Desirability functions are simple but useful tools for simultaneously optimizing several things at once. For each input, a translation function is used to map the input values between zero and one where zero is unacceptable and one is most desirable.
For example, Kuhn and Johnson (2019) use these functions during feature selection to help a genetic algorithm choose which predictors to include in a model that simultaneously improves performance and reduces the number of predictors.
The desirability2 package improves on the original desirability package by enabling in-line computations that can be used with dplyr pipelines.
A ranking example
Suppose a classification model with two tuning parameters (penalty and mixture) and several performance measures (multinomial log-loss, area under the precision-recall curve, and the area under the ROC curve). For each tuning parameter, the average number of features used in the model was also computed:
library(desirability2)
library(dplyr)
classification_results
#> # A tibble: 300 × 6
#> mixture penalty mn_log_loss pr_auc roc_auc num_features
#> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
#> 1 0 0.1 0.199 0.488 0.869 211
#> 2 0 0.0788 0.196 0.491 0.870 211
#> 3 0 0.0621 0.194 0.494 0.871 211
#> 4 0 0.0489 0.192 0.496 0.872 211
#> 5 0 0.0386 0.191 0.499 0.873 211
#> 6 0 0.0304 0.190 0.501 0.873 211
#> 7 0 0.0240 0.188 0.504 0.874 211
#> 8 0 0.0189 0.188 0.506 0.874 211
#> 9 0 0.0149 0.187 0.508 0.874 211
#> 10 0 0.0117 0.186 0.510 0.874 211
#> # ℹ 290 more rowsWe might want to pick a model in a way that maximizes the area under the ROC curve with a minimum number of model terms. We know that the ROC measures is usually between 0.5 and 1.0. We can define a desirability function to maximize this value using:
d_max(roc_auc, low = 1/2, high = 1)For the number of terms, if we wanted to minimize this under the condition that there should be less than 100 features, a minimal desirability function can be appropriate:
d_min(num_features, low = 1, high = 100)We can add these as columns to the data using a mutate() statement along with a call to the function that blends these values using a geometric mean:
classification_results %>%
select(-mn_log_loss, -pr_auc) %>%
mutate(
d_roc = d_max(roc_auc, low = 1/2, high = 1),
d_terms = d_min(num_features, low = 1, high = 50),
d_both = d_overall(d_roc, d_terms)
) %>%
# rank from most desirable to least:
arrange(desc(d_both))
#> # A tibble: 300 × 7
#> mixture penalty roc_auc num_features d_roc d_terms d_both
#> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
#> 1 1 0.0189 0.844 7 0.687 0.878 0.777
#> 2 1 0.0240 0.835 6 0.670 0.898 0.776
#> 3 0.889 0.0304 0.830 6 0.660 0.898 0.770
#> 4 0.778 0.0240 0.844 8 0.687 0.857 0.768
#> 5 0.778 0.0304 0.835 7 0.671 0.878 0.767
#> 6 0.889 0.0386 0.820 5 0.640 0.918 0.766
#> 7 0.889 0.0489 0.813 4 0.625 0.939 0.766
#> 8 0.667 0.0304 0.842 8 0.684 0.857 0.766
#> 9 0.778 0.0489 0.819 5 0.638 0.918 0.765
#> 10 0.778 0.0621 0.812 4 0.623 0.939 0.765
#> # ℹ 290 more rowsSee ?inline_desirability for details on the individual desirability functions.
Code of Conduct
Please note that the desirability2 project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.
Contributing
This project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.
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