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cont_qb_fun.R
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cont_qb_fun.R
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# Functions used particularly by our method
# Epanechnikov kernel
epa.kernel <- function(u) {
return(0.75 * (1 - u**2) * (abs(u) <= 1))
}
# Kernel with window h
K.h <- function(u, h) {
return(epa.kernel(u/h) / h)
}
# Function to compute conditional quantiles
cond.quant.estim <- function(X, t, resp.gmm, tau, device, verbose) {
X.tensor <- X
t.tensor <- t
message("Estimating the conditional quantiles using p(y|x,t)")
if (verbose) {
pb <- txtProgressBar(max=dim(X.tensor)[1], style=3)
}
Q.predict <- foreach(i=1:dim(X.tensor)[1], .combine="rbind") %do% {
# I want to plot the cdf of y|x,t for individual ind in data2
resp.dens <- resp.gmm(covariates=X.tensor[i, ], treatment=t.tensor[i])
min.x <- -10
max.x <- 10
cdf.min.one_tau.fun <- function(x) as.numeric(resp.dens$cdf(torch_tensor(x, device=device))$to(device="cpu"))-(1-tau)
cdf.min.tau.fun <- function(x) as.numeric(resp.dens$cdf(torch_tensor(x, device=device))$to(device="cpu"))-tau
one_tau.quant <- uniroot(f=cdf.min.one_tau.fun, interval=c(min.x, max.x))$root
tau.quant <- uniroot(f=cdf.min.tau.fun, interval=c(min.x, max.x))$root
if (verbose) {
setTxtProgressBar(pb, i)
}
c(one_tau.quant, tau.quant)
}
if (verbose) {
close(pb)
}
return(Q.predict)
}
# Function to compute the PEI for each provided window h
APO.QB.PEI.per.window <- function(X, Y, t, dose, alpha=0.05, lambda=1,
window=0.1, windows.range=NULL, B.param=50,
cond.quant.method=c("quantile_forest"),
boot.training=FALSE, max.iter=1500,
optimal.params.gps.nn=list(K.optim=25, lr.optim=0.0015, dim.hidden.optim=32),
optimal.params.capo.nn=list(K.optim=25, lr.optim=0.0015, dim.hidden.optim=32),
stabilization=TRUE,
use.AIPW=FALSE, AIPW.outcome.algo=c("nn_GMM"),
cond.dens.method=c("nn_GMM"), nn.init=NULL, d1.d2.ind=NULL, h1=0.2, h2=0.2, K=NULL, K.range=1:20, K.nrep=3,
xi.method=c("regression_forest"), xi.models,
compute.CI=TRUE, B=1000, use.parallel=TRUE, e.variables=NULL,
use.cross.fitting=TRUE, nb.folds=5, epsilon=10**(-12), seed=1, device, verbose=TRUE) {
# Put data in a dataframe
simul.data <- data.frame(X, Y, t)
# Number of observations
n.obs <- nrow(simul.data)
tau <- lambda / (1 + lambda)
windows.len <- length(windows.range) # Number of windows that we want to test
# If windows.range was provided
if (!is.null(windows.range)) {
PEI.bounds.per.window <- compute.PEI.cont.QB(dataset=simul.data,
dose=dose,
lambda=lambda,
windows=windows.range,
stabilization=stabilization,
use.AIPW=use.AIPW,
AIPW.outcome.algo=AIPW.outcome.algo,
cond.dens.method=cond.dens.method,
xi.method=xi.method,
xi.models=xi.models,
nn.init=nn.init,
d1.d2.ind=d1.d2.ind,
h1=h1, h2=h2, K=K,
e.variables=e.variables,
use.cross.fitting=use.cross.fitting,
nb.folds=nb.folds,
epsilon=epsilon, device=device)
PEI.min.max <- NULL
}
return(list(PEI.bounds.per.window=PEI.bounds.per.window, PEI.min.max=PEI.min.max,
dose=dose, use.AIPW=use.AIPW, AIPW.outcome.algo=AIPW.outcome.algo,
cond.dens.method=cond.dens.method, h1=h1, h2=h2, K=K,
use.cross.fitting=use.cross.fitting, nb.folds=nb.folds, e.variables=e.variables,
windows.range=windows.range, windows.len=windows.len,
simul.data=simul.data, n.obs=n.obs, lambda=lambda, tau=tau, epsilon=epsilon))
}
compute.PEI.cont.QB <- function(dataset, dose, lambda, windows,
stabilization,
use.AIPW, AIPW.outcome.algo,
cond.dens.method, nn.init,
xi.method, xi.models,
d1.d2.ind,
h1=0.2, h2=0.2, K=3,
e.variables,
use.cross.fitting, nb.folds=5,
epsilon=10**(-6), device) {
n.data <- nrow(dataset)
windows.length <- length(windows)
X <- subset(dataset, select=-c(Y, t))
n.cov <- ncol(X)
# Reorganize the predictions for the conditional quantiles
Q.predict <- matrix(NA, nrow=n.data, ncol=2)
Q.predict[d1.d2.ind$data1.ind, ] <- nn.init$Q.predict1
Q.predict[d1.d2.ind$data2.ind, ] <- nn.init$Q.predict2
################ Generalized Propensity Score estimation (p(t|x)) ################
