymc.sample` function. Defaults to an empty dictionary.
"""
super().__init__()
self.idata = None
self.sample_kwargs = sample_kwargs if sample_kwargs is not None else {}
[docs]
def build_model(self, X, y, coords) -> None:
"""Build the model, must be implemented by subclass."""
raise NotImplementedError("This method must be implemented by a subclass")
def _data_setter(self, X) -> None:
"""
Set data for the model.
This method is used internally to register new data for the model for
prediction.
"""
with self:
pm.set_data({"X": X})
[docs]
def fit(self, X, y, coords: Optional[Dict[str, Any]] = None) -> None:
"""Draw samples from posterior, prior predictive, and posterior predictive
distributions, placing them in the model's idata attribute.
"""
# Ensure random_seed is used in sample_prior_predictive() and
# sample_posterior_predictive() if provided in sample_kwargs.
random_seed = self.sample_kwargs.get("random_seed", None)
self.build_model(X, y, coords)
with self:
self.idata = pm.sample(**self.sample_kwargs)
self.idata.extend(pm.sample_prior_predictive(random_seed=random_seed))
self.idata.extend(
pm.sample_posterior_predictive(
self.idata, progressbar=False, random_seed=random_seed
)
)
return self.idata
[docs]
def predict(self, X):
"""
Predict data given input data `X`
.. caution::
Results in KeyError if model hasn't been fit.
"""
# Ensure random_seed is used in sample_prior_predictive() and
# sample_posterior_predictive() if provided in sample_kwargs.
random_seed = self.sample_kwargs.get("random_seed", None)
self._data_setter(X)
with self: # sample with new input data
post_pred = pm.sample_posterior_predictive(
self.idata,
var_names=["y_hat", "mu"],
progressbar=False,
random_seed=random_seed,
)
return post_pred
[docs]
def score(self, X, y) -> pd.Series:
"""Score the Bayesian :math:`R^2` given inputs ``X`` and outputs ``y``.
.. caution::
The Bayesian :math:`R^2` is not the same as the traditional coefficient of
determination, https://en.wikipedia.org/wiki/Coefficient_of_determination.
"""
yhat = self.predict(X)
yhat = az.extract(
yhat, group="posterior_predictive", var_names="y_hat"
).T.values
# Note: First argument must be a 1D array
return r2_score(y.flatten(), yhat)
[docs]
def calculate_impact(self, y_true, y_pred):
pre_data = xr.DataArray(y_true, dims=["obs_ind"])
impact = pre_data - y_pred["posterior_predictive"]["y_hat"]
return impact.transpose(..., "obs_ind")
[docs]
def calculate_cumulative_impact(self, impact):
return impact.cumsum(dim="obs_ind")
[docs]
def print_coefficients(self, labels, round_to=None) -> None:
def print_row(
max_label_length: int, name: str, coeff_samples: xr.DataArray, round_to: int
) -> None:
"""Print one row of the coefficient table"""
formatted_name = f" {name: <{max_label_length}}"
formatted_val = f"{round_num(coeff_samples.mean().data, round_to)}, 94% HDI [{round_num(coeff_samples.quantile(0.03).data, round_to)}, {round_num(coeff_samples.quantile(1-0.03).data, round_to)}]" # noqa: E501
print(f" {formatted_name} {formatted_val}")
print("Model coefficients:")
coeffs = az.extract(self.idata.posterior, var_names="beta")
# Determine the width of the longest label
max_label_length = max(len(name) for name in labels + ["sigma"])
for name in labels:
coeff_samples = coeffs.sel(coeffs=name)
print_row(max_label_length, name, coeff_samples, round_to)
# Add coefficient for measurement std
coeff_samples = az.extract(self.idata.posterior, var_names="sigma")
name = "sigma"
print_row(max_label_length, name, coeff_samples, round_to)
[docs]
class LinearRegression(PyMCModel):
"""
Custom PyMC model for linear regression.
Defines the PyMC model
.. math::
\\beta &\sim \mathrm{Normal}(0, 50)
\sigma &\sim \mathrm{HalfNormal}(1)
\mu &= X * \\beta
y &\sim \mathrm{Normal}(\mu, \sigma)
Example
--------
>>> import causalpy as cp
>>> import numpy as np
>>> from causalpy.pymc_models import LinearRegression
>>> rd = cp.load_data("rd")
>>> X = rd[["x", "treated"]]
>>> y = np.asarray(rd["y"]).reshape((rd["y"].shape[0],1))
>>> lr = LinearRegression(sample_kwargs={"progressbar": False})
>>> lr.fit(X, y, coords={
... 'coeffs': ['x', 'treated'],
... 'obs_indx': np.arange(rd.shape[0])
... },
... )
Inference data...
