This function computes the mean squared logarithmic error.
Usage
mean_squared_log_error(
true,
pred,
weights = NULL,
multi = c("average", "sum", "raw"),
root = FALSE,
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
- root
logical, whether to return the MSLE or the root mean squared logarithmic error (RMSLE)
- rweights
response weights
Value
the mean squared 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 squared logarithmic error (MSLE) is a measure of errors based on squared logarithmic losses. This metric is commonly preferred (e.g. over the MSE) when
Under-predicted estimates are more penalised than over-predicted ones.
Huge differences in the predicted and true values aren't to be penalised (when both are huge numbers).
The MSLE estimated over n observations is defined as
$$MSLE(y,\hat{y}) = \frac{1}{n}\sum_{i=1}^{n} (log(1 + y_{i}) - log(1 + \hat{y}_{i}))^{2}$$
where \(log\) is the natural logarithm, \(y_{i}\) is the true value of the \(i\)-th sample and \(\hat{y}_{i}\) is the predicted value. If observation weights are provided, then the weighted mean absolute error is computed as
$$wMSLE(w,y,\hat{y}) = \frac{1}{\sum_{i=1}^{n} w_{i}}\sum_{i=1}^{n} w_{i} * (log(1 + y_{i}) - log(1 + \hat{y}_{i}))^{2}$$
where \(w_{i}\) is the weighting factor assigned to the \(i\)-th observation.
The best possible score is zero.