Source code for nnpiv.semiparametrics.dml_mediated
"""
This module performs Debiased Machine Learning for mediation analysis, using joint or sequential estimation for longitudinal
nonparametric parameters (in the Nested NPIV framework). It provides tools for estimating causal effects with
mediation using a combination of machine learning models and instrumental variables techniques. The module supports different types of mediated estimands, cross-validation, kernel density estimation
for localization, and confidence interval computation with pointwise or uniform guarantees.
Classes:
DML_mediated: Main class for performing DML for mediation analysis with joint/sequential model fitting.
DML_mediated Methods:
__init__: Initialize the DML_mediated instance with data and model configurations.
_calculate_confidence_interval: Calculate confidence intervals for the estimates.
_localization: Perform localization using kernel density estimation.
_npivfit_outcome: Fit the outcome model using nonparametric instrumental variables.
_nnpivfit_outcome_m: Fit the mediated outcome model sequentially using nonparametric instrumental variables.
_propensity_score: Estimate the propensity score.
_npivfit_action: Fit the action model using nonparametric instrumental variables.
_nnpivfit_action_m: Fit the mediated action model sequentially using nonparametric instrumental variables.
_scores_mediated: Calculate the scores for the mediated effects.
_scores_Y1: Calculate the scores for the Y1 estimand.
_process_fold: Process a single fold for cross-validation.
_split_and_estimate: Split the data and estimate the model for each fold.
dml: Perform Debiased Machine Learning for Nonparametric Instrumental Variables.
"""
import numpy as np
from scipy.stats import norm
from sklearn.model_selection import KFold
from sklearn.linear_model import LogisticRegression
from sklearn.cluster import KMeans
from sklearn.preprocessing import PolynomialFeatures
from statsmodels.nonparametric.kde import kernel_switch
import warnings
from tqdm import tqdm # Import tqdm
import copy
import torch
from nnpiv.rkhs import RKHS2IVCV, ApproxRKHSIVCV, RKHS2IVL2
from joblib import Parallel, delayed, cpu_count
from scipy.optimize import minimize_scalar
DEVICE = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")
toT = lambda a: torch.as_tensor(a, dtype=torch.float32, device=DEVICE)
def _to_np(a):
"""
Convert a tensor to a numpy array if it is a tensor.
"""
return a.detach().cpu().numpy() if isinstance(a, torch.Tensor) else a
def _get(opts, key, default):
"""
Retrieve the value associated with 'key' in 'opts', or return 'default' if not present.
Parameters
----------
opts : dict
Dictionary of options.
key : str
Key to look up in 'opts'.
default : any
Default value to return if 'key' is not found.
Returns
-------
any
Value associated with 'key' or 'default'.
"""
return opts[key] if (opts is not None and key in opts) else default
def _transform_poly(X, opts):
"""
Transform the input data X using polynomial features.
Parameters
----------
X : array-like
Input data.
opts : dict
Options dictionary containing the polynomial degree ('lin_degree').
Returns
-------
array-like
Transformed data.
"""
degree = _get(opts, 'lin_degree', 1)
if degree == 1:
return X
else:
trans = PolynomialFeatures(degree=degree, include_bias=False)
return trans.fit_transform(X)
def _fun_threshold_alpha(alpha, g):
"""
Auxiliary function for computation of optimal alpha for improvement in overlap: CHIM
(Dealing with limited overlap in estimation of average treatment effects, Crump et al., Biometrika, 2009).
Parameters
----------
alpha : float
Alpha value.
g : array-like
Input array.
Returns
-------
float
Result of the threshold function.
"""
lambda_val = 1 / (alpha * (1 - alpha))
ind = (g <= lambda_val)
den = sum(ind)
num = ind * g
result = (2 * sum(num) / den - lambda_val) ** 2
return result
[docs]class DML_mediated:
"""
Debiased Machine Learning for mediation analysis (DML-mediation) class with joint/sequential model fitting.
Parameters
----------
Y : array-like
Outcome variable.
D : array-like
Treatment variable.
M : array-like
Mediator variable.
W : array-like
Negative control outcome.
Z : array-like
Instrumental variable.
X1 : array-like, optional
Additional covariates.
V : array-like, optional
Localization covariates.
v_values : array-like, optional
Values for localization.
include_V : bool, optional
Include localization covariates in the model.
ci_type : str, optional
Type of confidence interval ('pointwise', 'uniform').
loc_kernel : str, optional
Kernel for localization. Options include 'gau', 'epa', 'uni', 'tri', etc.
bw_loc : str, optional
Bandwidth for localization.
estimator : str, optional
Estimator type ('MR', 'OR', 'hybrid', 'IPW').
estimand : str, optional
Type of estimand ('ATE', 'Indirect', 'Direct', 'E[Y1]', 'E[Y0]', 'E[Y(1,M(0))]').
model1 : estimator /(list), optional
Model for the outcome stage - Can be a joint or sequential estimator; if the latter a list must be given
nn_1 : bool /(list), optional
Use neural network for the outcome stage.
modelq1 : estimator /(list), optional
Model for the q1 stage - Can be a joint or sequential estimator; if the latter a list must be given
nn_q1 : bool /(list), optional
Use neural network for the q1 stage.
model_y : estimator, optional
Model for the outcome - for use with 'E[Y1]', 'E[Y0]', 'Direct', 'Indirect', and 'ATE' estimands.
nn_y : bool, optional
Use neural network for the outcome model.
model_a : estimator, optional
Model for the action - for use with 'E[Y1]', 'E[Y0]', 'Direct', 'Indirect', and 'ATE' estimands.
nn_a : bool, optional
Use neural network for the action model.
alpha : float, optional
Significance level for confidence intervals.
n_folds : int, optional
Number of folds for estimation.
n_rep : int, optional
Number of repetitions for estimation.
inner_n_jobs : int, optional
Number of parallel jobs for inner fold processing. If None, defaults to
min(n_folds, available_cores).
random_seed : int, optional
Seed for random number generator.
prop_score : estimator, optional
Model for propensity score.
