The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula:

Where A_t is the actual value and F_t is the forecast value. Their difference is divided by the actual value A_t. The absolute value of this ratio is summed for every forecasted point in time and divided by the number of fitted points n. MAPE should be used with extreme caution in forecasting, because small actuals (target labels) can lead to highly inflated MAPE scores. wMAPE should be used instead of MAPE wherever possible (see section below).

Mean absolute percentage error is commonly used as a loss function for regression problems and in model evaluation, because of its very intuitive interpretation in terms of relative error.

Consider a standard regression setting in which the data are fully described by a random pair ${\displaystyle Z=(X,Y)}$ with values in ${\displaystyle \mathbb {R} ^{d}\times \mathbb {R} }$, and n i.i.d. copies ${\displaystyle (X_{1},Y_{1}),...,(X_{n},Y_{n})}$ of ${\displaystyle (X,Y)}$. Regression models aim at finding a good model for the pair, that is a measurable function g from ${\displaystyle \mathbb {R} ^{d}}$ to ${\displaystyle \mathbb {R} }$ such that ${\displaystyle g(X)}$ is close to Y.

In the classical regression setting, the closeness of ${\displaystyle g(X)}$ to Y is measured via the L₂ risk, also called the mean squared error (MSE). In the MAPE regression context, the closeness of ${\displaystyle g(X)}$ to Y is measured via the MAPE, and the aim of MAPE regressions is to find a model ${\displaystyle g_{\text{MAPE}}}$ such that:

$${\displaystyle g_{\mathrm {MAPE} }(x)=\arg \min _{g\in {\mathcal {G}}}\mathbb {E} {\Biggl [}\left|{\frac {g(X)-Y}{Y}}\right||X=x{\Biggr ]}}$$

where ${\displaystyle {\mathcal {G}}}$ is the class of models considered (e.g. linear models).

In practice