huber_loss: Huber loss

In yardstick: Tidy Characterizations of Model Performance

Huber loss

Description

Calculate the Huber loss, a loss function used in robust regression. This loss function is less sensitive to outliers than rmse(). This function is quadratic for small residual values and linear for large residual values.

Usage

huber_loss(data, ...)

## S3 method for class 'data.frame'
huber_loss(
  data,
  truth,
  estimate,
  delta = 1,
  na_rm = TRUE,
  case_weights = NULL,
  ...
)

huber_loss_vec(
  truth,
  estimate,
  delta = 1,
  na_rm = TRUE,
  case_weights = NULL,
  ...
)

Arguments

data	A data.frame containing the columns specified by the truth and estimate arguments.
...	Not currently used.
truth	The column identifier for the true results (that is numeric). 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 numeric vector.
estimate	The column identifier for the predicted results (that is also numeric). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For ⁠_vec()⁠ functions, a numeric vector.
delta	A single numeric value. Defines the boundary where the loss function transitions from quadratic to linear. Defaults to 1.
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().

Details

Huber loss is a metric that should be minimized. The output ranges from 0 to Inf, with 0 indicating perfect predictions.

The formula for Huber loss is:

L_\delta = \begin{cases} \frac{1}{2} a^2 & \text{if } |a| \le \delta \\ \delta (|a| - \frac{1}{2} \delta) & \text{otherwise} \end{cases}

where a = \text{truth}_i - \text{estimate}_i.

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

Author(s)

James Blair

References

Huber, P. (1964). Robust Estimation of a Location Parameter. Annals of Statistics, 53 (1), 73-101.

See Also

All numeric metrics

Other numeric metrics: ccc(), gini_coef(), huber_loss_pseudo(), iic(), mae(), mape(), mase(), mpe(), msd(), mse(), poisson_log_loss(), rmse(), rmse_relative(), rpd(), rpiq(), rsq(), rsq_trad(), smape()

Other accuracy metrics: ccc(), huber_loss_pseudo(), iic(), mae(), mape(), mase(), mpe(), msd(), mse(), poisson_log_loss(), rmse(), rmse_relative(), smape()

Examples

# Supply truth and predictions as bare column names
huber_loss(solubility_test, solubility, prediction)

library(dplyr)

set.seed(1234)
size <- 100
times <- 10

# create 10 resamples
solubility_resampled <- bind_rows(
  replicate(
    n = times,
    expr = sample_n(solubility_test, size, replace = TRUE),
    simplify = FALSE
  ),
  .id = "resample"
)

# Compute the metric by group
metric_results <- solubility_resampled |>
  group_by(resample) |>
  huber_loss(solubility, prediction)

metric_results

# Resampled mean estimate
metric_results |>
  summarise(avg_estimate = mean(.estimate))
# Using a different value of 'delta'... if you are adding the metric to a
# metric set, you can create a new metric function with the updated argument
# value:

huber_loss_2 <- metric_tweak("huber_loss_2", huber_loss, delta = 2)
multi_metrics <- metric_set(huber_loss, huber_loss_2)
multi_metrics(solubility_test, solubility, prediction)

yardstick documentation built on April 8, 2026, 1:06 a.m.