This function computes the mean absolute percentage error.
Usage
mean_absolute_percentage_error(
true,
pred,
weights = NULL,
multi = c("average", "sum", "raw"),
eps = 1e-10,
rweights = NULL
)Arguments
- true
a vector (or a matrix) of observed values. If a matrix is provided, a multi-response is assumed
- pred
a vector (or a matrix) of predicted values
- weights
observation weights
- multi
what to do when response has multiple output values
averageerrors of multiple outputs are averaged to get a single value for each observation
sumerrors of multiple outputs are summed up to get a single value for each observation
rawreturns a vector containing one error for each output
- eps
an arbitrary positive small number, used to correct the MAPE formula and avoid the division by zero
- rweights
response weights
Value
the mean absolute percentage error, a positive double or a vector of positive double values,
one for each response, if response has multiple output values and multi = "raw"
Details
The mean absolute percentage error (MAPE) is a measure of errors based on relative absolute values. The MAPE estimated over n observations is defined as
$$MAPE(y,\hat{y}) = \frac{1}{n}\sum_{i=1}^{n} \frac{\lvert y_{i} - \hat{y}_{i} \rvert}{\max{\lvert y_{i} \rvert, \epsilon}}$$
where \(y_{i}\) is the true value of the \(i\)-th sample, \(\hat{y}_{i}\) is the predicted value, and \(\epsilon\) is an arbitrary positive small number used to avoid a division by zero.
If observation weights are provided, then the weighted mean absolute percentage error is computed as
$$wMAPE(w,y,\hat{y}) = \frac{1}{\sum_{i=1}^{n} w_{i}}\sum_{i=1}^{n} w_{i} * \frac{\lvert y_{i} - \hat{y}_{i} \rvert}{\max{\lvert y_{i} \rvert, \epsilon}}$$
where \(w_{i}\) is the weighting factor assigned to the \(i\)-th observation. The best possible score is zero.