Define Custom Loss Functions • threedx

library(threedx)

Since learn_weights() fits a threedx model by evaluating all parameter combinations provided via the alphas_grid argument, we can use any kind of loss_function to compare models on the training data.

While threedx comes with a few built-in loss functions, they serve as defaults and as examples. You can define any other that fits your application, and you’re not limited to those for which you know the derivative.

Constructing a Loss Function

At the time of writing, learn_weights() passes three arguments to a loss function:

A numeric vector of observed actuals y without missing values
A numeric vector of one-step-ahead predictions y_hat of same length as y and also without missing values
Further arguments ... that might be provided in the future

For a loss function, the access to y and y_hat of course is essential to compute errors, or to assign weights to errors.

In return, learn_weights() expects to receive a non-missing numeric scalar value from the loss function. These scalars will be minimized across parameter combinations defined by alphas_grid to choose the optimal parameter combination.

One of the simplest possible loss functions that can be used is the mean absolute error loss function. Its implementation in threedx is straightforward:

print(loss_mae)
#> function (y_hat, y, ...) 
#> {
#>     mean(abs(y - y_hat))
#> }
#> <bytecode: 0x5606f2bd5b08>
#> <environment: namespace:threedx>

loss_mae(y_hat = c(5, -3, 2), y = c(1, 1, -2))
#> [1] 4

But you can go more complex. For example, threedx provides a loss that assigns weight (based on the size of the observation) to each absolute error before taking the mean:

print(loss_mae_with_observation_weight)
#> function (y_hat, y, ...) 
#> {
#>     sqrt(mean(abs(y - y_hat) * pmax(y, abs(y - y_hat))))
#> }
#> <bytecode: 0x5606f2f4a170>
#> <environment: namespace:threedx>

Wether this is a useful loss function will depend on your context. But it goes to show that you have a lot of flexibility.

Another idea could be to define a function that only ever takes the 20 most recent observations into account:

loss_mae_twenty_most_recent <- function(y_hat, y, ...) {
  loss_mae(utils::tail(y_hat, 20), utils::tail(y, 20), ...)
}

Or one that applies moving averages on observations and predictions first, or one that only takes into account the observations from the same seasonal period as the next one-step-ahead prediction will perform, or …