[Paper Review] Probabilistic Time Series Forecasting with Structured Shape and Temporal Diversity

Vincent Le Guen, Nicolas Thome|arXiv (Cornell University)|Oct 14, 2020

Time Series Analysis and Forecasting8 references20 citations

TL;DR

This paper proposes STRIPE, a probabilistic time series forecasting framework that models structured shape and temporal diversity using differentiable, positive semi-definite determinantal point process (DPP) kernels. By decoupling quality and diversity objectives via an iterative sampling mechanism in a disentangled latent space, STRIPE generates sharp, diverse, and accurate forecasts that outperform state-of-the-art methods in both diversity and predictive quality on synthetic and real-world datasets.

ABSTRACT

Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE model for representing structured diversity based on shape and time features, ensuring both probable predictions while being sharp and accurate. STRIPE is agnostic to the forecasting model, and we equip it with a diversification mechanism relying on determinantal point processes (DPP). We introduce two DPP kernels for modeling diverse trajectories in terms of shape and time, which are both differentiable and proved to be positive semi-definite. To have an explicit control on the diversity structure, we also design an iterative sampling mechanism to disentangle shape and time representations in the latent space. Experiments carried out on synthetic datasets show that STRIPE significantly outperforms baseline methods for representing diversity, while maintaining accuracy of the forecasting model. We also highlight the relevance of the iterative sampling scheme and the importance to use different criteria for measuring quality and diversity. Finally, experiments on real datasets illustrate that STRIPE is able to outperform state-of-the-art probabilistic forecasting approaches in the best sample prediction.

Motivation & Objective

• To address the challenge of generating sharp, diverse, and accurate probabilistic forecasts for non-stationary time series.
• To introduce a structured diversity mechanism that explicitly controls shape and temporal variation in predicted trajectories.
• To decouple quality and diversity objectives in probabilistic forecasting to avoid trade-offs between predictive accuracy and diversity.
• To enable explicit control over diversity structure through disentangled latent representations using iterative sampling.
• To demonstrate that combining structured diversity with quality-aware training improves both diversity and mean forecast performance.

Proposed method

• Proposes two differentiable, positive semi-definite DPP kernels for modeling diversity in shape (via DTW) and time (via TDI) features of future trajectories.
• Introduces a disentangled latent space representation where shape and time components are explicitly separated via an iterative sampling mechanism.
• Employs a DPP-based diversity mechanism that ensures diverse, non-redundant predictions while maintaining high-quality forecasts.
• Uses a forecasting model agnostic to STRIPE, enabling integration with both deterministic and generative models.
• Applies a multi-objective training strategy with separate loss functions for quality (e.g., DILATE) and diversity (via DPP kernels).
• Employs a sampling scheme that iteratively refines predictions to disentangle shape and time representations in the latent space.

Experimental results

Research questions

• RQ1 Can structured diversity in shape and time be effectively modeled using differentiable, positive semi-definite DPP kernels in probabilistic forecasting?
• RQ2 Does decoupling quality and diversity objectives lead to better trade-offs between forecast accuracy and diversity?
• RQ3 Can iterative sampling in a disentangled latent space improve the disentanglement of shape and temporal features in predicted trajectories?
• RQ4 How does STRIPE compare to state-of-the-art models in terms of both mean forecast quality and best-sample diversity?
• RQ5 To what extent does the choice of diversity and quality metrics impact the performance of probabilistic forecasting models?

Key findings

• STRIPE S+T outperforms all baseline methods in the best-sample trajectory evaluation on both synthetic and real-world datasets, achieving lower MSE and DILATE losses.
• On the ETTh1 and ECL datasets, STRIPE S+T achieves the best performance in the best sample prediction, outperforming even the SOTA deterministic model N-BEATS.
• The iterative sampling mechanism successfully disentangles shape and time representations, enabling more structured and interpretable diversity in predictions.
• Experiments show that STRIPE maintains or slightly improves mean forecast quality while significantly increasing diversity, unlike models that trade off quality for diversity.
• The scatterplot analysis confirms that STRIPE S+T achieves a better balance between shape diversity (DTW) and temporal diversity (TDI) with consistently low DILATE loss, unlike models that increase diversity at the cost of quality.
• Ablation studies demonstrate that using distinct criteria for quality and diversity is crucial—models using the same metric for both suffer from performance degradation due to conflicting objectives.