engression {engression}

Engression Function

Description

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

Usage

engression(
  X,
  Y,
  noise_dim = 5,
  hidden_dim = 100,
  num_layer = 3,
  dropout = 0.05,
  batch_norm = TRUE,
  num_epochs = 1000,
  lr = 10^(-3),
  beta = 1,
  silent = FALSE,
  standardize = TRUE
)

Arguments

X

A matrix or data frame representing the predictors.

Y

A matrix or vector representing the target variable(s). If Y is a factor a classification model is fitted (experimental).

noise_dim

The dimension of the noise introduced in the model (default: 5).

hidden_dim

The size of the hidden layer in the model (default: 100).

num_layer

The number of layers in the model (default: 3).

dropout

The dropout rate to be used in the model in case no batch normalization is used. Only active if batch normalization is off. (default: 0.01)

batch_norm

A boolean indicating whether to use batch-normalization (default: TRUE).

num_epochs

The number of epochs to be used in training (default: 1000).

lr

The learning rate to be used in training (default: 10^-3).

beta

The beta scaling factor for energy loss (default: 1).

silent

A boolean indicating whether to suppress output during model training (default: FALSE).

standardize

A boolean indicating whether to standardize the input data (default: TRUE).

Value

An engression model object with class "engression".

Examples

  n = 1000
  p = 5

  X = matrix(rnorm(n*p),ncol=p)
  Y = (X[,1]+rnorm(n)*0.1)^2 + (X[,2]+rnorm(n)*0.1) + rnorm(n)*0.1
  Xtest = matrix(rnorm(n*p),ncol=p)
  Ytest = (Xtest[,1]+rnorm(n)*0.1)^2 + (Xtest[,2]+rnorm(n)*0.1) + rnorm(n)*0.1

  ## fit engression object
  engr = engression(X,Y)
  print(engr)

  ## prediction on test data
  Yhat = predict(engr,Xtest,type="mean")
  cat("\n correlation between predicted and realized values:  ", signif(cor(Yhat, Ytest),3))
  plot(Yhat, Ytest,xlab="prediction", ylab="observation")

  ## quantile prediction
  Yhatquant = predict(engr,Xtest,type="quantiles")
  ord = order(Yhat)
  matplot(Yhat[ord], Yhatquant[ord,], type="l", col=2,lty=1,xlab="prediction", ylab="observation")
  points(Yhat[ord],Ytest[ord],pch=20,cex=0.5)

  ## sampling from estimated model
  Ysample = predict(engr,Xtest,type="sample",nsample=1)
   
  ## plot of realized values against first variable
  oldpar <- par()
  par(mfrow=c(1,2))
  plot(Xtest[,1], Ytest, xlab="Variable 1", ylab="Observation")
  ## plot of sampled values against first variable
  plot(Xtest[,1], Ysample, xlab="Variable 1", ylab="Sample from engression model")   
  par(oldpar)