Check and Preprocess Input Data

Description

This function checks whether input data is a data frame, matrix, vector, or factor variable, and converts it to a numeric matrix.

Usage

check_input(input)

Arguments

Value

A numeric matrix corresponding to the input data frame.

Convert Data Frame to Numeric Matrix

Description

This function converts a data frame into a numeric matrix. If the data frame contains factor variables, they are first converted to dummy variables (one-hot encoding). If the data frame contains character variables, they are first converted to factors and then to dummy variables.

Usage

dftomat(df)

Arguments

Value

A numeric matrix corresponding to the input data frame.

Distributional IV Model Function

Description

This function fits a distributional IV model to the data. It allows for the tuning of several parameters related to model complexity and model training. Variables are per default internally standardized (predictions are on the original scale).

Usage

div(
  Z,
  X,
  Y,
  W = NULL,
  epsx_dim = 50,
  epsy_dim = 50,
  epsh_dim = 50,
  hidden_dim = 100,
  num_layer = 3,
  num_epochs = 1000,
  lr = 10^(-3),
  beta = 1,
  silent = FALSE,
  standardize = TRUE
)

Arguments

Value

A distributional IV model object with class 'DIV'.

Examples

## Not run: 
# NOTE: This example requires torch runtime.
# Please install it with: torch::install_torch()

# Simulate data -------------------------------------------------------------
p_Z <- 4
p_X <- 2

set.seed(2209)
n_train <- 1000
Z <- matrix(rnorm(n_train * p_Z, mean = 2), ncol = p_Z)
H <- rnorm(n_train, mean = 0, sd = 1.5)
X1 <- 0.1 * (Z[, 1] + rnorm(n_train, sd = 0.1)) ^ 2 +
 (Z[, 2] + rnorm(n_train, sd = 1)) ^ 2 + H + rnorm(n_train, sd = 0.1)
X2 <- 0.5 * (Z[, 3] + Z[, 4]) ^ 2 + 0.1 * H ^ 2 + rnorm(n_train, sd = 0.1)
X <- matrix(cbind(X1, X2), ncol = p_X)
Y <- 0.5 * X[, 1] + 0.2 * (X[, 2] + rnorm(n_train, sd = 0.2) + H) ^ 2 +
 rnorm(n_train, sd = 0.1)

n_test <- n_train
Ztest <- matrix(rnorm(n_test * p_Z, mean = 2), ncol = p_Z)
Htest <- rnorm(n_test, mean = 0, sd = 1.5)
X1test <- 0.1 * (Ztest[, 1] + rnorm(n_test, sd = 0.1)) ^ 2 +
 (Ztest[, 2] + rnorm(n_test, sd = 1)) ^ 2 + Htest + rnorm(n_test, sd = 0.1)
X2test <- 0.5 * (Ztest[, 3] + Ztest[, 4]) ^ 2 + 0.1 * Htest ^ 2 + rnorm(n_test, sd = 0.1)
Xtest <- matrix(cbind(X1test, X2test), ncol = p_X)
Ytest <- 0.5 * Xtest[, 1] + 0.2 * (Xtest[, 2] + rnorm(n_test, sd = 0.2) + Htest) ^ 2 +
 rnorm(n_test, sd = 0.1)

# Fit generativeIV model ----------------------------------------------------
# Consider increasing number of epochs. Here: num_epochs = 100 for fast computation only.
DIV_model <- div(Z = Z, X = X, Y = Y, num_epochs = 100)
print(DIV_model)

# Prediction on test data ---------------------------------------------------
Yhat <- predict(object = DIV_model, Xtest = Xtest, type = "mean")
cat("\n Correlation between predicted and realized values: ", signif(cor(Yhat, Ytest), 3))
plot(Yhat, Ytest, xlab = "model prediction", ylab = "observation")
# Quantile prediction -------------------------------------------------------
Yhat_quant <- predict(object = DIV_model, Xtest = Xtest, type = "quantile")
ord <- order(Yhat)
matplot(Yhat[ord], Yhat_quant[ord,], type = "l", col = 2, lty = 1,
xlab = "model prediction", ylab = "observation")
points(Yhat[ord], Ytest[ord], pch = 20, cex = 0.5)

#' # Sampling from estimated model ---------------------------------------------
Ysample <- predict(object = DIV_model, Xtest = Xtest, type = "sample", nsample = 1)

#' # Plots of realized & sampled values against first variable -----------------
oldpar <- par(no.readonly = TRUE)
par(mfrow = c(1, 2))
plot(Xtest[, 1], Ytest, xlab = "Predictor Variable 1", ylab = "Observation")
plot(Xtest[, 1], Ysample, xlab = "Predictor Variable 1", ylab = "Model sample")
par(oldpar)

## End(Not run)

Distributional IV Model Fit Function

Description

This function fits a joint distributional IV model to the provided data. It allows for the tuning of several parameters related to model complexity and model training. The function is not meant to be exported but can be used within the package or for internal testing purposes.