if (cond.dens.method == "true") {
# Use the true GPS (only for simulated data from Jesson et al.)
cond.density <- true.cond.dens(dataset$t*100, dataset$X) # Use t*100 to transform into integers between 1 and 100
} else if (cond.dens.method == "nn_GMM") {
# GPS estimation via Gaussian Mixture Model fitted via neural networks
X.tensor <- torch_tensor(as.matrix(X), device=device)
t.tensor <- torch_tensor(dataset$t, device=device)
cond.density <- rep(NA, n.data)
# On D1
cond.density1 <- as.array(exp(nn.init$gps.gmm2(covariates=X.tensor[d1.d2.ind$data1.ind, ])$log_prob(x=t.tensor[d1.d2.ind$data1.ind])$to(device="cpu")))
# On D2
cond.density2 <- as.array(exp(nn.init$gps.gmm1(covariates=X.tensor[d1.d2.ind$data2.ind, ])$log_prob(x=t.tensor[d1.d2.ind$data2.ind])$to(device="cpu")))
# Reorganize the predictions
cond.density[d1.d2.ind$data1.ind] <- cond.density1
cond.density[d1.d2.ind$data2.ind] <- cond.density2
} else if (cond.dens.method == "kernel") {
# Use kernel density estimation (only for 1-dimensional covariates)
if (use.cross.fitting) {
# Cross-fitting
nb.data.per.fold <- n.data %/% nb.folds
cond.density <- rep(NA, n.data)
for (j in 1:nb.folds) {
if (j == nb.folds) { # For the last fold, we want to be sure we have used all the data
prediction.fold.ind <- (1+nb.data.per.fold*(j-1)):n.data
prediction.fold <- dataset[prediction.fold.ind, ]
training.fold <- dataset[-prediction.fold.ind, ]
} else {
prediction.fold.ind <- (1+nb.data.per.fold*(j-1)):(nb.data.per.fold*j)
prediction.fold <- dataset[prediction.fold.ind, ]
training.fold <- dataset[-prediction.fold.ind, ]
}
# Nadaraya-Watson-like conditional density estimator
num.fun <- function(x) sum(K.h(training.fold$t - dose, h1) * K.h(training.fold$X - x, h2))
denom.fun <- function(x) sum(K.h(training.fold$X - x, h2))
num <- vapply(X=prediction.fold$X, FUN=num.fun, FUN.VALUE=as.numeric(1))
denom <- vapply(X=prediction.fold$X, FUN=denom.fun, FUN.VALUE=as.numeric(1))
cond.density[prediction.fold.ind] <- num / denom + epsilon # epsilon = 10**(-12) added not to have 0
}
} else {
# Nadaraya-Watson-like conditional density estimator
num.fun <- function(x) sum(K.h(dataset$t - dose, h1) * K.h(dataset$X - x, h2))
denom.fun <- function(x) sum(K.h(dataset$X - x, h2))
num <- vapply(X=dataset$X, FUN=num.fun, FUN.VALUE=as.numeric(1))
denom <- vapply(X=dataset$X, FUN=denom.fun, FUN.VALUE=as.numeric(1))
cond.density <- num / denom + epsilon
}
} else if (cond.dens.method == "flexmix_GMM") {
# GPS estimation via mixture of linear regressions
if (use.cross.fitting) {
# Cross-fitting
nb.data.per.fold <- n.data %/% nb.folds
cond.density <- rep(NA, n.data) # Initialize conditional density vector
for (j in 1:nb.folds) {
if (j == nb.folds) { # For the last fold, we want to be sure we have used all the data
prediction.fold.ind <- (1+nb.data.per.fold*(j-1)):n.data
prediction.fold <- dataset[prediction.fold.ind, ]
training.fold <- dataset[-prediction.fold.ind, ]
} else {
prediction.fold.ind <- (1+nb.data.per.fold*(j-1)):(nb.data.per.fold*j)
prediction.fold <- dataset[prediction.fold.ind, ]
training.fold <- dataset[-prediction.fold.ind, ]
}
# Estimate the parameters of the Gaussian Mixture Model (GMM)
flexmix.gmm <- flexmix(formula=t ~ . - Y, data=training.fold, k=K)
