Mean absolute percentage error

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 At is the actual value and Ft is the forecast value. Their difference is divided by the actual value At. The absolute value of this ratio is summed for every forecasted point in time and divided by the number of fitted points n. 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 with values in , and n i.i.d. copies of . Regression models aim at finding a good model for the pair, that is a measurable function g from to such that is close to Y. In the classical regression setting, the closeness of to Y is measured via the L2 risk, also called the mean squared error (MSE). In the MAPE regression context, the closeness of to Y is measured via the MAPE, and the aim of MAPE regressions is to find a model such that: where is the class of models considered (e.g. linear models). In practice In practice can be estimated by the empirical risk minimization strategy, leading to From a practical point of view, the use of the MAPE as a quality function for regression model is equivalent to doing weighted mean absolute error (MAE) regression, also known as quantile regression. This property is trivial since As a consequence, the use of the MAPE is very easy in practice, for example using existing libraries for quantile regression allowing weights. The use of the MAPE as a loss function for regression analysis is feasible both on a practical point of view and on a theoretical one, since the existence of an optimal model and the consistency of the empirical risk minimization can be proved. WMAPE (sometimes spelled wMAPE) stands for weighted mean absolute percentage error.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related people (1)

Related units (1)

Related concepts (3)

Related courses (4)

Related lectures (81)

Linear Regression Basics CS-233(a): Introduction to machine learning (BA3)

Covers the basics of linear regression in machine learning, including model training, loss functions, and evaluation metrics.

Mean-Square-Error Inference EE-566: Adaptation and learning

Covers the concept of mean-square-error inference and optimal estimators for inference problems using different design criteria.

Regression Models: Performance and Evaluation ENG-209: Data science for engineers with Python

Explores regression model performance, learning errors, and building regression trees using the CART algorithm.

ME-421: System identification

Identification of discrete-time linear models using experimental data is studied. The correlation method and spectral analysis are used to identify nonparametric models and the subspace and prediction

ME-419: Production management

Production management deals with producing goods sustainably at the right time, quantity, and quality with the minimum cost. This course equips students with practical skills and tools for effectively

MATH-342: Time series

A first course in statistical time series analysis and applications.

Mean absolute percentage error

Forecasting

Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results creating a variance actual analysis. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself.

Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.