Usage

divfit(
  Z,
  X,
  Y,
  W,
  epsx_dim = epsx_dim,
  epsy_dim = epsy_dim,
  epsh_dim = epsh_dim,
  hidden_dim = hidden_dim,
  num_layer = num_layer,
  num_epochs = num_epochs,
  lr = lr,
  beta = beta,
  silent = silent
)

Arguments

Value

A list containing the trained DIV model and a matrix of loss values.

Energy Loss Calculation

Description

This function calculates the energy loss for given tensors. The loss is calculated as the mean of the L2 norms between 'x0' and 'x' and between 'x0' and 'xp', subtracted by half the mean of the L2 norm between 'x' and 'xp'.

Usage

energyloss(x0, x, xp, verbose = FALSE)

Arguments

Value

A vector containing the calculated energy loss, 's1', and 's2', or a scalar representing the calculated energy loss.

Energy Loss Calculation with Beta Scaling

Description

This function calculates the energy loss for given tensors. The loss is calculated as the mean of the L2 norms between 'x0' and 'x' and between 'x0' and 'xp', each raised to the power of 'beta', subtracted by half the mean of the L2 norm between 'x' and 'xp', also raised to the power of 'beta'.

Usage

energylossbeta(x0, x, xp, beta, verbose = FALSE)

Arguments

Value

A scalar representing the calculated energy loss.

Define a Stochastic Generative Neural Network Model with Noise at Input Layer

Description

This function defines a generative neural network model for a certain architecture and adds noise to the input layer.

Usage

nn_model(in_dim, noise_dim, hidden_dim = 100, out_dim, num_layer = 3)

Arguments

Value

A generative neural network model with intermediate noise injection.

Prediction Function for a DIV Model Object

Description

This function computes predictions from a trained DIV model. It allows for estimation of the interventional mean and quantiles, as well as sampling from the fitted interventional distribution. If the model includes exogenous predictors, it allows for estimation of the conditional interventional mean and quantiles, as well as sampling from the fitted conditional interventional distribution.

Usage

## S3 method for class 'DIV'
predict(
  object,
  Xtest,
  Wtest = NULL,
  type = c("mean", "sample", "quantile")[1],
  trim = 0.05,
  quantiles = 0.1 * (1:9),
  nsample = 200,
  drop = TRUE,
  ...
)

Arguments

Value

A vector or matrix/array of predictions.

Examples

## Not run: 
# NOTE: This example requires torch runtime.
# Please install it with: torch::install_torch()

# Simulate data -------------------------------------------------------------
p_Z <- 4
p_X <- 2

set.seed(2209)
n_train <- 1000
Z <- matrix(rnorm(n_train * p_Z, mean = 2), ncol = p_Z)
H <- rnorm(n_train, mean = 0, sd = 1.5)
X1 <- 0.1 * (Z[, 1] + rnorm(n_train, sd = 0.1)) ^ 2 +
 (Z[, 2] + rnorm(n_train, sd = 1)) ^ 2 + H + rnorm(n_train, sd = 0.1)
X2 <- 0.5 * (Z[, 3] + Z[, 4]) ^ 2 + 0.1 * H ^ 2 + rnorm(n_train, sd = 0.1)
X <- matrix(cbind(X1, X2), ncol = p_X)
Y <- 0.5 * X[, 1] + 0.2 * (X[, 2] + rnorm(n_train, sd = 0.2) + H) ^ 2 +
 rnorm(n_train, sd = 0.1)
n_test <- n_train
Ztest <- matrix(rnorm(n_test * p_Z, mean = 2), ncol = p_Z)
Htest <- rnorm(n_test, mean = 0, sd = 1.5)
X1test <- 0.1 * (Ztest[, 1] + rnorm(n_test, sd = 0.1)) ^ 2 +
 (Ztest[, 2] + rnorm(n_test, sd = 1)) ^ 2 + Htest + rnorm(n_test, sd = 0.1)
X2test <- 0.5 * (Ztest[, 3] + Ztest[, 4]) ^ 2 + 0.1 * Htest ^ 2 + rnorm(n_test, sd = 0.1)
Xtest <- matrix(cbind(X1test, X2test), ncol = p_X)
Ytest <- 0.5 * Xtest[, 1] + 0.2 * (Xtest[, 2] + rnorm(n_test, sd = 0.2) + Htest) ^ 2 +
 rnorm(n_test, sd = 0.1)

