预测误差指标:MAPE和WMAPE有何差距? [英] What's the gaps for the forecast error metrics: MAPE and WMAPE?

问题描述

我知道MAPE和WMAPE作为预测错误度量标准，它们有一些好处.但是有什么差距呢?有人说:

I know that MAPE and WMAPE as a forecast error metrics, they have some benefits. But what's the gaps? Someone says:

For MAPE:
"Combinations with very small or zero volumes can cause large skew in results"

And for WMAPE:
"Combinations with large weights can skew the results in their favor" 

我不明白，有人可以针对这两个指标的弱点来解释这两个陈述吗?谢谢.

I can't understand, can anyone explain the two statements for the weakness of the two metrics? Thanks.

推荐答案

对于MAPE，平均绝对百分比误差[1]，假设我们用 A 表示实际值，用表示预测值> P .您在时间1到n拥有一系列数据，然后

For MAPE, Mean absolute percentage error [1], suppose we denote the actual value with A, and predicted value with P. You have a series of data at time 1 thru n, then

MAPE = 100/n * ( Sum of |(A(t) - P(t))/A(t)| ), for t in 1..n
where A(t) is the actual value at time t, P(t) is the predicted value at time t.

由于A(t)在分母中，所以每当A(t)很小或接近于零时，该除法就如同被1除以零，这会在绝对百分比误差中产生很大的变化.如此大的变化的组合肯定会导致结果出现较大的偏差.

Since A(t) is in the denominator, whenever you have a very small or near-zero A(t), that division is like one divided by zero which creates very large changes in the Absolute Percentage Error. Combinations of such large changes causes large skew in results for sure.

对于WMAPE，加权平均绝对百分比误差

For WMAPE, Weighted mean absolute percentage error,

         Sum of |(A(t) - P(t))/A(t)| * W(t)
WMPAE = -------------------------------------, for t in 1..n
                    Sum of W(t)

        where W(t) is the weight you associate with the prediction at time t.

由于这是加权度量，因此它不具有与MAPE相同的问题，例如，由于体积很小或为零而导致过度倾斜.

Since this is a weighted measure, it does not have the same problems as MAPE, e.g., over-skewing due to very small or zero volumes.

但是，加权因子将表明我们希望在每个预测上都具有主观重要性[2].

However, a weighting factor would indicate the subjective importance we wish to place on each prediction [2].

例如，考虑发布 日期，我们可以通过以下方式分配权重: 重量，我们对新近的重要性越来越高 数据.在这种情况下，即使MAE 在合理的阈值范围内，系统的性能 在分析此特定功能时可能不够用.

For instance, considering the release date, we can assign weights in such a way that the higher the weight, the higher importance we are placing on more recent data. In this case we could observe that even when the MAE is under reasonable threshold, the performance of a system might be inadequate when analyzing this particular feature.

这就是最近的数据偏向结果的方式.

This is how a favor of more recent data skews the results.

[1] http://en.wikipedia.org/wiki/Mean_absolute_percentage_error
[2] http://ir.ii.uam.es/rue2012/papers/rue2012-cleger-tamayo.pdf

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