CHIM : bool, optional
Use CHIM method:
Dropping observations with extreme values of the propensity score - CHIM (2009)
verbose : bool, optional
Print progress information.
fitargs1 : dict, optional
Arguments for fitting the outcome stage model.
fitargsq1 : dict, optional
Arguments for fitting the q1 stage model.
fitargsy : dict, optional
Arguments for fitting the one stage outcome model.
fitargsa : dict, optional
Arguments for fitting the one stage action model.
opts : dict, optional
Additional options.
"""
def __init__(self, Y, D, M, W, Z, X1=None,
V=None,
v_values=None,
include_V=True,
ci_type='pointwise',
loc_kernel='gau',
bw_loc='silverman',
estimator='MR',
estimand='ATE',
model1=RKHS2IVL2(kernel='rbf', gamma=.0013, delta_scale='auto', delta_exp=10),
nn_1=False,
modelq1=RKHS2IVL2(kernel='rbf', gamma=.0013, delta_scale='auto', delta_exp=10),
nn_q1=False,
model_y=ApproxRKHSIVCV(kernel_approx='nystrom', n_components=100,
kernel='rbf', gamma=.1, delta_scale='auto',
delta_exp=.4, alpha_scales=np.geomspace(1, 10000, 10), cv=5),
nn_y=False,
model_a=ApproxRKHSIVCV(kernel_approx='nystrom', n_components=100,
kernel='rbf', gamma=.1, delta_scale='auto',
delta_exp=.4, alpha_scales=np.geomspace(1, 10000, 10), cv=5),
nn_a=False,
alpha=0.05,
n_folds=5,
n_rep=1,
inner_n_jobs=None,
random_seed=123,
prop_score=LogisticRegression(),
CHIM=False,
verbose=True,
fitargs1=None,
fitargsq1=None,
fitargsy=None,
fitargsa=None,
opts=None
):
self.Y = Y
self.D = D
self.M = M
self.W = W
self.Z = Z
self.X1 = X1
self.V = V
self.v_values = v_values
self.include_V = include_V
self.ci_type = ci_type
self.loc_kernel = loc_kernel
self.bw_loc = bw_loc
self.estimator = estimator
self.estimand = estimand
self.model_y = copy.deepcopy(model_y)
self.model_a = copy.deepcopy(model_a)
self.nn_y = nn_y
self.nn_a = nn_a
self.prop_score = prop_score
self.CHIM = CHIM
self.alpha = alpha
self.n_folds = n_folds
self.n_rep = n_rep
self.inner_n_jobs = self._resolve_inner_n_jobs(inner_n_jobs)
self.random_seed = random_seed
self.verbose = verbose
self.fitargsy = fitargsy
self.fitargsa = fitargsa
self.opts = opts
if isinstance(model1, list):
self.model1 = copy.deepcopy(model1[0])
self.model2 = copy.deepcopy(model1[1])
self.sequential_o = True
if not isinstance(nn_1, list):
warnings.warn("Sequential outcome model fitting requires nn_1 to be a list. Assuming [nn_1, nn_1]", UserWarning)
self.nn_1 = nn_1
self.nn_2 = nn_1
else:
self.nn_1 = nn_1[0]
self.nn_2 = nn_1[1]
if not isinstance(fitargs1, list):
warnings.warn("Sequential outcome model fitting requires fitargs1 to be a list. Assuming [fitargs1, fitargs1]", UserWarning)
self.fitargs1 = fitargs1
self.fitargs2 = fitargs1
else:
self.fitargs1 = fitargs1[0]
self.fitargs2 = fitargs1[1]
else:
self.model1 = copy.deepcopy(model1)
self.nn_1 = nn_1
self.fitargs1 = fitargs1
self.sequential_o = False
if isinstance(modelq1, list):
self.modelq1 = copy.deepcopy(modelq1[0])
self.modelq2 = copy.deepcopy(modelq1[1])
self.sequential_a = True
if not isinstance(nn_q1, list):
warnings.warn("Sequential outcome model fitting requires nn_q1 to be a list. Assuming [nn_q1, nn_q1]", UserWarning)
self.nn_q1 = nn_q1
self.nn_q2 = nn_q1
else:
self.nn_q1 = nn_q1[0]
self.nn_q2 = nn_q1[1]
if not isinstance(fitargsq1, list):
warnings.warn("Sequential outcome model fitting requires fitargsq1 to be a list. Assuming [fitargsq1, fitargsq1]", UserWarning)
self.fitargsq1 = fitargsq1
self.fitargsq2 = fitargsq1
else:
self.fitargsq1 = fitargsq1[0]
self.fitargsq2 = fitargsq1[1]
else:
self.modelq1 = copy.deepcopy(modelq1)
self.nn_q1 = nn_q1
self.fitargsq1 = fitargsq1
self.sequential_a = False
if self.X1 is None:
if self.V is not None and self.include_V == True:
self.X = self.V
else:
self.X = np.ones((self.Y.shape[0], 1))
else:
if self.V is not None and self.include_V == True:
self.X = np.column_stack([self.X1, self.V])
else:
self.X = self.X1
lengths = [len(Y), len(D), len(M), len(W), len(Z), len(self.X)]
if len(set(lengths)) != 1:
raise ValueError("All input vectors must have the same length.")