""" # noqa: W605
[docs]
def build_model(self, X, y, coords):
"""
Defines the PyMC model
"""
with self:
self.add_coords(coords)
X = pm.Data("X", X, dims=["obs_ind", "coeffs"])
y = pm.Data("y", y[:, 0], dims="obs_ind")
beta = pm.Normal("beta", 0, 50, dims="coeffs")
sigma = pm.HalfNormal("sigma", 1)
mu = pm.Deterministic("mu", pm.math.dot(X, beta), dims="obs_ind")
pm.Normal("y_hat", mu, sigma, observed=y, dims="obs_ind")
[docs]
class WeightedSumFitter(PyMCModel):
"""
Used for synthetic control experiments.
Defines the PyMC model:
.. math::
\sigma &\sim \mathrm{HalfNormal}(1)
\\beta &\sim \mathrm{Dirichlet}(1,...,1)
\mu &= X * \\beta
y &\sim \mathrm{Normal}(\mu, \sigma)
Example
--------
>>> import causalpy as cp
>>> import numpy as np
>>> from causalpy.pymc_models import WeightedSumFitter
>>> sc = cp.load_data("sc")
>>> X = sc[['a', 'b', 'c', 'd', 'e', 'f', 'g']]
>>> y = np.asarray(sc['actual']).reshape((sc.shape[0], 1))
>>> wsf = WeightedSumFitter(sample_kwargs={"progressbar": False})
>>> wsf.fit(X,y)
Inference data...
""" # noqa: W605
[docs]
def build_model(self, X, y, coords):
"""
Defines the PyMC model
"""
with self:
self.add_coords(coords)
n_predictors = X.shape[1]
X = pm.Data("X", X, dims=["obs_ind", "coeffs"])
y = pm.Data("y", y[:, 0], dims="obs_ind")
# TODO: There we should allow user-specified priors here
beta = pm.Dirichlet("beta", a=np.ones(n_predictors), dims="coeffs")
# beta = pm.Dirichlet(
# name="beta", a=(1 / n_predictors) * np.ones(n_predictors),
# dims="coeffs"
# )
sigma = pm.HalfNormal("sigma", 1)
mu = pm.Deterministic("mu", pm.math.dot(X, beta), dims="obs_ind")
pm.Normal("y_hat", mu, sigma, observed=y, dims="obs_ind")
[docs]
class InstrumentalVariableRegression(PyMCModel):
"""Custom PyMC model for instrumental linear regression
Example
--------
>>> import causalpy as cp
>>> import numpy as np
>>> from causalpy.pymc_models import InstrumentalVariableRegression
>>> N = 10
>>> e1 = np.random.normal(0, 3, N)
>>> e2 = np.random.normal(0, 1, N)
>>> Z = np.random.uniform(0, 1, N)
>>> ## Ensure the endogeneity of the the treatment variable
>>> X = -1 + 4 * Z + e2 + 2 * e1
>>> y = 2 + 3 * X + 3 * e1
>>> t = X.reshape(10,1)
>>> y = y.reshape(10,1)
>>> Z = np.asarray([[1, Z[i]] for i in range(0,10)])
>>> X = np.asarray([[1, X[i]] for i in range(0,10)])
>>> COORDS = {'instruments': ['Intercept', 'Z'], 'covariates': ['Intercept', 'X']}
>>> sample_kwargs = {
... "tune": 5,
... "draws": 10,
... "chains": 2,
... "cores": 2,
... "target_accept": 0.95,
... "progressbar": False,
... }
>>> iv_reg = InstrumentalVariableRegression(sample_kwargs=sample_kwargs)
>>> iv_reg.fit(X, Z,y, t, COORDS, {
... "mus": [[-2,4], [0.5, 3]],
... "sigmas": [1, 1],
... "eta": 2,
... "lkj_sd": 1,
... }, None)
Inference data...
