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Fall-out (False Positive Rate)

Source: R/class-fall_out.R
fall_out.Rd

These functions calculate the fall-out (false positive rate) of a measurement system compared to a reference result (the "truth" or gold standard). Fall-out is defined as 1 - specificity, or equivalently, the proportion of negatives that are incorrectly classified as positives.

Usage

fall_out(data, ...)

# S3 method for class 'data.frame'
fall_out(
  data,
  truth,
  estimate,
  estimator = NULL,
  na_rm = TRUE,
  case_weights = NULL,
  event_level = yardstick_event_level(),
  ...
)

fall_out_vec(
  truth,
  estimate,
  estimator = NULL,
  na_rm = TRUE,
  case_weights = NULL,
  event_level = yardstick_event_level(),
  ...
)

Arguments

data

Either a data.frame containing the columns specified by the truth and estimate arguments, or a table/matrix where the true class results should be in the columns of the table.

...

Not currently used.

truth

The column identifier for the true class results (that is a factor). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For _vec() functions, a factor vector.

estimate

The column identifier for the predicted class results (that is also factor). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For _vec() functions, a factor vector.

estimator

One of: "binary", "macro", "macro_weighted", or "micro" to specify the type of averaging to be done. "binary" is only relevant for the two class case. The other three are general methods for calculating multiclass metrics. The default will automatically choose "binary" or "macro" based on estimate.

na_rm

A logical value indicating whether NA values should be stripped before the computation proceeds.

case_weights

The optional column identifier for case weights. This should be an unquoted column name that evaluates to a numeric column in data. For _vec() functions, a numeric vector, hardhat::importance_weights(), or hardhat::frequency_weights().

event_level

A single string. Either "first" or "second" to specify which level of truth to consider as the "event". This argument is only applicable when estimator = "binary". The default uses an internal helper that defaults to "first".

Value

A tibble with columns .metric, .estimator, and .estimate and 1 row of values.

For grouped data frames, the number of rows returned will be the same as the number of groups.

For fall_out_vec(), a single numeric value (or NA).

Details

Fall-out is also known as the false positive rate (FPR) or the probability of false alarm.

When the denominator of the calculation is 0, fall-out is undefined. This happens when both # true_negative = 0 and # false_positive = 0 are true, which means that there were no negatives. When computing binary fall-out, a NA value will be returned with a warning. When computing multiclass fall-out, the individual NA values will be removed, and the computation will proceed, with a warning.

Suppose a 2x2 table with notation:

Reference
PredictedPositiveNegative
PositiveAB
NegativeCD

The formula used here is:

$$\text{Fall-out} = \frac{B}{B + D}$$

Fall-out is a metric that should be minimized. The output ranges from 0 to 1, with 0 indicating that all actual negatives were correctly predicted as negative (no false positives).

Relevant Level

There is no common convention on which factor level should automatically be considered the "event" or "positive" result when computing binary classification metrics. In yardstick, the default is to use the first level. To alter this, change the argument event_level to "second" to consider the last level of the factor the level of interest. For multiclass extensions involving one-vs-all comparisons (such as macro averaging), this option is ignored and the "one" level is always the relevant result.

Multiclass

Macro, micro, and macro-weighted averaging is available for this metric. The default is to select macro averaging if a truth factor with more than 2 levels is provided. Otherwise, a standard binary calculation is done. See vignette("multiclass", "yardstick") for more information.

See also

All class metrics

Other class metrics: accuracy(), bal_accuracy(), detection_prevalence(), f_meas(), j_index(), kap(), mcc(), miss_rate(), npv(), ppv(), precision(), recall(), sens(), spec()

Other sensitivity metrics: miss_rate(), npv(), ppv(), sens(), spec()

Examples

# Two class
data("two_class_example")
fall_out(two_class_example, truth, predicted)
#> # A tibble: 1 × 3
#>   .metric  .estimator .estimate
#>   <chr>    <chr>          <dbl>
#> 1 fall_out binary         0.207

# Multiclass
library(dplyr)
data(hpc_cv)

hpc_cv |>
  filter(Resample == "Fold01") |>
  fall_out(obs, pred)
#> # A tibble: 1 × 3
#>   .metric  .estimator .estimate
#>   <chr>    <chr>          <dbl>
#> 1 fall_out macro          0.114

# Groups are respected
hpc_cv |>
  group_by(Resample) |>
  fall_out(obs, pred)
#> # A tibble: 10 × 4
#>    Resample .metric  .estimator .estimate
#>    <chr>    <chr>    <chr>          <dbl>
#>  1 Fold01   fall_out macro          0.114
#>  2 Fold02   fall_out macro          0.118
#>  3 Fold03   fall_out macro          0.101
#>  4 Fold04   fall_out macro          0.121
#>  5 Fold05   fall_out macro          0.119
#>  6 Fold06   fall_out macro          0.127
#>  7 Fold07   fall_out macro          0.134
#>  8 Fold08   fall_out macro          0.116
#>  9 Fold09   fall_out macro          0.133
#> 10 Fold10   fall_out macro          0.125

# Weighted macro averaging
hpc_cv |>
  group_by(Resample) |>
  fall_out(obs, pred, estimator = "macro_weighted")
#> # A tibble: 10 × 4
#>    Resample .metric  .estimator     .estimate
#>    <chr>    <chr>    <chr>              <dbl>
#>  1 Fold01   fall_out macro_weighted     0.184
#>  2 Fold02   fall_out macro_weighted     0.185
#>  3 Fold03   fall_out macro_weighted     0.161
#>  4 Fold04   fall_out macro_weighted     0.197
#>  5 Fold05   fall_out macro_weighted     0.188
#>  6 Fold06   fall_out macro_weighted     0.205
#>  7 Fold07   fall_out macro_weighted     0.210
#>  8 Fold08   fall_out macro_weighted     0.186
#>  9 Fold09   fall_out macro_weighted     0.205
#> 10 Fold10   fall_out macro_weighted     0.199

# Vector version
fall_out_vec(
  two_class_example$truth,
  two_class_example$predicted
)
#> [1] 0.2066116

# Making Class2 the "relevant" level
fall_out_vec(
  two_class_example$truth,
  two_class_example$predicted,
  event_level = "second"
)
#> [1] 0.120155