# Predict the values of the generalized propensity score
cond.density[prediction.fold.ind] <- est.dens.mat(Y=prediction.fold$t,
X=subset(prediction.fold, select=-c(Y, t)),
flexmix.model=flexmix.gmm)
}
} else {
# Create the formula that will be given to flexmix()
# Estimate the parameters of the Gaussian Mixture Model (GMM)
flexmix.gmm <- flexmix(formula=t ~ . - Y, data=dataset, k=K)
# Predict the values of the generalized propensity score
# cond.density <- est.dens.mat(Y=dose, X=subset(dataset.ordered, select=-c(Y, t)), flexmix.model=flexmix.gmm)
cond.density <- est.dens.mat(Y=dataset$t, X=X, flexmix.model=flexmix.gmm)
}
} else {
stop("cond.dens.method must be 'true', 'kernel', 'flexmix_GMM' or 'nn_GMM'")
}
# Weight trimming
trim.lq <- 0.1
trim.quant <- quantile(cond.density, probs=c(trim.lq))
# Replace all weights with the quantiles of order trim.lq if they are lower than trim.lq
cond.density[cond.density < trim.quant[1]] <- trim.quant[1]
################ CAPO estimation (E[Y|X=x,T=t]) under ignorability assumption ################
if (use.AIPW) {
if (AIPW.outcome.algo == "lm") {
# Fit the outcome model
outcome.model <- lm(Y ~ ., dataset)
# Predict the outcome for the dose assigned to each individual
Y.predict.all <- predict(outcome.model, dataset)
# Predict the outcome for a specific dose
predict.dataset <- dataset
predict.dataset$t <- dose
Y.predict.dose <- predict(outcome.model, predict.dataset)
} else if (AIPW.outcome.algo == "regression_forest") {
# Fit the outcome model
outcome.model <- regression_forest(X=data.frame(X=X, t=dataset$t), Y=dataset$Y, num.trees=100) # To be changed if X is not univariate
# Predict the outcome for the dose assigned to each individual
Y.predict.all <- predict(outcome.model, data.frame(X, t=dataset$t))$predictions
# Predict the outcome for a specific dose
Y.predict.dose <- predict(outcome.model, data.frame(X, t=rep(dose, nrow(dataset))))$predictions
} else if (AIPW.outcome.algo == "nn_GMM") {
X.tensor <- torch_tensor(as.matrix(X), device=device)
t.tensor <- torch_tensor(dataset$t, device=device)
Y.predict.all <- rep(NA, n.data)
Y.predict.dose <- rep(NA, n.data)
# The estimated density for particular values of X and t
Y.density.all1 <- nn.init$resp.gmm2(covariates=X.tensor[d1.d2.ind$data1.ind, ],
treatment=t.tensor[d1.d2.ind$data1.ind])
Y.density.all2 <- nn.init$resp.gmm1(covariates=X.tensor[d1.d2.ind$data2.ind, ],
treatment=t.tensor[d1.d2.ind$data2.ind])
mix.prob.all1 <- Y.density.all1$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.all1 <- Y.density.all1$.component_distribution$mean # The fitted means for each component
Y.predict.all1 <- torch_sum(mix.prob.all1 * dist.mean.all1, dim=-1)
Y.predict.all1 <- as.array(Y.predict.all1$to(device="cpu"))
mix.prob.all2 <- Y.density.all2$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.all2 <- Y.density.all2$.component_distribution$mean # The fitted means for each component
Y.predict.all2 <- torch_sum(mix.prob.all2 * dist.mean.all2, dim=-1)
Y.predict.all2 <- as.array(Y.predict.all2$to(device="cpu"))
# Reorganize the predictions
Y.predict.all[d1.d2.ind$data1.ind] <- c(Y.predict.all1)
Y.predict.all[d1.d2.ind$data2.ind] <- c(Y.predict.all2)
# The estimated density for particular values of X and t
Y.density.dose1 <- nn.init$resp.gmm2(covariates=X.tensor[d1.d2.ind$data1.ind, ],