"""
[docs]
def build_model(self, X, Z, y, t, coords, priors):
"""Specify model with treatment regression and focal regression data and priors
:param X: A pandas dataframe used to predict our outcome y
:param Z: A pandas dataframe used to predict our treatment variable t
:param y: An array of values representing our focal outcome y
:param t: An array of values representing the treatment t of
which we're interested in estimating the causal impact
:param coords: A dictionary with the coordinate names for our
instruments and covariates
:param priors: An optional dictionary of priors for the mus and
sigmas of both regressions
:code:`priors = {"mus": [0, 0], "sigmas": [1, 1],
"eta": 2, "lkj_sd": 2}`
"""
# --- Priors ---
with self:
self.add_coords(coords)
beta_t = pm.Normal(
name="beta_t",
mu=priors["mus"][0],
sigma=priors["sigmas"][0],
dims="instruments",
)
beta_z = pm.Normal(
name="beta_z",
mu=priors["mus"][1],
sigma=priors["sigmas"][1],
dims="covariates",
)
sd_dist = pm.Exponential.dist(priors["lkj_sd"], shape=2)
chol, corr, sigmas = pm.LKJCholeskyCov(
name="chol_cov",
eta=priors["eta"],
n=2,
sd_dist=sd_dist,
)
# compute and store the covariance matrix
pm.Deterministic(name="cov", var=pt.dot(l=chol, r=chol.T))
# --- Parameterization ---
mu_y = pm.Deterministic(name="mu_y", var=pm.math.dot(X, beta_z))
# focal regression
mu_t = pm.Deterministic(name="mu_t", var=pm.math.dot(Z, beta_t))
# instrumental regression
mu = pm.Deterministic(name="mu", var=pt.stack(tensors=(mu_y, mu_t), axis=1))
# --- Likelihood ---
pm.MvNormal(
name="likelihood",
mu=mu,
chol=chol,
observed=np.stack(arrays=(y.flatten(), t.flatten()), axis=1),
shape=(X.shape[0], 2),
)
[docs]
def sample_predictive_distribution(self, ppc_sampler="jax"):
"""Function to sample the Multivariate Normal posterior predictive
Likelihood term in the IV class. This can be slow without
using the JAX sampler compilation method. If using the
JAX sampler it will sample only the posterior predictive distribution.
If using the PYMC sampler if will sample both the prior
and posterior predictive distributions."""
random_seed = self.sample_kwargs.get("random_seed", None)
if ppc_sampler == "jax":
with self:
self.idata.extend(
pm.sample_posterior_predictive(
self.idata,
random_seed=random_seed,
compile_kwargs={"mode": "JAX"},
)
)
elif ppc_sampler == "pymc":
with self:
self.idata.extend(pm.sample_prior_predictive(random_seed=random_seed))
self.idata.extend(
pm.sample_posterior_predictive(
self.idata,
random_seed=random_seed,
)
)
[docs]
def fit(self, X, Z, y, t, coords, priors, ppc_sampler=None):
"""Draw samples from posterior distribution and potentially
from the prior and posterior predictive distributions. The
fit call can take values for the
ppc_sampler = ['jax', 'pymc', None]
We default to None, so the user can determine if they wish
to spend time sampling the posterior predictive distribution
independently.
"""
# Ensure random_seed is used in sample_prior_predictive() and
# sample_posterior_predictive() if provided in sample_kwargs.
# Use JAX for ppc sampling of multivariate likelihood
self.build_model(X, Z, y, t, coords, priors)
with self:
self.idata = pm.sample(**self.sample_kwargs)
self.sample_predictive_distribution(ppc_sampler=ppc_sampler)
return self.idata
[docs]
class PropensityScore(PyMCModel):
"""
Custom PyMC model for inverse propensity score models
.. note:
Generally, the `.fit()` method should be used rather than
calling `.build_model()` directly.
Defines the PyMC model
.. math::
\\beta &\sim \mathrm{Normal}(0, 1)
\sigma &\sim \mathrm{HalfNormal}(1)
\mu &= X * \\beta
p &= logit^{-1}(mu)
t &\sim \mathrm{Bernoulli}(p)
Example
--------
>>> import causalpy as cp
>>> import numpy as np
>>> from causalpy.pymc_models import PropensityScore
>>> df = cp.load_data('nhefs')
>>> X = df[["age", "race"]]
>>> t = np.asarray(df["trt"])
>>> ps = PropensityScore(sample_kwargs={"progressbar": False})
>>> ps.fit(X, t, coords={
... 'coeffs': ['age', 'race'],
... 'obs_indx': np.arange(df.shape[0])
... },
... )
Inference...
""" # noqa: W605
[docs]
def build_model(self, X, t, coords):
"Defines the PyMC propensity model"
with self:
self.add_coords(coords)
X_data = pm.MutableData("X", X, dims=["obs_ind", "coeffs"])
t_data = pm.MutableData("t", t.flatten(), dims="obs_ind")
b = pm.Normal("b", mu=0, sigma=1, dims="coeffs")
mu = pm.math.dot(X_data, b)
p = pm.Deterministic("p", pm.math.invlogit(mu))
pm.Bernoulli("t_pred", p=p, observed=t_data, dims="obs_ind")
[docs]
def fit(self, X, t, coords):
"""Draw samples from posterior, prior predictive, and posterior predictive
distributions. We overwrite the base method because the base method assumes
a variable y and we use t to indicate the treatment variable here.
"""
# Ensure random_seed is used in sample_prior_predictive() and
# sample_posterior_predictive() if provided in sample_kwargs.
random_seed = self.sample_kwargs.get("random_seed", None)
self.build_model(X, t, coords)
with self:
self.idata = pm.sample(**self.sample_kwargs)
self.idata.extend(pm.sample_prior_predictive(random_seed=random_seed))
self.idata.extend(
pm.sample_posterior_predictive(
self.idata, progressbar=False, random_seed=random_seed
)
)
return self.idata
