Area under the precision recall curve

average_precision() is an alternative to pr_auc() that avoids any ambiguity about what the value of precision should be when recall == 0 and there are not yet any false positive values (some say it should be 0, others say 1, others say undefined).

It computes a weighted average of the precision values returned from pr_curve(), where the weights are the increase in recall from the previous threshold. See pr_curve() for the full curve.

Usage

average_precision(data, ...)

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

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

Arguments

data: A data.frame containing the columns specified by truth and ....
...: A set of unquoted column names or one or more dplyr selector functions to choose which variables contain the class probabilities. If truth is binary, only 1 column should be selected, and it should correspond to the value of event_level. Otherwise, there should be as many columns as factor levels of truth and the ordering of the columns should be the same as the factor levels of truth.
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.
estimator: One of "binary", "macro", or "macro_weighted" to specify the type of averaging to be done. "binary" is only relevant for the two class case. The other two are general methods for calculating multiclass metrics. The default will automatically choose "binary" or "macro" based on truth.
na_rm: A logical value indicating whether NA values should be stripped before the computation proceeds.
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".
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().
estimate: If truth is binary, a numeric vector of class probabilities corresponding to the "relevant" class. Otherwise, a matrix with as many columns as factor levels of truth. It is assumed that these are in the same order as the levels of truth.

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 average_precision_vec(), a single numeric value (or NA).

Details

The computation for average precision is a weighted average of the precision values. Assuming you have n rows returned from pr_curve(), it is a sum from 2 to n, multiplying the precision value p_i by the increase in recall over the previous threshold, r_i - r_(i-1).

$$AP = \sum (r_{i} - r_{i-1}) * p_i$$

By summing from 2 to n, the precision value p_1 is never used. While pr_curve() returns a value for p_1, it is technically undefined as tp / (tp + fp) with tp = 0 and fp = 0. A common convention is to use 1 for p_1, but this metric has the nice property of avoiding the ambiguity. On the other hand, r_1 is well defined as long as there are some events (p), and it is tp / p with tp = 0, so r_1 = 0.

When p_1 is defined as 1, the average_precision() and roc_auc() values are often very close to one another.

Multiclass

Macro 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.

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.

Examples

# ---------------------------------------------------------------------------
# Two class example

# `truth` is a 2 level factor. The first level is `"Class1"`, which is the
# "event of interest" by default in yardstick. See the Relevant Level
# section above.
data(two_class_example)

# Binary metrics using class probabilities take a factor `truth` column,
# and a single class probability column containing the probabilities of
# the event of interest. Here, since `"Class1"` is the first level of
# `"truth"`, it is the event of interest and we pass in probabilities for it.
average_precision(two_class_example, truth, Class1)
#> # A tibble: 1 × 3
#>   .metric           .estimator .estimate
#>   <chr>             <chr>          <dbl>
#> 1 average_precision binary         0.947

# ---------------------------------------------------------------------------
# Multiclass example

# `obs` is a 4 level factor. The first level is `"VF"`, which is the
# "event of interest" by default in yardstick. See the Relevant Level
# section above.
data(hpc_cv)

# You can use the col1:colN tidyselect syntax
library(dplyr)
hpc_cv %>%
  filter(Resample == "Fold01") %>%
  average_precision(obs, VF:L)
#> # A tibble: 1 × 3
#>   .metric           .estimator .estimate
#>   <chr>             <chr>          <dbl>
#> 1 average_precision macro          0.617

# Change the first level of `obs` from `"VF"` to `"M"` to alter the
# event of interest. The class probability columns should be supplied
# in the same order as the levels.
hpc_cv %>%
  filter(Resample == "Fold01") %>%
  mutate(obs = relevel(obs, "M")) %>%
  average_precision(obs, M, VF:L)
#> # A tibble: 1 × 3
#>   .metric           .estimator .estimate
#>   <chr>             <chr>          <dbl>
#> 1 average_precision macro          0.617

# Groups are respected
hpc_cv %>%
  group_by(Resample) %>%
  average_precision(obs, VF:L)
#> # A tibble: 10 × 4
#>    Resample .metric           .estimator .estimate
#>    <chr>    <chr>             <chr>          <dbl>
#>  1 Fold01   average_precision macro          0.617
#>  2 Fold02   average_precision macro          0.625
#>  3 Fold03   average_precision macro          0.699
#>  4 Fold04   average_precision macro          0.685
#>  5 Fold05   average_precision macro          0.625
#>  6 Fold06   average_precision macro          0.656
#>  7 Fold07   average_precision macro          0.617
#>  8 Fold08   average_precision macro          0.659
#>  9 Fold09   average_precision macro          0.632
#> 10 Fold10   average_precision macro          0.611

# Weighted macro averaging
hpc_cv %>%
  group_by(Resample) %>%
  average_precision(obs, VF:L, estimator = "macro_weighted")
#> # A tibble: 10 × 4
#>    Resample .metric           .estimator     .estimate
#>    <chr>    <chr>             <chr>              <dbl>
#>  1 Fold01   average_precision macro_weighted     0.750
#>  2 Fold02   average_precision macro_weighted     0.745
#>  3 Fold03   average_precision macro_weighted     0.794
#>  4 Fold04   average_precision macro_weighted     0.757
#>  5 Fold05   average_precision macro_weighted     0.740
#>  6 Fold06   average_precision macro_weighted     0.747
#>  7 Fold07   average_precision macro_weighted     0.751
#>  8 Fold08   average_precision macro_weighted     0.759
#>  9 Fold09   average_precision macro_weighted     0.714
#> 10 Fold10   average_precision macro_weighted     0.742

# Vector version
# Supply a matrix of class probabilities
fold1 <- hpc_cv %>%
  filter(Resample == "Fold01")

average_precision_vec(
   truth = fold1$obs,
   matrix(
     c(fold1$VF, fold1$F, fold1$M, fold1$L),
     ncol = 4
   )
)
#> [1] 0.6173363