treatment=torch_squeeze(torch_tensor(rep(dose, length(d1.d2.ind$data1.ind)), device=device), dim=1))
Y.density.dose2 <- nn.init$resp.gmm1(covariates=X.tensor[d1.d2.ind$data2.ind, ],
treatment=torch_squeeze(torch_tensor(rep(dose, length(d1.d2.ind$data2.ind)), device=device), dim=1))
mix.prob.dose1 <- Y.density.dose1$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.dose1 <- Y.density.dose1$.component_distribution$mean # The fitted means for each component
Y.predict.dose1 <- torch_sum(mix.prob.dose1 * dist.mean.dose1, dim=-1)
Y.predict.dose1 <- as.array(Y.predict.dose1$to(device="cpu"))
mix.prob.dose2 <- Y.density.dose2$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.dose2 <- Y.density.dose2$.component_distribution$mean # The fitted means for each component
Y.predict.dose2 <- torch_sum(mix.prob.dose2 * dist.mean.dose2, dim=-1)
Y.predict.dose2 <- as.array(Y.predict.dose2$to(device="cpu"))
# Reorganize the predictions
Y.predict.dose[d1.d2.ind$data1.ind] <- c(Y.predict.dose1)
Y.predict.dose[d1.d2.ind$data2.ind] <- c(Y.predict.dose2)
} else {
stop("AIPW.outcome.algo must be 'lm' or 'regression_forest'")
}
} else {
Y.predict.dose <- rep(0, n.data)
Y.predict.all <- rep(0, n.data)
}
if (is.null(xi.method)) {
} else if (xi.method == "regression_forest") {
# Predictions of the xi function that brings double robustness
# Model fitting on D1
X.t.d1 <- as.matrix(subset(dataset, select=-c(Y))[d1.d2.ind$data1.ind, ])
# Model fitting on D2
X.t.d2 <- as.matrix(subset(dataset, select=-c(Y))[d1.d2.ind$data2.ind, ])
xi.t.predict.down <- rep(NA, n.data)
xi.t.predict.up <- rep(NA, n.data)
# Predict on D1 with model fitted on D2
xi.t.predict.down[d1.d2.ind$data1.ind] <- predict(xi.models$xi.model.down.d2, X.t.d1)$predictions * attr(xi.models$Y.gamma.down.d2, 'scaled:scale') + attr(xi.models$Y.gamma.down.d2, 'scaled:center')
xi.t.predict.up[d1.d2.ind$data1.ind] <- predict(xi.models$xi.model.up.d2, X.t.d1)$predictions * attr(xi.models$Y.gamma.up.d2, 'scaled:scale') + attr(xi.models$Y.gamma.up.d2, 'scaled:center')
# Predict on D2 with model fitted on D1
xi.t.predict.down[d1.d2.ind$data2.ind] <- predict(xi.models$xi.model.down.d1, X.t.d2)$predictions * attr(xi.models$Y.gamma.down.d1, 'scaled:scale') + attr(xi.models$Y.gamma.down.d1, 'scaled:center')
xi.t.predict.up[d1.d2.ind$data2.ind] <- predict(xi.models$xi.model.up.d1, X.t.d2)$predictions * attr(xi.models$Y.gamma.up.d1, 'scaled:scale') + attr(xi.models$Y.gamma.up.d1, 'scaled:center')
# Covariates with t replaced with the dose of interest
X.dose.d1 <- subset(dataset, select=-c(Y))[d1.d2.ind$data1.ind, ]
X.dose.d1$t <- dose
X.dose.d1 <- as.matrix(X.dose.d1)
X.dose.d2 <- subset(dataset, select=-c(Y))[d1.d2.ind$data2.ind, ]
X.dose.d2$t <- dose
X.dose.d2 <- as.matrix(X.dose.d2)
xi.dose.predict.down <- rep(NA, n.data)
xi.dose.predict.up <- rep(NA, n.data)
# Predict on D1 with model fitted on D2
xi.dose.predict.down[d1.d2.ind$data1.ind] <- predict(xi.models$xi.model.down.d2, X.dose.d1)$predictions * attr(xi.models$Y.gamma.down.d2, 'scaled:scale') + attr(xi.models$Y.gamma.down.d2, 'scaled:center')
xi.dose.predict.up[d1.d2.ind$data1.ind] <- predict(xi.models$xi.model.up.d2, X.dose.d1)$predictions * attr(xi.models$Y.gamma.up.d2, 'scaled:scale') + attr(xi.models$Y.gamma.up.d2, 'scaled:center')
