Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting

Joint probabilistic modeling is essential for forecasting irregular multivariate time series (IMTS) to accurately quantify uncertainty. Existing approaches often struggle to balance model expressivity with consistent marginalization, frequently leading to unreliable or contradictory forecasts. To address this, we propose CircuITS, a novel architecture for probabilistic IMTS forecasting based on sum-product networks (SPNs). Our model is flexible in capturing intricate dependencies between time series channels while structurally guaranteeing valid joint distributions. Experiments on five real-world datasets demonstrate that CircuITS achieves superior joint and marginal density estimation compared to state-of-the-art baselines.

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 $54.7\%$ in forecasting and $15.8\%$ in classification across diverse datasets and backbone architectures. Code is available at: https://github.com/Meaningfull9502/QuITE.

Time series foundation models (TSFMs) have recently delivered impressive zero-shot performance across diverse forecasting tasks. However, real-world decision-making frequently relies on 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 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 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 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 $30$B observations that retains the native sampling sparsity of its sources. Experiments on three IMTS benchmarks and a standard regular-MTS benchmark show that our model achieves state-of-the-art zero-shot performance on IMTS and remains competitive when transferred to regular forecasting.