DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment
This addresses a fundamental issue in time-series forecasting for applications requiring accurate probabilistic predictions, though it is an incremental advance over existing distribution alignment methods.
The paper tackles the problem of biased conditional distribution alignment in time-series forecasting due to label autocorrelation by proposing DistDF, which uses a joint-distribution Wasserstein discrepancy to upper bound and minimize this discrepancy, resulting in state-of-the-art performance improvements across diverse models.
Training time-series forecast models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach resorts to minimize the conditional negative log-likelihood of the label sequence, typically estimated using the mean squared error. However, this estimation proves to be biased in the presence of label autocorrelation. In this paper, we propose DistDF, which achieves alignment by alternatively minimizing a discrepancy between the conditional forecast and label distributions. Because conditional discrepancies are difficult to estimate from finite time-series observations, we introduce a newly proposed joint-distribution Wasserstein discrepancy for time-series forecasting, which provably upper bounds the conditional discrepancy of interest. This discrepancy admits tractable, differentiable estimation from empirical samples and integrates seamlessly with gradient-based training. Extensive experiments show that DistDF improves the performance diverse forecast models and achieves the state-of-the-art forecasting performance. Code is available at https://anonymous.4open.science/r/DistDF-F66B.