multinomial_ml {ocf}

Multinomial Machine Learning

Description

Estimation strategy to estimate conditional choice probabilities for ordered non-numeric outcomes.

Usage

multinomial_ml(y = NULL, X = NULL, learner = "forest", scale = TRUE)

Arguments

y

Outcome vector.

X

Covariate matrix (no intercept).

learner

String, either "forest" or "l1". Selects the base learner to estimate each expectation.

scale

Logical, whether to scale the covariates. Ignored if learner is not "l1".

Details

Multinomial machine learning expresses conditional choice probabilities as expectations of binary variables:

p_m \left( X_i \right) = \mathbb{E} \left[ 1 \left( Y_i = m \right) | X_i \right]

This allows us to estimate each expectation separately using any regression algorithm to get an estimate of conditional probabilities.

multinomial_ml combines this strategy with either regression forests or penalized logistic regression with an L1 penalty, according to the user-specified parameter learner.

If learner == "l1", the penalty parameters are chosen via 10-fold cross-validation and model.matrix is used to handle non-numeric covariates. Additionally, if scale == TRUE, the covariates are scaled to have zero mean and unit variance.

Value

Object of class mml.

Author(s)

Riccardo Di Francesco

See Also

ordered_ml, ocf

Examples

## Load data from orf package.
set.seed(1986)

library(orf)
data(odata)
odata <- odata[1:100, ] # Subset to reduce elapsed time.

y <- as.numeric(odata[, 1])
X <- as.matrix(odata[, -1])

## Training-test split.
train_idx <- sample(seq_len(length(y)), floor(length(y) * 0.5))

y_tr <- y[train_idx]
X_tr <- X[train_idx, ]

y_test <- y[-train_idx]
X_test <- X[-train_idx, ]

## Fit multinomial machine learning on training sample using two different learners.
multinomial_forest <- multinomial_ml(y_tr, X_tr, learner = "forest")
multinomial_l1 <- multinomial_ml(y_tr, X_tr, learner = "l1")

## Predict out of sample.
predictions_forest <- predict(multinomial_forest, X_test)
predictions_l1 <- predict(multinomial_l1, X_test)

## Compare predictions.
cbind(head(predictions_forest), head(predictions_l1))