if self.estimator not in ['MR', 'OR', 'hybrid', 'IPW']:
warnings.warn(f"Invalid estimator: {estimator}. Estimator must be one of ['MR', 'OR', 'hybrid', 'IPW']. Using MR instead.", UserWarning)
self.estimator = 'MR'
if self.estimand not in ['ATE', 'Indirect', 'Direct', 'E[Y1]', 'E[Y0]', 'E[Y(1,M(0))]']:
warnings.warn(f"Invalid estimator: {estimator}. Estimator must be one of ['ATE', 'Indirect', 'Direct', 'E[Y1]', 'E[Y0]', 'E[Y(1,M(0))]']. Using ATE instead.", UserWarning)
self.estimand = 'ATE'
if self.estimand in ['ATE', 'E[Y1]', 'E[Y0]'] and self.estimator=='hybrid':
warnings.warn(f"Invalid estimator: {estimator}. Estimator must be one of ['MR', 'OR', 'IPW'] when estimand is {estimand}. Using MR instead.", UserWarning)
self.estimator = 'MR'
if self.ci_type not in ['pointwise', 'uniform']:
warnings.warn(f"Invalid confidence interval type: {ci_type}. Confidence interval type must be one of ['pointwise', 'uniform']. Using pointwise instead.", UserWarning)
self.ci_type = 'pointwise'
if self.ci_type == 'uniform' and (self.v_values is None or self.v_values.shape[0] == 1 or self.V is None):
warnings.warn(f"Uniform confidence intervals are not supported for less than one localization value. Using pointwise instead.", UserWarning)
self.ci_type = 'pointwise'
if self.loc_kernel not in list(kernel_switch.keys()):
warnings.warn(f"Invalid kernel: {loc_kernel}. Kernel must be one of {list(kernel_switch.keys())}. Using gau instead.", UserWarning)
self.loc_kernel = 'gau'
if isinstance(self.bw_loc, str):
if self.bw_loc not in ['silverman', 'scott']:
warnings.warn(f"Invalid bw rule: {bw_loc}. Bandwidth rule must be one of ['silverman', 'scott'] or provided by the user. Using silverman instead.", UserWarning)
self.bw_loc = 'silverman'
if self.V is not None:
if self.v_values is None:
warnings.warn(f"v_values is None. Computing localization around mean(V).", UserWarning)
self.v_values = np.mean(self.V, axis=0)
def _resolve_inner_n_jobs(self, inner_n_jobs):
if inner_n_jobs is None:
return max(1, min(int(self.n_folds), int(cpu_count())))
if isinstance(inner_n_jobs, bool):
raise ValueError(f"inner_n_jobs must be an integer >= 1, got {inner_n_jobs!r}.")
try:
value = int(inner_n_jobs)
except Exception as exc:
raise ValueError(f"inner_n_jobs must be an integer >= 1, got {inner_n_jobs!r}.") from exc
if value < 1:
raise ValueError(f"inner_n_jobs must be an integer >= 1, got {inner_n_jobs!r}.")
return min(value, int(self.n_folds))
def _calculate_confidence_interval(self, theta, theta_var, theta_cov):
"""
Calculate the confidence interval for the given estimates.
Parameters
----------
theta : array-like
Estimated values.
theta_var : array-like
Variance of the estimates.
theta_cov : array-like
Covariance matrix of the estimates.
Returns
-------
array-like
Lower and upper bounds of the confidence intervals.
"""
n = self.Y.shape[0]
if self.ci_type == 'pointwise':
z_alpha_half = norm.ppf(1 - self.alpha / 2)
margin_of_error = z_alpha_half * np.sqrt(theta_var / n)
else:
S = np.diag(np.diag(theta_cov))
S_inv_sqrt = np.diag(1.0 / np.sqrt(np.diag(S)))
Sigma_hat = S_inv_sqrt @ theta_cov @ S_inv_sqrt
# Sample Q from N(0, Sigma_hat)
Q_samples = np.random.multivariate_normal(np.zeros(theta.shape[0]), Sigma_hat, 5000)
# Compute the (1 - alpha) quantile of the sampled |Q|_infty
Q_infinity_norms = np.max(np.abs(Q_samples), axis=1)
c_alpha = np.quantile(Q_infinity_norms, 1 - self.alpha)
margin_of_error = c_alpha * np.sqrt(np.diag(theta_cov) / n)
lower_bound = theta - margin_of_error
upper_bound = theta + margin_of_error
return np.column_stack((lower_bound, upper_bound))
def _localization(self, V, v_val, bw):
"""
Perform localization using kernel density estimation.
Parameters
----------
V : array-like
Localization covariates.
v_val : array-like
Values for localization.
bw : float
Bandwidth for localization.
Returns
-------
array-like
Weights for localization.
"""
if kernel_switch[self.loc_kernel]().domain is None:
def K(x):
return kernel_switch[self.loc_kernel]()(x)
else:
def K(x):
y = kernel_switch[self.loc_kernel]()(x)*((kernel_switch[self.loc_kernel]().domain[0]<=x) & (x<=kernel_switch[self.loc_kernel]().domain[1]))
return y
v = (V-v_val)/bw
KK = np.prod(list(map(K, v)),axis=1)
omega = np.mean(KK,axis=0)
ell = KK/omega
return ell.reshape(-1,1)
def _nnpivfit_outcome_m(self, Y, D, M, W, X, Z):
"""
Fit the mediated outcome model using nonparametric instrumental variables.
Parameters
----------
Y : array-like
Outcome variable.
D : array-like
Treatment variable.
M : array-like
Mediator variable.
W : array-like
Negative control outcome.
X : array-like
Covariates.
Z : array-like
Instrumental variable.
Returns
-------
tuple
Fitted models for treatment and control groups.