# Predict on D2 with model fitted on D1
xi.dose.predict.down[d1.d2.ind$data2.ind] <- predict(xi.models$xi.model.down.d1, X.dose.d2)$predictions * attr(xi.models$Y.gamma.down.d1, 'scaled:scale') + attr(xi.models$Y.gamma.down.d1, 'scaled:center')
xi.dose.predict.up[d1.d2.ind$data2.ind] <- predict(xi.models$xi.model.up.d1, X.dose.d2)$predictions * attr(xi.models$Y.gamma.up.d1, 'scaled:scale') + attr(xi.models$Y.gamma.up.d1, 'scaled:center')
} else if (xi.method == "neural_network") {
X.tensor <- torch_tensor(as.matrix(X), device=device)
t.tensor <- torch_tensor(dataset$t, device=device)
xi.t.predict.down <- rep(NA, n.data)
xi.t.predict.up <- rep(NA, n.data)
xi.dose.predict.down <- rep(NA, n.data)
xi.dose.predict.up <- rep(NA, n.data)
# For the lower bound
# The estimated density for particular values of X and t
xi.density.t.down1 <- xi.models$xi.gmm.down2(covariates=X.tensor[d1.d2.ind$data1.ind, ],
treatment=t.tensor[d1.d2.ind$data1.ind])
xi.density.t.down2 <- xi.models$xi.gmm.down1(covariates=X.tensor[d1.d2.ind$data2.ind, ],
treatment=t.tensor[d1.d2.ind$data2.ind])
mix.prob.t.down1 <- xi.density.t.down1$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.t.down1 <- xi.density.t.down1$.component_distribution$mean # The fitted means for each component
xi.t.predict.down1 <- torch_sum(mix.prob.t.down1 * dist.mean.t.down1, dim=-1)
xi.t.predict.down1 <- as.array(xi.t.predict.down1$to(device="cpu"))
mix.prob.t.down2 <- xi.density.t.down2$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.t.down2 <- xi.density.t.down2$.component_distribution$mean # The fitted means for each component
xi.t.predict.down2 <- torch_sum(mix.prob.t.down2 * dist.mean.t.down2, dim=-1)
xi.t.predict.down2 <- as.array(xi.t.predict.down2$to(device="cpu"))
# Reorganize the predictions
xi.t.predict.down[d1.d2.ind$data1.ind] <- c(xi.t.predict.down1) * attr(xi.models$y.train.down2, 'scaled:scale') + attr(xi.models$y.train.down2, 'scaled:center')
xi.t.predict.down[d1.d2.ind$data2.ind] <- c(xi.t.predict.down2) * attr(xi.models$y.train.down1, 'scaled:scale') + attr(xi.models$y.train.down1, 'scaled:center')
# For the upper bound
# The estimated density for particular values of X and t
xi.density.t.up1 <- xi.models$xi.gmm.up2(covariates=X.tensor[d1.d2.ind$data1.ind, ],
treatment=t.tensor[d1.d2.ind$data1.ind])
xi.density.t.up2 <- xi.models$xi.gmm.up1(covariates=X.tensor[d1.d2.ind$data2.ind, ],
treatment=t.tensor[d1.d2.ind$data2.ind])
mix.prob.t.up1 <- xi.density.t.up1$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.t.up1 <- xi.density.t.up1$.component_distribution$mean # The fitted means for each component
xi.t.predict.up1 <- torch_sum(mix.prob.t.up1 * dist.mean.t.up1, dim=-1)
xi.t.predict.up1 <- as.array(xi.t.predict.up1$to(device="cpu"))
mix.prob.t.up2 <- xi.density.t.up2$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.t.up2 <- xi.density.t.up2$.component_distribution$mean # The fitted means for each component
xi.t.predict.up2 <- torch_sum(mix.prob.t.up2 * dist.mean.t.up2, dim=-1)
xi.t.predict.up2 <- as.array(xi.t.predict.up2$to(device="cpu"))
# Reorganize the predictions
xi.t.predict.up[d1.d2.ind$data1.ind] <- c(xi.t.predict.up1) * attr(xi.models$y.train.up2, 'scaled:scale') + attr(xi.models$y.train.up2, 'scaled:center')
xi.t.predict.up[d1.d2.ind$data2.ind] <- c(xi.t.predict.up2) * attr(xi.models$y.train.up1, 'scaled:scale') + attr(xi.models$y.train.up1, 'scaled:center')
