DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment

TL;DR

DistDF introduces a novel joint-distribution Wasserstein discrepancy for time-series forecasting, improving alignment between forecast and label distributions and enhancing model performance.

Contribution

It proposes a new discrepancy measure for better distribution alignment in time-series forecasting, addressing biases in traditional likelihood-based methods.

Findings

DistDF improves forecasting accuracy across various models.

The proposed method achieves state-of-the-art performance.

The discrepancy measure is tractable and compatible with gradient-based optimization.

Abstract

Training time-series forecasting models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach resorts to minimizing the conditional negative log-likelihood, typically estimated by the mean squared error. However, this estimation proves biased when the label sequence exhibits autocorrelation. In this paper, we propose DistDF, which achieves alignment by minimizing a distributional discrepancy between the conditional distributions of forecast and label sequences. Since such conditional discrepancies are difficult to estimate from finite time-series observations, we introduce a joint-distribution Wasserstein discrepancy for time-series forecasting, which provably upper bounds the conditional discrepancy of interest. The proposed discrepancy is tractable, differentiable, and readily compatible with gradient-based optimization. Extensive experiments show that DistDF improves diverse forecasting models and achieves leading performance. Code is available at https://anonymous.4open.science/r/DistDF-F66B.