"""
if self.estimator == 'MR' or self.estimator == 'OR' or self.estimator == 'hybrid':
model_1 = copy.deepcopy(self.model1)
model_2 = copy.deepcopy(self.model2)
#First stage
if self.nn_1==True:
Y, D, M, W, X, Z = map(toT, [Y, D, M, W, X, Z])
ind = (torch.nonzero(D.reshape(-1) == 1).squeeze(1) if self.nn_1 else np.where(D==1)[0])
M1 = M[ind]
W1 = W[ind]
X1 = X[ind,:]
Z1 = Z[ind]
Y1 = Y[ind]
if self.nn_1==True:
A2 = torch.cat((M1,X1,Z1),1)
A1 = torch.cat((M1,X1,W1),1)
else:
A2 = _transform_poly(np.column_stack((M1,X1,Z1)),self.opts)
A1 = _transform_poly(np.column_stack((M1,X1,W1)),self.opts)
if self.fitargs1 is not None:
bridge_1 = model_1.fit(A2, A1, Y1, **self.fitargs1)
else:
bridge_1 = model_1.fit(A2, A1, Y1)
if self.nn_1==True:
A1 = torch.cat((M,X,W),1)
_pred = bridge_1.predict(A1.to(DEVICE), model='avg', burn_in=_get(self.opts, 'burnin', 0))
bridge_1_hat = _pred if isinstance(_pred, torch.Tensor) else toT(_pred)
else:
A1 = _transform_poly(np.column_stack((M,X,W)),self.opts)
bridge_1_hat = bridge_1.predict(A1)
bridge_1_hat = bridge_1_hat.reshape(A1.shape[:1] + Y.shape[1:])
else:
bridge_1 = None
if self.estimator == 'MR' or self.estimator == 'OR':
#Second stage
if self.nn_1!=self.nn_2:
if self.nn_2==False:
D, W, X, Z, bridge_1_hat = map(_to_np, [D, W, X, Z, bridge_1_hat])
else:
D, W, X, Z, bridge_1_hat = map(toT, [D, W, X, Z, bridge_1_hat])
ind = (torch.nonzero(D.reshape(-1) == 0).squeeze(1) if self.nn_2 else np.where(D==0)[0])
W0 = W[ind]
X0 = X[ind,:]
Z0 = Z[ind]
bridge_1_hat = bridge_1_hat[ind]
if self.nn_2==True:
B2 = torch.cat((X0,Z0),1)
B1 = torch.cat((X0,W0),1)
else:
B2 = _transform_poly(np.column_stack((X0,Z0)),self.opts)
B1 = _transform_poly(np.column_stack((X0,W0)),self.opts)
if self.fitargs2 is not None:
bridge_2 = model_2.fit(B2, B1, bridge_1_hat, **self.fitargs2)
else:
bridge_2 = model_2.fit(B2, B1, bridge_1_hat)
else:
bridge_2 = None
Y, D, M, W, X, Z = map(_to_np, [Y, D, M, W, X, Z])
return bridge_1, bridge_2
def _npivfit_outcome(self, Y, D, X, Z):
"""
Fit the outcome model using nonparametric instrumental variables.
Parameters
----------
Y : array-like
Outcome variable.
D : array-like
Treatment variable.
X : array-like
Covariates.
Z : array-like
Instrumental variable.
Returns
-------
object
Fitted model.
"""
model_y1 = copy.deepcopy(self.model_y)
# First stage
if self.nn_y==True:
Y, D, X, Z = map(toT, [Y, D, X, Z])
else:
Y, D, X, Z = map(_to_np, [Y, D, X, Z])
X = _transform_poly(X, self.opts)
Z = _transform_poly(Z, self.opts)
ind = (torch.nonzero(D.reshape(-1) == 1).squeeze(1) if self.nn_y else np.where(D==1)[0])
Y1 = Y[ind]
X1 = X[ind, :]
Z1 = Z[ind]
if self.fitargsy is not None:
bridge_1 = model_y1.fit(Z1, X1, Y1, **self.fitargsy)
else:
bridge_1 = model_y1.fit(Z1, X1, Y1)
Y, D, X, Z = map(_to_np, [Y, D, X, Z])
return bridge_1
def _propensity_score(self, M, X, W, D):
"""
Estimate the propensity score.
Parameters
----------
M : array-like
Mediator variable.
X : array-like
Covariates.
W : array-like
Negative control outcome.
D : array-like
Treatment variable.
Returns
-------
tuple
Estimated propensity scores and threshold alpha.
"""
M, X, W, D = map(_to_np, (M, X, W, D))
model_ps = copy.deepcopy(self.prop_score)
X1 = np.column_stack((X,W))
X0 = np.column_stack((M,X,W))
#First stage
model_ps.fit(X1, D.flatten())
ps_hat_0 = model_ps.predict_proba(X1)[:,0]
if self.estimand in ['Indirect', 'Direct', 'E[Y(1,M(0))]']:
#Second stage
model_ps.fit(X0, D.flatten())
ps_hat_00 = model_ps.predict_proba(X0)[:,0]
else:
ps_hat_00 = ps_hat_0
# Overlap assumption
ps_hat_0 = np.where(ps_hat_0 == 1, 0.99, ps_hat_0)
ps_hat_0 = np.where(ps_hat_0 == 0, 0.01, ps_hat_0)
ps_hat_00 = np.where(ps_hat_00 == 1, 0.99, ps_hat_00)
ps_hat_00 = np.where(ps_hat_00 == 0, 0.01, ps_hat_00)
if self.CHIM==True:
# Dropping observations with extreme values of the propensity score - CHIM (2009)
# One finds the smallest value of \alpha\in [0,0.5] s.t.
# $\lambda:=\frac{1}{\alpha(1-\alpha)}$
# $2\frac{\sum 1(g(X)\leq\lambda)*g(X)}{\sum 1(g(X)\leq\lambda)}-\lambda\geq 0$
#
# Equivalently the first value of alpha (in increasing order) such that the constraint is achieved by equality
# (as the constraint is a monotone increasing function in alpha)
g_values = [1/(ps_hat_0*(1-ps_hat_0)), 1/(ps_hat_00*(1-ps_hat_00))]
optimized_alphas = []
for g in g_values:
def _objective_function(alpha):
return _fun_threshold_alpha(alpha, g)
result = minimize_scalar(_objective_function, bounds=(0.001, 0.499))
optimized_alphas.append(result.x)
alfa = max(optimized_alphas)
else:
alfa = 0.0
M, X, W, D = map(toT, (M, X, W, D))
return ps_hat_0.reshape(-1,1), ps_hat_00.reshape(-1,1), alfa
def _nnpivfit_action_m(self, ps_hat_0, ps_hat_00, D, M, W, X, Z, alfa=0.0):
"""
Fit the mediated action model using nonparametric instrumental variables.
Parameters
----------
ps_hat_0 : array-like
Estimated propensity scores for control group.
ps_hat_00 : array-like
Estimated propensity scores for mediated control group.
D : array-like
Treatment variable.
M : array-like
Mediator variable.