# Fit DIV model -------------------------------------------------------------
# Consider increasing number of epochs. Here: num_epochs = 100 for fast computation only.
DIV_model <- div(Z = Z, X = X, Y = Y, num_epochs = 100)
print(DIV_model)

# Prediction on test data ---------------------------------------------------
Yhat <- predict(object = DIV_model, Xtest = Xtest, type = "mean")
cat("\n Correlation between predicted and realized values: ", signif(cor(Yhat, Ytest), 3))
plot(Yhat, Ytest, xlab = "model prediction", ylab = "observation")
# Quantile prediction -------------------------------------------------------
Yhat_quant <- predict(object = DIV_model, Xtest = Xtest, type = "quantile")
ord <- order(Yhat)
matplot(Yhat[ord], Yhat_quant[ord,], type = "l", col = 2, lty = 1,
xlab = "model prediction", ylab = "observation")
points(Yhat[ord], Ytest[ord], pch = 20, cex = 0.5)

#' # Sampling from estimated model ---------------------------------------------
Ysample <- predict(object = DIV_model, Xtest = Xtest, type = "sample", nsample = 1)

#' # Plots of realized & sampled values against first variable -----------------
oldpar <- par(no.readonly = TRUE)
par(mfrow = c(1, 2))
plot(Xtest[, 1], Ytest, xlab = "Predictor Variable 1", ylab = "Observation")
plot(Xtest[, 1], Ysample, xlab = "Predictor Variable 1", ylab = "Model sample")
par(oldpar)

## End(Not run)

Print Function for a DIV Model Object

Description

This function is a utility that displays a summary of a fitted DIV model object.

Usage

## S3 method for class 'DIV'
print(x, ...)

Arguments

Value

This function does not return anything. It prints a summary of the model, including information about its architecture and training process, and the loss values achieved at several epochs during training.

Examples

## Not run: 
# NOTE: This example requires torch runtime.
# Please install it with: torch::install_torch()
# Simulate data -------------------------------------------------------------
p_Z <- 4
p_X <- 2

set.seed(2209)
n_train <- 1000
Z <- matrix(rnorm(n_train * p_Z, mean = 2), ncol = p_Z)
H <- rnorm(n_train, mean = 0, sd = 1.5)
X1 <- 0.1 * (Z[, 1] + rnorm(n_train, sd = 0.1)) ^ 2 +
 (Z[, 2] + rnorm(n_train, sd = 1)) ^ 2 + H + rnorm(n_train, sd = 0.1)
X2 <- 0.5 * (Z[, 3] + Z[, 4]) ^ 2 + 0.1 * H ^ 2 + rnorm(n_train, sd = 0.1)
X <- matrix(cbind(X1, X2), ncol = p_X)
Y <- 0.5 * X[, 1] + 0.2 * (X[, 2] + rnorm(n_train, sd = 0.2) + H) ^ 2 +
 rnorm(n_train, sd = 0.1)
n_test <- n_train
Ztest <- matrix(rnorm(n_test * p_Z, mean = 2), ncol = p_Z)
Htest <- rnorm(n_test, mean = 0, sd = 1.5)
X1test <- 0.1 * (Ztest[, 1] + rnorm(n_test, sd = 0.1)) ^ 2 +
 (Ztest[, 2] + rnorm(n_test, sd = 1)) ^ 2 + Htest + rnorm(n_test, sd = 0.1)
X2test <- 0.5 * (Ztest[, 3] + Ztest[, 4]) ^ 2 + 0.1 * Htest ^ 2 + rnorm(n_test, sd = 0.1)
Xtest <- matrix(cbind(X1test, X2test), ncol = p_X)
Ytest <- 0.5 * Xtest[, 1] + 0.2 * (Xtest[, 2] + rnorm(n_test, sd = 0.2) + Htest) ^ 2 +
 rnorm(n_test, sd = 0.1)

# Fit DIV model ----------------------------------------------------
# Consider increasing number of epochs. Here: num_epochs = 100 for fast computation only.
DIV_model <- div(Z = Z, X = X, Y = Y, num_epochs = 100)
print(DIV_model)

## End(Not run)