在短时间序列数据上,均值缩放得分更可靠,避免模型选择偏差。
Model selection with proper scoring rules on data sets of time series: prefer the mean scaled score
- 用均值缩放得分聚合多序列评分,抗偏倚能力强
- 短测试集时,其他方法易选错模型,因分数分布偏斜
- 实验验证其在不同缩放因子下结果稳定,适合真实场景
我们研究在多个时间序列数据集上进行概率预测模型选择的问题。单个时间序列的模型性能由测试集上适当评分规则的平均值衡量,但扩展到多序列数据集需对这些得分进行聚合。常用方法或采用缩放后平均(均值缩放得分),或避免缩放使用均秩、胜率等统计量。然而这些方法可能得出矛盾结论。我们发现,这种差异源于分数分布的偏斜,尤其在测试集较短时显著。偏斜会导致非均值类指标(如均秩、中位数、胜率)选出误设模型。相反,均值得分不受此问题影响。我们进一步证明,随着测试集规模增大,所有聚合方法会收敛至相同选择结果,缓解分歧。在间歇性需求时间序列上的实验,包括M5竞赛数据,强调了足够大测试集的重要性;均值缩放得分表现更可靠,且实证显示其决策在不同缩放因子下保持一致。
原文摘要 · Abstract (English)
We study the problem of model selection among probabilistic forecasting models evaluated on datasets of multiple time series. The performance of a model on a single time series is quantified by the average value (score) of a proper scoring rule over a test set, but extending model selection to data sets of time series requires aggregating these scores. Common approaches either rely on scaling scores and averaging them (mean scaled score) or avoid scaling by using alternative statistics such as mean ranks or win rates. However, these approaches can yield conflicting conclusions. We show that such discrepancies arise from the skewness of the distribution of the scores, which is particularly pronounced when test sets are short. The skewness can cause non-mean criteria (e.g., mean rank, median, win rate) to select misspecified models. In contrast, the mean score is immune from this problem. We further show that, as the size of the test sets increases, all aggregation criteria converge to the same model selection decision, mitigating these discrepancies. Our experiments on intermittent demand time series, including data from the M5 competition, highlight the importance of sufficiently large test sets; the mean scaled score appears to be the more reliable approach, also because empirically we found its decision to remain consistent when different scaling factors are adopted.
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