Abstract
Irregular multivariate time series forecasting is critical in many real-world applications, where time series are irregularly sampled and exhibit dynamically evolving missingness patterns. Although existing methods perform well in offline settings, they often suffer from significant performance degradation when deployed online due to dynamic shifts in data distribution. Maintaining forecasting capability in such dynamic scenarios typically necessitates online adaptation techniques. Since irregular sampling fundamentally undermines temporal continuity and periodicity, we cannot leverage these widely studied characteristics from regular MTS for online learning. To this end, we study the problem of online IMTS forecasting and propose Under-Cali, an uncertainty-driven dual-expert calibration framework consisting of three core components: an uncertainty estimator, a dual-expert calibration module, and an adaptive routing module. We design an uncertainty estimator that serves as the core control signal to jointly manage inference and adaptation processes. In our framework, the uncertainty estimator first assesses uncertainty for each incoming batch. The adaptive routing module then directs samples with high uncertainty to the unreliable expert for calibration, while low uncertainty samples remain with the reliable expert. Subsequently, the system updates the reliable expert and the uncertainty estimator using well-calibrated reliable samples, and updates the unreliable expert with challenging samples, enabling stable and efficient online learning. Under-Cali keeps the source forecasting model frozen and performs adaptation only through a lightweight, model-agnostic calibration module, enabling efficient adaptation. Extensive experiments on IMTS benchmarks demonstrate consistent improvements with low computational cost. Our code is available at https://github.com/HaonanWen/Under-Cali.
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Sep 19, 2026cs.LG
Time series foundation models (TSFMs) have recently delivered impressive zero-shot performance across diverse forecasting tasks. However, real-world decision-making frequently relies on \emph{irregular multivariate time series} (IMTS), where inconsistent inter-observation intervals and asynchronous sampling across variables coexist with informative missingness. Existing TSFMs handle such inputs either through imputation that injects spurious values or through index-based positional encodings that ignore continuous time. There is still a gap in the foundation model that follows the original IMTS patterns. In this paper, we propose a hybrid attention model that learns a unified time-aware patch representation for IMTS forecasting. We first design a \emph{time-aware patch encoding} that maps a variable number of intra-patch timestamps into a fixed-size embedding, producing a uniform format for irregular patches without resorting to imputation. We then introduce a \emph{time bias attention} mechanism that calibrates inter-patch temporal misalignment and asynchronous cross-channel dependencies as auxiliary attention offset. Finally, on top of a decoder-only Transformer backbone, we adopt a \emph{hybrid causal mask} that preserves a bidirectional full view over the historical context while keeping the forecast horizon strictly autoregressive. To support large-scale pretraining under irregular settings, we also curate VersaTSA, an archive of
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May 27, 2026cs.LG
Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven Multivariate Time Series (MTS) models, or (ii) map IMTS onto regular temporal grids through interpolation, which may distort temporal dynamics by introducing artificial values. To address these limitations, we propose a new input-embedding-based approach. We identify that the key bottleneck lies not in the backbone architecture, but in conventional embedding layers that assume uniform sampling. In this work, we introduce QuITE (Query-Based Irregular Time Series Embedding), a simple yet effective plug-and-play embedding module for IMTS. QuITE employs learnable query tokens to aggregate irregular observations through a single self-attention layer, directly producing backbone-compatible latent representations without artificial value generation or architectural modification. Extensive experiments on real-world benchmarks show that QuITE consistently improves MTS models, yielding average relative gains of up to
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