# For a particular value of dose
# For the lower bound
# The estimated density for particular values of X and t
xi.density.dose.down1 <- xi.models$xi.gmm.down2(covariates=X.tensor[d1.d2.ind$data1.ind, ],
treatment=torch_squeeze(torch_tensor(rep(dose, length(d1.d2.ind$data1.ind)), device=device), dim=1))
xi.density.dose.down2 <- xi.models$xi.gmm.down1(covariates=X.tensor[d1.d2.ind$data2.ind, ],
treatment=torch_squeeze(torch_tensor(rep(dose, length(d1.d2.ind$data2.ind)), device=device), dim=1))
mix.prob.dose.down1 <- xi.density.dose.down1$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.dose.down1 <- xi.density.dose.down1$.component_distribution$mean # The fitted means for each component
xi.dose.predict.down1 <- torch_sum(mix.prob.dose.down1 * dist.mean.dose.down1, dim=-1)
xi.dose.predict.down1 <- as.array(xi.dose.predict.down1$to(device="cpu"))
mix.prob.dose.down2 <- xi.density.dose.down2$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.dose.down2 <- xi.density.dose.down2$.component_distribution$mean # The fitted means for each component
xi.dose.predict.down2 <- torch_sum(mix.prob.dose.down2 * dist.mean.dose.down2, dim=-1)
xi.dose.predict.down2 <- as.array(xi.dose.predict.down2$to(device="cpu"))
# Reorganize the predictions
xi.dose.predict.down[d1.d2.ind$data1.ind] <- c(xi.dose.predict.down1) * attr(xi.models$y.train.down2, 'scaled:scale') + attr(xi.models$y.train.down2, 'scaled:center')
xi.dose.predict.down[d1.d2.ind$data2.ind] <- c(xi.dose.predict.down2) * attr(xi.models$y.train.down1, 'scaled:scale') + attr(xi.models$y.train.down1, 'scaled:center')
# For the upper bound
# The estimated density for particular values of X and t
xi.density.dose.up1 <- xi.models$xi.gmm.up2(covariates=X.tensor[d1.d2.ind$data1.ind, ],
treatment=torch_squeeze(torch_tensor(rep(dose, length(d1.d2.ind$data1.ind)), device=device), dim=1))
xi.density.dose.up2 <- xi.models$xi.gmm.up1(covariates=X.tensor[d1.d2.ind$data2.ind, ],
treatment=torch_squeeze(torch_tensor(rep(dose, length(d1.d2.ind$data2.ind)), device=device), dim=1))
mix.prob.dose.up1 <- xi.density.dose.up1$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.dose.up1 <- xi.density.dose.up1$.component_distribution$mean # The fitted means for each component
xi.dose.predict.up1 <- torch_sum(mix.prob.dose.up1 * dist.mean.dose.up1, dim=-1)
xi.dose.predict.up1 <- as.array(xi.dose.predict.up1$to(device="cpu"))
mix.prob.dose.up2 <- xi.density.dose.up2$.mixture_distribution$probs # The fitted probabilities of each component
dist.mean.dose.up2 <- xi.density.dose.up2$.component_distribution$mean # The fitted means for each component
xi.dose.predict.up2 <- torch_sum(mix.prob.dose.up2 * dist.mean.dose.up2, dim=-1)
xi.dose.predict.up2 <- as.array(xi.dose.predict.up2$to(device="cpu"))
# Reorganize the predictions
xi.dose.predict.up[d1.d2.ind$data1.ind] <- c(xi.dose.predict.up1) * attr(xi.models$y.train.up2, 'scaled:scale') + attr(xi.models$y.train.up2, 'scaled:center')
xi.dose.predict.up[d1.d2.ind$data2.ind] <- c(xi.dose.predict.up2) * attr(xi.models$y.train.up1, 'scaled:scale') + attr(xi.models$y.train.up1, 'scaled:center')
} else {
stop('xi.method must be "regression_forest" or "neural_network"')
}
# For each bandwidth/window
PEI.bounds <- foreach(i=1:windows.length, .combine="rbind") %do% {
