Towards Accurate and Interpretable Time-series Forecasting: A Polynomial Learning Approach

As forecasts increasingly drive decisions in fields such as energy, transportation, and healthcare, understanding the historical data behind these predictions has become as crucial as the predictions themselves. Although existing interpretable-by-design forecasters reveal their internal structures, they offer no guarantee that these structures faithfully reflect the underlying evidence driving the predictions. In contrast, while faithfulness-oriented methods explicitly verify model behavior, they are almost exclusively designed for post-hoc classification tasks. To bridge this gap, we propose IB-Forecast, an inherently interpretable multivariate time-series forecasting framework. It decomposes forecasting into a learned periodic component and a residual component computed with explainable masks over input tokens. With a budget-constrained information bottleneck, end-to-end optimization enables users to directly control explanation sparsity. With a rigorous faithfulness evaluation protocol, extensive experiments demonstrate that IB-Forecast matches the forecasting error of leading black-box models while providing faithful explanations at no additional inference cost. Furthermore, under a matched sparsity budget, these native explanations consistently surpass gradient-based, occlusion-based, and optimization-based baselines across all evaluated datasets. Ultimately, whereas the native explanations of existing interpretable forecasters exhibit poor faithfulness, IB-Forecast guarantees high explanation fidelity, requiring only 14-20% of the observations to deliver low-error predictions.

Time series forecasting, which predicts future values from past observations, plays a central role in many domains and has driven the development of highly accurate neural network models. However, the complexity of these models often limits human understanding of the rationale behind their predictions. We propose PatchDecomp, a neural network-based time series forecasting method that achieves both high accuracy and interpretability. PatchDecomp divides input time series into subsequences (patches) and generates predictions by aggregating the contributions of each patch. This enables clear attribution of each patch, including those from exogenous variables, to the final prediction. Experiments on multiple benchmark datasets demonstrate that PatchDecomp provides predictive performance comparable to recent forecasting methods. Furthermore, we show that the model's explanations not only influence predicted values quantitatively but also offer qualitative interpretability through visualization of patch-wise contributions.

State-of-the-art multivariate time-series forecasters can model complex temporal and cross-variable dependencies, yet their opaque representations provide limited insight into why a particular forecast is produced. This lack of transparency restricts their use in settings where practitioners must understand and assess the factors underlying a prediction. We introduce ConceptTS, an interpretable forecasting framework that organizes its predictions around named, human-readable concepts. ConceptTS uses a large language model to propose task-relevant concepts and generate executable labeling rules, translating the language model's domain knowledge into direct supervision without costly manual concept annotation. The proposed concepts are organized into three complementary bottlenecks that describe the historical context, local forecast intervals, and the full forecast horizon. A shared decoder combines representations derived from their predicted activations to construct the forecast, making the model's decision process explicit and supporting direct concept-level interventions. Experiments on the Beijing Multi-Site Air Quality dataset show that ConceptTS achieves accuracy competitive with strong black-box baselines while producing semantically meaningful concept activations.