multi-temporal aggregation

This work addresses the limitations of existing black-box model ensembling approaches—namely, their reliance on model architecture and poor generalization. We propose Minimal Empirical Variance Aggregation (MEVA), a model-agnostic linear ensemble method that performs end-to-end optimization solely on model predictions. Its core innovation lies in replacing conventional error minimization with empirical variance minimization as the aggregation objective; we theoretically establish that this strategy yields superior statistical robustness under finite-sample regimes and unifies ensemble learning with general error estimation. MEVA requires no access to internal model parameters or gradients, making it compatible with diverse predictors—including machine learning models and numerical PDE solvers. Extensive experiments across data science and partial differential equation solving tasks demonstrate consistent improvements in both predictive accuracy and stability, validating MEVA’s generality and practical efficacy.

In time series forecasting, single models often lack robust generalization across diverse samples and suffer from model isolation. To address this, we propose TimeFuse—a novel framework for sample-level adaptive fusion of heterogeneous forecasting models. TimeFuse introduces a lightweight fusor network that extracts meta-features and learns differentiable, sample-specific fusion weights. It supports joint meta-training across multiple datasets and enables zero-shot cross-dataset transfer. Extensive experiments on both long-term and short-term forecasting tasks demonstrate that TimeFuse consistently outperforms state-of-the-art single-model baselines, delivering near-universal performance gains. It significantly reduces dependency on manual model selection and establishes a general-purpose, model-agnostic fusion paradigm for time series forecasting.

Real-world multivariate time series face three key challenges: complex inter-channel dependencies, asynchronous sampling (with varying periods), and pervasive missing values. Existing methods typically assume synchronous sampling and complete observations, limiting their applicability to real-world scenarios. This paper proposes ChannelTokenFormer—the first Transformer-based architecture unifying channel dependency modeling, asynchronous sampling handling, and missing-value imputation. Its core innovations include: (i) channel-adaptive tokenization, (ii) asynchronous timestamp encoding, (iii) missingness-aware attention, and (iv) adaptive masked reconstruction. Evaluated on three public imputation benchmarks and one industrial dataset, ChannelTokenFormer consistently outperforms state-of-the-art methods. Notably, it maintains over 92% relative prediction accuracy under high missingness (30%) and extreme asynchrony (5× sampling rate variance), demonstrating superior robustness and generalization capability.

This work addresses subdomain aggregation over time-series and image data, proposing the first unified modeling framework grounded in category theory. Methodologically, it formalizes classical aggregation operations—including summation, extremum computation, and sliding-window statistics—as bifunctors on double categories, thereby achieving functional abstraction of aggregation semantics across diverse data structures. Integrating functorial semantic modeling with Blelloch’s parallel scan algorithm, the framework derives novel aggregation operators with provably parallel implementations, substantially extending the applicability of the scan paradigm. Key contributions are: (1) the first functional aggregation framework supporting formal verification of parallelizability; (2) systematic definition and generation of previously unformalized subdomain aggregation patterns; and (3) a composable, extensible mathematical foundation for cross-modal data aggregation. The approach bridges abstract categorical semantics with practical parallel computation, enabling rigorous, scalable, and interoperable aggregation across heterogeneous data modalities.

Time-series ensemble forecasting faces a critical trade-off between predictive accuracy and computational cost. This paper systematically evaluates ten base models and eight ensemble strategies on the M5 and VN1 retail datasets, measuring performance in point forecasting (RMSE) and probabilistic forecasting (CRPS), alongside computational overhead. Methodologically, we analyze ensemble size scalability, propose an “efficiency-driven ensemble” paradigm, and assess downsampling-based retraining frequency reduction. Key contributions: (1) Ensembles of only two to three models achieve near-optimal accuracy; (2) The efficiency-driven paradigm reduces average computational cost by over 40% while retaining ≥95% of baseline accuracy; (3) Reducing retraining frequency cuts training overhead by up to 70%, with negligible impact on point forecasts and robust performance in probabilistic forecasting. Results confirm that ensembling consistently improves prediction—especially probabilistic calibration—but high accuracy typically incurs high cost. Our framework delivers a scalable, cost-effective ensemble strategy for resource-constrained deployment.

This work addresses regression prediction from heterogeneous, noisy sensor data in the absence of ground-truth labels by proposing the Neural Conjugate Aggregation Model (NCAM). NCAM integrates neural networks with conjugate Gaussian inference within a hierarchical Bayesian framework to unsupervisedly learn each sensor’s bias and reliability, enabling uncertainty decomposition and posterior aggregation for the target variable. To mitigate structural non-identifiability, the model incorporates sensor anchoring and variance regularization. Coupled with locally adaptive Monte Carlo conformal prediction, NCAM yields heteroscedastic prediction intervals that simultaneously offer Bayesian interpretability and finite-sample coverage guarantees. Experiments demonstrate that NCAM significantly outperforms baseline methods—including mean aggregation, probabilistic PCA, and Kalman filtering—on both synthetic and real-world air quality datasets, while providing well-calibrated uncertainty estimates.

This work addresses the often statistically unstable performance gains and unclear attribution in existing time series forecasting models. It proposes CombinationTS, a framework that decouples architectures into five orthogonal modules—input transformation, embedding, encoder, decoder, and output transformation—and quantifies each component’s contribution to both predictive performance (μ) and stability (σ) under a unified evaluation protocol. Through large-scale paired experiments and probabilistic assessment, the study uncovers the “identity paradox”: with effective embeddings, a parameter-free identity encoder can match or even surpass sophisticated backbone encoders. Furthermore, it demonstrates that input transformations incorporating structural priors yield greater benefits than merely increasing encoder complexity. This work establishes a principled baseline for architectural necessity, shifting model evaluation from holistic selection toward fine-grained, component-level attribution.

This study addresses the challenge of uncertainty quantification in aggregated time series forecasting, particularly for annual totals and year-over-year growth rates. It proposes a simulation-augmented multi-step split conformal prediction method (SA-MSCP), which generates future trajectories via block bootstrap resampling from cross-validated residuals and constructs calibrated prediction intervals using empirical quantiles. By innovatively integrating a simulation-augmentation mechanism into the multi-step split conformal prediction framework, the method significantly improves empirical coverage for both aggregate totals and their growth rates, yielding more reliable uncertainty estimates without compromising predictive accuracy.

This work investigates the interplay between interpolation and aggregation in regression tasks and its implications for learnability. By introducing the γ-graph dimension, the study characterizes the learnability boundary for a broad class of natural aggregation procedures and proposes a minimalist aggregation method that takes the median of three interpolating hypotheses. Theoretical analysis demonstrates that this median aggregation achieves optimal sample complexity among all finite interpolating aggregations and strictly outperforms standard interpolating learning. Moreover, the work reveals that certain hypothesis classes are learnable only via infinite or non-interpolating aggregations, thereby establishing fundamental limitations and optimality conditions for finite interpolating aggregation schemes.