超越均方误差：用于概率时间序列预测的序数交叉熵
Beyond MSE: Ordinal Cross-Entropy for Probabilistic Time Series Forecasting
AI总结：
OCE-TS通过引入序数交叉熵损失改进时间序列预测的不确定性估计和鲁棒性，优于传统MSE方法。
摘要：
时间序列预测是一项重要的任务，涉及分析时间依赖性和潜在模式（如趋势、周期性和季节性）在历史数据中的预测未来值或趋势。当前基于深度学习的预测模型主要使用均方误差（MSE）损失函数进行回归建模。尽管能够直接预测值，但这种方法无法估计不确定性，且对异常值鲁棒性差。为了解决这些限制，我们提出OCE-TS，一种新的时间序列预测序数分类方法，用序数交叉熵（OCE）损失替代MSE，保留预测顺序的同时通过概率输出量化不确定性。具体来说，OCE-TS首先将观测值离散化为有序区间，并通过参数分布推导其概率作为监督信号。使用简单的线性模型，我们然后为每个时间步预测概率分布。OCE损失是在预测和真实概率的累积分布之间计算的，显式地保留预测值之间的序数关系。通过使用影响函数进行理论分析，我们建立了交叉熵（CE）损失比MSE损失在稳定性和异常值鲁棒性方面更优。实验上，我们比较了OCE-TS与五个基线模型——Autoformer、DLinear、iTransformer、TimeXer和TimeBridge，在七个公共时间序列数据集上的表现。使用MSE和平均绝对误差（MAE）作为评估指标，结果表明OCE-TS在所有情况下都优于基准模型。代码已公开在：https://github.com/Shi-hm/OCE-TS。
英文摘要：
Time series forecasting is an important task that involves analyzing temporal dependencies and underlying patterns (such as trends, cyclicality, and seasonality) in historical data to predict future values or trends. Current deep learning-based forecasting models primarily employ Mean Squared Error (MSE) loss functions for regression modeling. Despite enabling direct value prediction, this method offers no uncertainty estimation and exhibits poor outlier robustness. To address these limitations, we propose OCE-TS, a novel ordinal classification approach for time series forecasting that replaces MSE with Ordinal Cross-Entropy (OCE) loss, preserving prediction order while quantifying uncertainty through probability output. Specifically, OCE-TS begins by discretizing observed values into ordered intervals and deriving their probabilities via a parametric distribution as supervision signals. Using a simple linear model, we then predict probability distributions for each timestep. The OCE loss is computed between the cumulative distributions of predicted and ground-truth probabilities, explicitly preserving ordinal relationships among forecasted values. Through theoretical analysis using influence functions, we establish that cross-entropy (CE) loss exhibits superior stability and outlier robustness compared to MSE loss. Empirically, we compared OCE-TS with five baseline models-Autoformer, DLinear, iTransformer, TimeXer, and TimeBridge-on seven public time series datasets. Using MSE and Mean Absolute Error (MAE) as evaluation metrics, the results demonstrate that OCE-TS consistently outperforms benchmark models. The codeis publicly available at: https://github.com/Shi-hm/OCE-TS.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
