mlr3measures (version 1.0.0)

linex: Linear-Exponential Loss (per observation)

Description

Measure to compare true observed response with predicted response in regression tasks.

Note that this is an unaggregated measure, returning the losses per observation.

Usage

linex(truth, response, a = -1, b = 1, ...)

Value

Performance value as numeric(length(truth)).

Arguments

truth

(numeric())
True (observed) values. Must have the same length as response.

response

(numeric())
Predicted response values. Must have the same length as truth.

a

(numeric(1))
Shape parameter controlling asymmetry. Negative values penalize overestimation more, positive values penalize underestimation more. As a approaches 0, the loss resembles squared error loss. Default is -1.

b

(numeric(1))
Positive scaling factor for the loss. Larger values increase the loss magnitude. Default is 1.

...

(any)
Additional arguments. Currently ignored.

Meta Information

• Type: "regr"

• Range (per observation): \([0, \infty)\)

• Minimize (per observation): TRUE

• Required prediction: response

Details

The Linear-Exponential Loss is defined as $$ b (\exp (t_i - r_i) - a (t_i - r_i) - 1), $$ where \(a \neq 0, b > 0\).

References

Varian, R. H (1975). “A Bayesian Approach to Real Estate Assessment.” In Fienberg SE, Zellner A (eds.), Studies in Bayesian Econometrics and Statistics: In Honor of Leonard J. Savage, 195--208. North-Holland, Amsterdam.

See Also

Other Regression Measures: ae(), ape(), bias(), ktau(), mae(), mape(), maxae(), maxse(), medae(), medse(), mse(), msle(), pbias(), pinball(), rae(), rmse(), rmsle(), rrse(), rse(), rsq(), sae(), se(), sle(), smape(), srho(), sse()

Examples

set.seed(1)
truth = 1:10
response = truth + rnorm(10)
linex(truth, response)