# Compute the kernel estimations
kernel.est.down <- K.h(dataset$t - dose, windows[i])
kernel.est.up <- kernel.est.down # Keep same kernel estimation for lower and upper bounds
data.min.idx <- dataset$Y <= Q.predict[, 1] # q_{1-gamma}^{X_i, T_i}
data.max.idx <- dataset$Y > Q.predict[, 2] # q_{gamma}^{X_i, T_i}
if (stabilization) {
stab.min <- mean((kernel.est.down[data.min.idx] / cond.density[data.min.idx]))
stab.min.unconf <- mean((kernel.est.down[data.min.idx] / cond.density[data.min.idx]))
stab.max <- mean((kernel.est.up[data.max.idx] / cond.density[data.max.idx]))
stab.max.unconf <- mean((kernel.est.up[data.max.idx] / cond.density[data.max.idx]))
} else {
stab.max <- 1
stab.max.unconf <- 1
stab.min <- 1
stab.min.unconf <- 1
}
tau <- lambda / (1 + lambda)
if (is.null(xi.method)) { # If no method for xi was provided, compute simple estimators
# Minimization problem (lower bound)
minimum <- mean(Y.predict.dose) + ((2*tau-1)/tau) * mean((kernel.est.down[data.min.idx] * (dataset$Y[data.min.idx] - Y.predict.all[data.min.idx]) / cond.density[data.min.idx])) / stab.min
minimum.unconf <- mean(Y.predict.dose) + ((2*tau-1)/tau) * mean((kernel.est.down[data.min.idx] * (dataset$Y[data.min.idx] - Y.predict.all[data.min.idx]) / cond.density[data.min.idx])) / stab.min.unconf
# Maximization problem (upper bound)
maximum <- mean(Y.predict.dose) + ((2*tau-1)/tau) * mean((kernel.est.up[data.max.idx] * (dataset$Y[data.max.idx] - Y.predict.all[data.max.idx]) / cond.density[data.max.idx])) / stab.max
maximum.unconf <- mean(Y.predict.dose) + ((2*tau-1)/tau) * mean((kernel.est.up[data.max.idx] * (dataset$Y[data.max.idx] - Y.predict.all[data.max.idx]) / cond.density[data.max.idx])) / stab.max.unconf
} else { # Else, compute doubly robust estimators
minimum <- mean(xi.dose.predict.down) + mean(kernel.est.down * (dataset$Y * lambda**(-sign(dataset$Y - Q.predict[, 1])) - xi.t.predict.down) / cond.density) / mean(kernel.est.down / cond.density) # Essayer de stabiliser
minimum.unconf <- minimum # Finally, this is not used
maximum <- mean(xi.dose.predict.up) + mean(kernel.est.up * (dataset$Y * lambda**(sign(dataset$Y - Q.predict[, 2])) - xi.t.predict.up) / cond.density) / mean(kernel.est.up / cond.density)
maximum.unconf <- maximum # Finally, this is not used
}
c(minimum, maximum, minimum.unconf, maximum.unconf)
}
return(PEI.bounds)
}
# The neural network used to compute the generalized propensity score (GPS) p(t|x)
base_neural_network_gps <- nn_module(classname="BaseNN_GPS",
initialize=function(dim_cov, dim_output, num_components, dim_hidden) {
self$feature_extractor <- nn_sequential(
nn_linear(dim_cov, dim_hidden, bias=T),
nn_leaky_relu(negative_slope=0.04),
nn_dropout(p=0.04),
nn_linear(dim_hidden, dim_hidden, bias=T),
nn_leaky_relu(negative_slope=0.04),
nn_dropout(p=0.04)
)
self$density_estimator <- nn_sequential(
nn_linear(dim_hidden, dim_hidden*2, bias=T),
nn_leaky_relu(negative_slope=0.04),
nn_dropout(p=0.04),
nn_linear(dim_hidden*2, dim_hidden*2, bias=T),
nn_leaky_relu(negative_slope=0.04),
nn_dropout(p=0.04),
gaussian_mixture_regression(dim_hidden*2, dim_output, num_components))
},
forward=function(covariates) {
phi <- self$feature_extractor(covariates) # Of dim n.obs*dim_hidden
return(self$density_estimator(phi))
})