W : array-like
Negative control outcome.
X : array-like
Covariates.
Z : array-like
Instrumental variable.
alfa : float, optional
Threshold alpha for propensity scores.
Returns
-------
tuple
Fitted models for mediated action.
"""
if self.estimator == 'MR' or self.estimator == 'IPW' or self.estimator == 'hybrid':
mask = np.where((ps_hat_0 >= alfa) & (ps_hat_0 <= 1 - alfa) &
(ps_hat_00 >= alfa) & (ps_hat_00 <= 1 - alfa))[0]
ps_hat_0 = ps_hat_0[mask]
ps_hat_00 = ps_hat_00[mask]
ps_hat_01 = 1 - ps_hat_00
D = D[mask]
M = M[mask]
W = W[mask]
X = X[mask,:]
Z = Z[mask]
model_q1 = copy.deepcopy(self.modelq1)
model_q2 = copy.deepcopy(self.modelq2)
#First stage
if self.nn_q1==True:
ps_hat_0, ps_hat_00, ps_hat_01, D, M, W, X, Z = map(toT, [ps_hat_0, ps_hat_00, ps_hat_01, D, M, W, X, Z])
else:
ps_hat_0, ps_hat_00, ps_hat_01, D, M, W, X, Z = map(_to_np, [ps_hat_0, ps_hat_00, ps_hat_01, D, M, W, X, Z])
ind = (torch.nonzero(D.reshape(-1) == 0).squeeze(1) if self.nn_q1 else np.where(D==0)[0])
ps_hat_0 = ps_hat_0[ind]
W1 = W[ind]
X1 = X[ind,:]
Z1 = Z[ind]
if self.nn_q1==True:
A2 = torch.cat((X1,W1),1)
A1 = torch.cat((X1,Z1),1)
else:
A2 = _transform_poly(np.column_stack((X1,W1)),self.opts)
A1 = _transform_poly(np.column_stack((X1,Z1)),self.opts)
if self.fitargsq1 is not None:
bridge_1 = model_q1.fit(A2, A1, 1/ps_hat_0, **self.fitargsq1)
else:
bridge_1 = model_q1.fit(A2, A1, 1/ps_hat_0)
if self.nn_q1==True:
A1 = torch.cat((X,Z),1)
_pred = bridge_1.predict(A1.to(DEVICE), model='avg', burn_in=_get(self.opts, 'burnin', 0))
bridge_1_hat = _pred if isinstance(_pred, torch.Tensor) else toT(_pred)
else:
A1 = _transform_poly(np.column_stack((X,Z)),self.opts)
bridge_1_hat = bridge_1.predict(A1)
bridge_1_hat = bridge_1_hat.reshape(A1.shape[:1] + ps_hat_0.shape[1:])
else:
bridge_1 = None
if self.estimator == 'MR' or self.estimator == 'IPW':
#Second stage
if self.nn_q1!=self.nn_q2:
if self.nn_q2==False:
D, M, W, X, Z, bridge_1_hat, ps_hat_00, ps_hat_01 = map(_to_np, [D, M, W, X, Z, bridge_1_hat, ps_hat_00, ps_hat_01])
else:
D, M, W, X, Z, bridge_1_hat, ps_hat_00, ps_hat_01 = map(toT, [D, M, W, X, Z, bridge_1_hat, ps_hat_00, ps_hat_01])
bridge_1_hat = bridge_1_hat*(ps_hat_00/ps_hat_01)
ind = (torch.nonzero(D.reshape(-1) == 1).squeeze(1) if self.nn_q2 else np.where(D==1)[0])
M0 = M[ind]
W0 = W[ind]
X0 = X[ind,:]
Z0 = Z[ind]
bridge_1_hat = bridge_1_hat[ind]
if self.nn_q2==True:
B2 = torch.cat((M0,X0,W0),1)
B1 = torch.cat((M0,X0,Z0),1)
else:
B2 = _transform_poly(np.column_stack((M0,X0,W0)),self.opts)
B1 = _transform_poly(np.column_stack((M0,X0,Z0)),self.opts)
if self.fitargsq2 is not None:
bridge_2 = model_q2.fit(B2, B1, bridge_1_hat, **self.fitargsq2)
else:
bridge_2 = model_q2.fit(B2, B1, bridge_1_hat)
else:
bridge_2 = None
ps_hat_0, ps_hat_00, D, M, W, X, Z = map(_to_np, [ps_hat_0, ps_hat_00, D, M, W, X, Z])
return bridge_1, bridge_2
def _npivfit_action(self, ps_hat_1, W, X, Z, alfa=0.0):
"""
Fit the action model using nonparametric instrumental variables.
Parameters
----------
ps_hat_1 : array-like
Estimated propensity scores.
W : array-like
Negative control outcome.
X : array-like
Covariates.
Z : array-like
Instrumental variable.
alfa : float, optional
Threshold alpha for propensity scores.
Returns
-------
object
Fitted model for the action.
"""
mask = np.where((ps_hat_1 >= alfa) & (ps_hat_1 <= 1 - alfa))[0]
ps_hat_1 = ps_hat_1[mask]
W = W[mask]
X = X[mask, :]
Z = Z[mask]
model_a1 = copy.deepcopy(self.model_a)
# First stage
if self.nn_a==True:
ps_hat_1, W, X, Z = map(toT, [ps_hat_1, W, X, Z])
A2 = torch.cat((X, W), 1)
A1 = torch.cat((X, Z), 1)
else:
ps_hat_1, W, X, Z = map(_to_np, [ps_hat_1, W, X, Z])
A2 = _transform_poly(np.column_stack((X, W)), self.opts)
A1 = _transform_poly(np.column_stack((X, Z)), self.opts)
if self.fitargsa is not None:
bridge_1 = model_a1.fit(A2, A1, 1 / ps_hat_1, **self.fitargsa)
else:
bridge_1 = model_a1.fit(A2, A1, 1 / ps_hat_1)
ps_hat_1, W, X, Z = map(_to_np, [ps_hat_1, W, X, Z])
return bridge_1
def _scores_mediated(self, train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_M, test_W, test_X, test_Z):
"""
Calculate the scores for the mediated effects.
