A Decomposition-based State Space Model for Multivariate Time-Series Forecasting

Multivariate time series (MTS) forecasting is crucial for decision-making in domains such as weather, energy, and finance. It remains challenging because real-world sequences intertwine slow trends, multi-rate seasonalities, and irregular residuals. Existing methods often rely on rigid, hand-crafted decompositions or generic end-to-end architectures that entangle components and underuse structure shared across variables. To address these limitations, we propose DecompSSM, an end-to-end decomposition framework using three parallel deep state space model branches to capture trend, seasonal, and residual components. The model features adaptive temporal scales via an input-dependent predictor, a refinement module for shared cross-variable context, and an auxiliary loss that enforces reconstruction and orthogonality. Across standard benchmarks (ECL, Weather, ETTm2, and PEMS04), DecompSSM outperformed strong baselines, indicating the effectiveness of combining component-wise deep state space models and global context refinement.

Large-scale Score-based Variational Posterior Inference for Bayesian Deep Neural Networks

Bayesian (deep) neural networks (BNN) are often more attractive than the mainstream point-estimate vanilla deep learning in various aspects including uncertainty quantification, robustness to noise, resistance to overfitting, and more. The variational inference (VI) is one of the most widely adopted approximate inference methods. Whereas the ELBO-based variational free energy method is a dominant choice in the literature, in this paper we introduce a score-based alternative for BNN variational inference. Although there have been quite a few score-based variational inference methods proposed in the community, most are not adequate for large-scale BNNs for various computational and technical reasons. We propose a novel scalable VI method where the learning objective combines the score matching loss and the proximal penalty term in iterations, which helps our method avoid the reparametrized sampling, and allows for noisy unbiased mini-batch scores through stochastic gradients. This in turn makes our method scalable to large-scale neural networks including Vision Transformers, and allows for richer variational density families. On several benchmarks including visual recognition and time-series forecasting with large-scale deep networks, we empirically show the effectiveness of our approach.

HealthMamba: An Uncertainty-aware Spatiotemporal Graph State Space Model for Effective and Reliable Healthcare Facility Visit Prediction

Healthcare facility visit prediction is essential for optimizing healthcare resource allocation and informing public health policy. Despite advanced machine learning methods being employed for better prediction performance, existing works usually formulate this task as a time-series forecasting problem without considering the intrinsic spatial dependencies of different types of healthcare facilities, and they also fail to provide reliable predictions under abnormal situations such as public emergencies. To advance existing research, we propose HealthMamba, an uncertainty-aware spatiotemporal framework for accurate and reliable healthcare facility visit prediction. HealthMamba comprises three key components: (i) a Unified Spatiotemporal Context Encoder that fuses heterogeneous static and dynamic information, (ii) a novel Graph State Space Model called GraphMamba for hierarchical spatiotemporal modeling, and (iii) a comprehensive uncertainty quantification module integrating three uncertainty quantification mechanisms for reliable prediction. We evaluate HealthMamba on four large-scale real-world datasets from California, New York, Texas, and Florida. Results show HealthMamba achieves around 6.0% improvement in prediction accuracy and 3.5% improvement in uncertainty quantification over state-of-the-art baselines.

Day-Ahead Electricity Price Forecasting for Volatile Markets Using Foundation Models with Regularization Strategy

Electricity price forecasting (EPF) is essential for energy markets stakeholders (e.g. grid operators, energy traders, policymakers) but remains challenging due to the inherent volatility and nonlinearity of price signals. Traditional statistical and deep learning (DL) models often struggle to capture complex temporal dependencies and integrate heterogeneous data effectively. While time series foundation models (TSFMs) have shown strong performance in general time series forecasting tasks, such as traffic forecasting and weather forecasting. However, their effectiveness in day-ahead EPF, particularly in volatile markets, remains underexplored. This paper presents a spike regularization strategy and evaluates a wide range of TSFMs, including Tiny Time Mixers (TTMs), MOIRAI, MOMENT, and TimesFM, against traditional statistical and DL models such as Autoregressive Integrated Moving Average (ARIMA), Long-short Term Memory (LSTM), and Convolutional Neural Network - LSTM (CNN-LSTM) using half-hourly wholesale market data with volatile trends in Singapore. Exogenous factors (e.g. weather and calendar variables) are also incorporated into models where applicable. Results demonstrate that TSFMs consistently outperform traditional approaches, achieving up to 37.4% improvement in MAPE across various evaluation settings. The findings offer practical guidance for improving forecast accuracy and decision-making in volatile electricity markets.

Let Experts Feel Uncertainty: A Multi-Expert Label Distribution Approach to Probabilistic Time Series Forecasting

Time series forecasting in real-world applications requires both high predictive accuracy and interpretable uncertainty quantification. Traditional point prediction methods often fail to capture the inherent uncertainty in time series data, while existing probabilistic approaches struggle to balance computational efficiency with interpretability. We propose a novel Multi-Expert Learning Distributional Labels (LDL) framework that addresses these challenges through mixture-of-experts architectures with distributional learning capabilities. Our approach introduces two complementary methods: (1) Multi-Expert LDL, which employs multiple experts with different learned parameters to capture diverse temporal patterns, and (2) Pattern-Aware LDL-MoE, which explicitly decomposes time series into interpretable components (trend, seasonality, changepoints, volatility) through specialized sub-experts. Both frameworks extend traditional point prediction to distributional learning, enabling rich uncertainty quantification through Maximum Mean Discrepancy (MMD). We evaluate our methods on aggregated sales data derived from the M5 dataset, demonstrating superior performance compared to baseline approaches. The continuous Multi-Expert LDL achieves the best overall performance, while the Pattern-Aware LDL-MoE provides enhanced interpretability through component-wise analysis. Our frameworks successfully balance predictive accuracy with interpretability, making them suitable for real-world forecasting applications where both performance and actionable insights are crucial.

