This function computes the absolute error.
Usage
absolute_error(
true,
pred,
weights = NULL,
rweights = NULL,
multi = c("average", "sum", "raw")
)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. This argument is for consistency, but not currently used.
- rweights
response 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
Value
the absolute error, a vector of positive double values or a matrix,
having one column for each response, if response has multiple output values and multi = "raw"
Details
The absolute error (AE) is based on absolute values and it is defined as
$$AE(y_{i},\hat{y}_{i}) = \lvert y_{i} - \hat{y}_{i} \rvert$$
where \(y_{i}\) is the true value of the \(i\)-th sample and \(\hat{y}_{i}\) is the predicted value.
If the observed data has multiple output values and weights are provided, then the error is weighted.
$$wAE(w,y,\hat{y}) = \frac{1}{\sum_{j=1}^{n} w_{j}} w * \lvert y_{i} - \hat{y}_{i} \rvert$$
where \(w_{j}\) is the weighting factor assigned to the \(j\)-th response. The best possible score is zero.