Parameters
----------
train_Y : array-like
Training outcome variable.
train_D : array-like
Training treatment variable.
train_M : array-like
Training mediator variable.
train_W : array-like
Training negative control outcome.
train_X : array-like
Training covariates.
train_Z : array-like
Training instrumental variable.
test_Y : array-like
Testing outcome variable.
test_D : array-like
Testing treatment variable.
test_M : array-like
Testing mediator variable.
test_W : array-like
Testing negative control outcome.
test_X : array-like
Testing covariates.
test_Z : array-like
Testing instrumental variable.
Returns
-------
array-like
Estimated moment functions for the test data.
"""
model_1 = copy.deepcopy(self.model1)
model_q1 = copy.deepcopy(self.modelq1)
# Outcome model
if self.estimator == 'MR' or self.estimator == 'OR' or self.estimator == 'hybrid':
if self.sequential_o==True:
gamma_1, gamma_0 = self._nnpivfit_outcome_m(train_Y, train_D, train_M, train_W, train_X, train_Z)
# Evaluate the estimated moment functions using test_data
if self.estimator == 'MR' or self.estimator == 'hybrid':
if self.nn_1 == True:
test_M, test_X, test_W = map(toT, [test_M, test_X, test_W])
gamma_1_hat = gamma_1.predict(torch.cat((test_M, test_X, test_W), 1).to(DEVICE),
model='avg', burn_in=_get(self.opts, 'burnin', 0)).reshape(-1, 1)
else:
test_M, test_X, test_W = map(_to_np, [test_M, test_X, test_W])
gamma_1_hat = gamma_1.predict(_transform_poly(np.column_stack((test_M, test_X, test_W)), opts=self.opts)).reshape(-1, 1)
if self.estimator == 'MR' or self.estimator == 'OR':
if self.nn_2 == True:
test_X, test_W = map(toT, [test_X, test_W])
gamma_0_hat = gamma_0.predict(torch.cat((test_X, test_W), 1).to(DEVICE),
model='avg', burn_in=_get(self.opts, 'burnin', 0)).reshape(-1, 1)
else:
test_X, test_W = map(_to_np, [test_X, test_W])
gamma_0_hat = gamma_0.predict(_transform_poly(np.column_stack((test_X, test_W)), opts=self.opts)).reshape(-1, 1)
else:
A_train = np.column_stack((train_M, train_X, train_W))
E_train = np.column_stack((train_M, train_X, train_Z))
B_train = np.column_stack((train_X, train_W))
C_train = np.column_stack((train_X, train_Z))
B_test = np.column_stack((test_X, test_W))
A_test = np.column_stack((test_M, test_X, test_W))
if self.nn_1 == True:
A_train, E_train, B_train, C_train, B_test, A_test, train_Y, train_D = map(toT,
[A_train, E_train, B_train, C_train, B_test, A_test, train_Y, train_D])
else:
A_train = _transform_poly(A_train, self.opts)
E_train = _transform_poly(E_train, self.opts)
B_train = _transform_poly(B_train, self.opts)
C_train = _transform_poly(C_train, self.opts)
B_test = _transform_poly(B_test, self.opts)
A_test = _transform_poly(A_test, self.opts)
if self.fitargs1 is not None:
model_1.fit(A_train, B_train, C_train, E_train, train_Y, subsetted=True, subset_ind1=train_D, **self.fitargs1)
else:
model_1.fit(A_train, B_train, C_train, E_train, train_Y, subsetted=True, subset_ind1=train_D)
if self.nn_1 == True:
gamma_0_hat, gamma_1_hat = model_1.predict(B_test.to(DEVICE), A_test.to(DEVICE), model='avg', burn_in=_get(self.opts, 'burnin', 0))
gamma_0_hat = gamma_0_hat.reshape(-1, 1)
gamma_1_hat = gamma_1_hat.reshape(-1, 1)
else:
gamma_0_hat, gamma_1_hat = model_1.predict(B_test, A_test)
gamma_0_hat = gamma_0_hat.reshape(-1, 1)
gamma_1_hat = gamma_1_hat.reshape(-1, 1)
# Action model
if self.estimator == 'MR' or self.estimator == 'IPW' or self.estimator == 'hybrid':
if self.sequential_a==True:
ps_hat_0, ps_hat_00, alfa = self._propensity_score(train_M, train_X, train_W, train_D)
q_0, q_1 = self._nnpivfit_action_m(ps_hat_0, ps_hat_00, train_D, train_M, train_W, train_X, train_Z, alfa=alfa)
# Evaluate the estimated moment functions using test_data
if self.estimator == 'MR' or self.estimator == 'hybrid':
if self.nn_q1 == True:
test_X, test_Z = map(toT, [test_X, test_Z])
q_0_hat = q_0.predict(torch.cat((test_X, test_Z), 1).to(DEVICE),
model='avg', burn_in=_get(self.opts, 'burnin', 0)).reshape(-1, 1)
else:
test_X, test_Z = map(_to_np, [test_X, test_Z])
q_0_hat = q_0.predict(_transform_poly(np.column_stack((test_X, test_Z)), opts=self.opts)).reshape(-1, 1)
if self.estimator == 'MR' or self.estimator == 'IPW':
if self.nn_q2 == True:
test_M, test_X, test_Z = map(toT, [test_M, test_X, test_Z])
q_1_hat = q_1.predict(torch.cat((test_M, test_X, test_Z), 1).to(DEVICE),
model='avg', burn_in=_get(self.opts, 'burnin', 0)).reshape(-1, 1)
else:
test_M, test_X, test_Z = map(_to_np, [test_M, test_X, test_Z])
q_1_hat = q_1.predict(_transform_poly(np.column_stack((test_M, test_X, test_Z)), opts=self.opts)).reshape(-1, 1)
else:
A_train = np.column_stack((train_X, train_Z))
E_train = np.column_stack((train_X, train_W))