Bounded-Abstention Multi-horizon Time-series Forecasting

Multi-horizon time-series forecasting involves simultaneously making predictions for a consecutive sequence of subsequent time steps. This task arises in many application domains, such as healthcare and finance, where mispredictions can have a high cost and reduce trust. The learning with abstention framework tackles these problems by allowing a model to abstain from offering a prediction when it is at an elevated risk of making a misprediction. Unfortunately, existing abstention strategies are ill-suited for the multi-horizon setting: they target problems where a model offers a single prediction for each instance. Hence, they ignore the structured and correlated nature of the predictions offered by a multi-horizon forecaster. We formalize the problem of learning with abstention for multi-horizon forecasting setting and show that its structured nature admits a richer set of abstention problems. Concretely, we propose three natural notions of how a model could abstain for multi-horizon forecasting. We theoretically analyze each problem to derive the optimal abstention strategy and propose an algorithm that implements it. Extensive evaluation on 24 datasets shows that our proposed algorithms significantly outperforms existing baselines.

Assessing Electricity Demand Forecasting with Exogenous Data in Time Series Foundation Models

Time-series foundation models have emerged as a new paradigm for forecasting, yet their ability to effectively leverage exogenous features -- critical for electricity demand forecasting -- remains unclear. This paper empirically evaluates foundation models capable of modeling cross-channel correlations against a baseline LSTM with reversible instance normalization across Singaporean and Australian electricity markets at hourly and daily granularities. We systematically assess MOIRAI, MOMENT, TinyTimeMixers, ChronosX, and Chronos-2 under three feature configurations: all features, selected features, and target-only. Our findings reveal highly variable effectiveness: while Chronos-2 achieves the best performance among foundation models (in zero-shot settings), the simple baseline frequently outperforms all foundation models in Singapore's stable climate, particularly for short-term horizons. Model architecture proves critical, with synergistic architectural implementations (TTM's channel-mixing, Chronos-2's grouped attention) consistently leveraging exogenous features, while other approaches show inconsistent benefits. Geographic context emerges as equally important, with foundation models demonstrating advantages primarily in variable climates. These results challenge assumptions about universal foundation model superiority and highlight the need for domain-specific models, specifically in the energy domain.

CoGenCast: A Coupled Autoregressive-Flow Generative Framework for Time Series Forecasting

Time series forecasting can be viewed as a generative problem that requires both semantic understanding over contextual conditions and stochastic modeling of continuous temporal dynamics. Existing approaches typically rely on either autoregressive large language models (LLMs) for semantic context modeling or diffusion-like models for continuous probabilistic generation. However, neither method alone can adequately model both aspects simultaneously. In this work, we propose CoGenCast, a hybrid generative framework that couples pre-trained LLMs with flow-matching mechanism for effective time series forecasting. Specifically, we reconfigure pre-trained decoder-only LLMs into a native forecasting encoder-decoder backbone by modifying only the attention topology, enabling bidirectional context encoding and causal representation generation. Building on this, a flow-matching mechanism is further integrated to model temporal evolution, capturing continuous stochastic dynamics conditioned on the autoregressively generated representation. Notably, CoGenCast naturally supports multimodal forecasting and cross-domain unified training. Extensive experiments on multiple benchmarks show that CoGenCast consistently outperforms previous compared baselines. Code is available at https://github.com/liuyaguo/_CoGenCast.

Pruning for Generalization: A Transfer-Oriented Spatiotemporal Graph Framework

Multivariate time series forecasting in graph-structured domains is critical for real-world applications, yet existing spatiotemporal models often suffer from performance degradation under data scarcity and cross-domain shifts. We address these challenges through the lens of structure-aware context selection. We propose TL-GPSTGN, a transfer-oriented spatiotemporal framework that enhances sample efficiency and out-of-distribution generalization by selectively pruning non-optimized graph context. Specifically, our method employs information-theoretic and correlation-based criteria to extract structurally informative subgraphs and features, resulting in a compact, semantically grounded representation. This optimized context is subsequently integrated into a spatiotemporal convolutional architecture to capture complex multivariate dynamics. Evaluations on large-scale traffic benchmarks demonstrate that TL-GPSTGN consistently outperforms baselines in low-data transfer scenarios. Our findings suggest that explicit context pruning serves as a powerful inductive bias for improving the robustness of graph-based forecasting models.

Geographically-aware Transformer-based Traffic Forecasting for Urban Motorway Digital Twins

The operational effectiveness of digital-twin technology in motorway traffic management depends on the availability of a continuous flow of high-resolution real-time traffic data. To function as a proactive decision-making support layer within traffic management, a digital twin must also incorporate predicted traffic conditions in addition to real-time observations. Due to the spatio-temporal complexity and the time-variant, non-linear nature of traffic dynamics, predicting motorway traffic remains a difficult problem. Sequence-based deep-learning models offer clear advantages over classical machine learning and statistical models in capturing long-range, temporal dependencies in time-series traffic data, yet limitations in forecasting accuracy and model complexity point to the need for further improvements. To improve motorway traffic forecasting, this paper introduces a Geographically-aware Transformer-based Traffic Forecasting GATTF model, which exploits the geographical relationships between distributed sensors using their mutual information (MI). The model has been evaluated using real-time data from the Geneva motorway network in Switzerland and results confirm that incorporating geographical awareness through MI enhances the accuracy of GATTF forecasting compared to a standard Transformer, without increasing model complexity.