B_train = np.column_stack((train_M, train_X, train_Z))
C_train = np.column_stack((train_M, train_X, train_W))
B_test = np.column_stack((test_M, test_X, test_Z))
A_test = np.column_stack((test_X, test_Z))
ps_hat_0, ps_hat_00, alfa = self._propensity_score(train_M, train_X, train_W, train_D)
mask = np.where((ps_hat_0 >= alfa) & (ps_hat_0 <= 1 - alfa) &
(ps_hat_00 >= alfa) & (ps_hat_00 <= 1 - alfa))[0]
ps_hat_0 = ps_hat_0[mask]
ps_hat_00 = ps_hat_00[mask]
ps_hat_01 = 1 - ps_hat_00
A_train, E_train, B_train, C_train, train_D = map(lambda x: x[mask],
[A_train, E_train, B_train, C_train, train_D])
if self.nn_q1 == True:
A_train, E_train, B_train, C_train, train_D, ps_hat_0, ps_hat_00, ps_hat_01, B_test, A_test = map(
toT, [A_train, E_train, B_train, C_train, train_D, ps_hat_0, ps_hat_00, ps_hat_01, B_test, A_test]
)
else:
A_train = _transform_poly(A_train, self.opts)
E_train = _transform_poly(E_train, self.opts)
B_train = _transform_poly(B_train, self.opts)
C_train = _transform_poly(C_train, self.opts)
B_test = _transform_poly(B_test, self.opts)
A_test = _transform_poly(A_test, self.opts)
if self.fitargsq1 is not None:
#Using weights in the action stage
model_q1.fit(
A_train, B_train, C_train, E_train, 1/ps_hat_0,
W=(ps_hat_00/ps_hat_01), subsetted=True, subset_ind1=1-train_D,
**self.fitargsq1
)
else:
model_q1.fit(A_train, B_train, C_train, E_train, 1/ps_hat_0, W=(ps_hat_00/ps_hat_01), subsetted=True, subset_ind1=1-train_D)
if self.nn_q1 == True:
q_1_hat, q_0_hat = model_q1.predict(B_test.to(DEVICE), A_test.to(DEVICE), model='avg', burn_in=_get(self.opts, 'burnin', 0))
q_0_hat = q_0_hat.reshape(-1, 1)
q_1_hat = q_1_hat.reshape(-1, 1)
else:
q_1_hat, q_0_hat = model_q1.predict(B_test, A_test)
q_0_hat = q_0_hat.reshape(-1, 1)
q_1_hat = q_1_hat.reshape(-1, 1)
# Calculate the score function depending on the estimator
if self.estimator == 'MR':
psi_hat = (gamma_0_hat +
test_D * q_1_hat * (test_Y - gamma_1_hat) +
(1 - test_D) * q_0_hat * (gamma_1_hat - gamma_0_hat))
if self.estimator == 'OR':
psi_hat = gamma_0_hat
if self.estimator == 'hybrid':
psi_hat = (1 - test_D) * q_0_hat * gamma_1_hat
if self.estimator == 'IPW':
psi_hat = test_D * q_1_hat * test_Y
return psi_hat
def _scores_Y1(self, train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_X, test_Z):
"""
Calculate the scores for the Y1 estimand.
Parameters
----------
train_Y : array-like
Training outcome variable.
train_D : array-like
Training treatment variable.
train_M : array-like
Training mediator variable.
train_W : array-like
Training negative control outcome.
train_X : array-like
Training covariates.
train_Z : array-like
Training instrumental variable.
test_Y : array-like
Testing outcome variable.
test_D : array-like
Testing treatment variable.
test_X : array-like
Testing covariates.
test_Z : array-like
Testing instrumental variable.
Returns
-------
array-like
Estimated moment functions for the test data.
"""
if self.estimator == 'MR' or self.estimator == 'OR':
gamma_1 = self._npivfit_outcome(train_Y, train_D, train_X, train_Z)
if self.estimator == 'MR' or self.estimator == 'IPW' or self.estimator == 'hybrid':
ps_hat_0, _, alfa = self._propensity_score(train_M, train_X, train_W, train_D)
q_1 = self._npivfit_action(1-ps_hat_0, train_W, train_X, train_Z, alfa=alfa)
# Evaluate the estimated moment functions using test_data
if self.estimator == 'MR' or self.estimator == 'OR':
if self.nn_y == True:
test_X = toT(test_X)
gamma_1_hat = gamma_1.predict(test_X.to(DEVICE),
model='avg', burn_in=_get(self.opts, 'burnin', 0)).reshape(-1, 1)
else:
test_X = _to_np(test_X)
gamma_1_hat = gamma_1.predict(_transform_poly(test_X, opts=self.opts)).reshape(-1, 1)
if self.estimator == 'MR' or self.estimator == 'IPW' or self.estimator == 'hybrid':
if self.nn_a == True:
test_X, test_Z = map(toT, [test_X, test_Z])
q_1_hat = q_1.predict(torch.cat((test_X, test_Z), 1).to(DEVICE),
model='avg', burn_in=_get(self.opts, 'burnin', 0)).reshape(-1, 1)
else:
test_X, test_Z = map(_to_np, [test_X, test_Z])
q_1_hat = q_1.predict(_transform_poly(np.column_stack((test_X, test_Z)), opts=self.opts)).reshape(-1, 1)
# Calculate the score function depending on the estimator
if self.estimator == 'MR':
psi_hat = gamma_1_hat + test_D * q_1_hat * (test_Y - gamma_1_hat)
if self.estimator == 'OR':
psi_hat = gamma_1_hat
if self.estimator == 'IPW' or self.estimator == 'hybrid':
psi_hat = test_D * q_1_hat * test_Y
return psi_hat
def _process_fold(self, fold_idx, train_data, test_data):
"""
Process a single fold for cross-validation.
Parameters
----------
fold_idx : int
Fold index.
train_data : tuple
Training data for the fold.
test_data : tuple
Testing data for the fold.
Returns
-------
array-like
Estimated moment functions for the test data.
"""
train_Y, test_Y = train_data[0], test_data[0]
train_D, test_D = train_data[1], test_data[1]
train_M, test_M = train_data[2], test_data[2]
train_W, test_W = train_data[3], test_data[3]
train_X, test_X = train_data[4], test_data[4]
train_Z, test_Z = train_data[5], test_data[5]
if self.V is not None:
train_V, test_V = train_data[6], test_data[6]
if self.estimand == 'ATE':
psi_hat_1 = self._scores_Y1(train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_X, test_Z)
psi_hat_0 = self._scores_Y1(train_Y, 1-train_D, train_M, train_W, train_X, train_Z,
test_Y, 1-test_D, test_X, test_Z)
psi_hat = psi_hat_1 - psi_hat_0
if self.estimand == 'Indirect':
psi_hat_mediated = self._scores_mediated(train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_M, test_W, test_X, test_Z)
psi_hat_1 = self._scores_Y1(train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_X, test_Z)
psi_hat = psi_hat_1 - psi_hat_mediated
if self.estimand == 'Direct':
psi_hat_mediated = self._scores_mediated(train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_M, test_W, test_X, test_Z)
psi_hat_0 = self._scores_Y1(train_Y, 1-train_D, train_M, train_W, train_X, train_Z,
test_Y, 1-test_D, test_X, test_Z)
psi_hat = psi_hat_mediated - psi_hat_0
if self.estimand == 'E[Y1]':
psi_hat = self._scores_Y1(train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_X, test_Z)
if self.estimand == 'E[Y0]':
psi_hat = self._scores_Y1(train_Y, 1-train_D, train_M, train_W, train_X, train_Z,
test_Y, 1-test_D, test_X, test_Z)
if self.estimand == 'E[Y(1,M(0))]':
psi_hat = self._scores_mediated(train_Y, train_D, train_M, train_W, train_X, train_Z,
test_Y, test_D, test_M, test_W, test_X, test_Z)
# Localization
if self.V is not None:
if isinstance(self.bw_loc, str):
if self.bw_loc == 'silverman':
IQR = np.percentile(train_V, 75, axis=0)-np.percentile(train_V, 25, axis=0)
A = np.min([np.std(train_V, axis=0), IQR/1.349], axis=0)
n = train_V.shape[0]
bw = .9 * A * n ** (-0.2)
elif self.bw_loc == 'scott':
A = np.std(train_V, axis=0)
n = train_V.shape[0]
bw = 1.059 * A * n ** (-0.2)
else:
if len(self.bw_loc)==1:
bw = np.ones((train_V.shape[1]))*self.bw_loc[0]
else:
if len(self.bw_loc)==train_V.shape[1]:
bw = self.bw_loc
else:
warnings.warn(f"bw_loc has incorrect length. Using first element instead.", UserWarning)
bw = np.ones((train_V.shape[1]))*self.bw_loc[0]
ell = [self._localization(test_V, v, bw) for v in self.v_values]
ell = np.column_stack(ell)
psi_hat = ell * psi_hat
# Print progress bar using tqdm
if self.verbose==True:
self.progress_bar.update(1)
return psi_hat
def _split_and_estimate(self):
"""
Split the data and estimate the model for each fold.
Returns
-------
tuple
Estimated values, variances, and confidence intervals.
"""
theta = []
theta_var = []
theta_cov = []
for rep in range(self.n_rep):
if self.verbose==True:
print(f"Rep: {rep+1}")
self.progress_bar = tqdm(total=self.n_folds, position=0)
kf = KFold(n_splits=self.n_folds, shuffle=True, random_state=self.random_seed+rep)
if self.V is None:
fold_results = Parallel(n_jobs=self.inner_n_jobs, backend='threading')(
delayed(self._process_fold)(
fold_idx,
(self.Y[train_index], self.D[train_index], self.M[train_index], self.W[train_index],
self.X[train_index], self.Z[train_index]),
(self.Y[test_index], self.D[test_index], self.M[test_index], self.W[test_index],
self.X[test_index], self.Z[test_index]))
for fold_idx, (train_index, test_index) in enumerate(kf.split(self.Y))
)
else:
fold_results = Parallel(n_jobs=self.inner_n_jobs, backend='threading')(
delayed(self._process_fold)(
fold_idx,
(self.Y[train_index], self.D[train_index], self.M[train_index], self.W[train_index],
self.X[train_index], self.Z[train_index], self.V[train_index]),
(self.Y[test_index], self.D[test_index], self.M[test_index], self.W[test_index],
self.X[test_index], self.Z[test_index], self.V[test_index]))
for fold_idx, (train_index, test_index) in enumerate(kf.split(self.Y))
)
if self.verbose==True:
self.progress_bar.close()
# Calculate the average of psi_hat_array for each rep
psi_hat_array = np.concatenate(fold_results, axis=0)
theta_rep = np.mean(psi_hat_array, axis=0)
theta_var_rep = np.var(psi_hat_array, axis=0, ddof=1)
theta_cov_rep = np.cov(psi_hat_array, rowvar=False)
# Store results for each rep
theta.append(theta_rep)
theta_var.append(theta_var_rep)
theta_cov.append(theta_cov_rep)
# Calculate the overall average of theta and theta_var
theta_hat = np.mean(np.stack(theta, axis=0), axis=0)
theta_var_hat = np.mean(np.stack(theta_var, axis=0), axis=0)
theta_cov_hat = np.mean(np.stack(theta_cov, axis=0), axis=0)
# Calculate the confidence interval
confidence_interval = self._calculate_confidence_interval(theta_hat, theta_var_hat, theta_cov_hat)
return theta_hat, theta_var_hat, confidence_interval, theta_cov_hat
def dml(self):
"""
Perform Debiased Machine Learning for Nonparametric Instrumental Variables.
Returns
-------
tuple
Estimated values, variances, and confidence intervals.
"""
theta, theta_var, confidence_interval, theta_cov_hat = self._split_and_estimate()
if self.V is None:
return theta[0], theta_var[0], confidence_interval[0]
else:
return theta, theta_cov_hat, confidence_interval