Time series forecasts of different temporal granularity are widely used in real-world applications, e.g., sales prediction in days and weeks for making different inventory plans. However, these tasks are usually solved separately without ensuring coherence, which is crucial for aligning downstream decisions. Previous works mainly focus on ensuring coherence with some straightforward methods, e.g., aggregation from the forecasts of fine granularity to the coarse ones, and allocation from the coarse granularity to the fine ones. These methods merely take the temporal hierarchical structure to maintain coherence without improving the forecasting accuracy. In this paper, we propose a novel granularity message-passing mechanism (GMP) that leverages temporal hierarchy information to improve forecasting performance and also utilizes an adaptive reconciliation (AR) strategy to maintain coherence without performance loss. Furthermore, we introduce an optimization module to achieve task-based targets while adhering to more real-world constraints. Experiments on real-world datasets demonstrate that our framework (GMP-AR) achieves superior performances on temporal hierarchical forecasting tasks compared to state-of-the-art methods. In addition, our framework has been successfully applied to a real-world task of payment traffic management in Alipay by integrating with the task-based optimization module.

Accurate workload forecasting is critical for efficient resource management in cloud computing systems, enabling effective scheduling and autoscaling. Despite recent advances with transformer-based forecasting models, challenges remain due to the non-stationary, nonlinear characteristics of workload time series and the long-term dependencies. In particular, inconsistent performance between long-term history and near-term forecasts hinders long-range predictions. This paper proposes a novel framework leveraging self-supervised multiscale representation learning to capture both long-term and near-term workload patterns. The long-term history is encoded through multiscale representations while the near-term observations are modeled via temporal flow fusion. These representations of different scales are fused using an attention mechanism and characterized with normalizing flows to handle non-Gaussian/non-linear distributions of time series. Extensive experiments on 9 benchmarks demonstrate superiority over existing methods.

Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shift. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure which measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates that CIL learns features that satisfy the invariant constraint with infinite samples. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS) forecasting includes two sub-tasks, i.e., forecasting and reconciliation. In the previous works, hierarchical information is only integrated in the reconciliation step to maintain coherency, but not in forecasting step for accuracy improvement. In this paper, we propose two novel tree-based feature integration mechanisms, i.e., top-down convolution and bottom-up attention to leverage the information of the hierarchical structure to improve the forecasting performance. Moreover, unlike most previous reconciliation methods which either rely on strong assumptions or focus on coherent constraints only, we utilize deep neural optimization networks, which not only achieve coherency without any assumptions, but also allow more flexible and realistic constraints to achieve task-based targets, e.g., lower under-estimation penalty and meaningful decision-making loss to facilitate the subsequent downstream tasks. Experiments on real-world datasets demonstrate that our tree-based feature integration mechanism achieves superior performances on hierarchical forecasting tasks compared to the state-of-the-art methods, and our neural optimization networks can be applied to real-world tasks effectively without any additional effort under coherence and task-based constraints.

State space model (SSM) provides a general and flexible forecasting framework for time series. Conventional SSM with fixed-order Markovian assumption often falls short in handling the long-range temporal dependencies and/or highly non-linear correlation in time-series data, which is crucial for accurate forecasting. To this extend, we present External Memory Augmented State Space Model (EMSSM) within the sequential Monte Carlo (SMC) framework. Unlike the common fixed-order Markovian SSM, our model features an external memory system, in which we store informative latent state experience, whereby to create ``memoryful" latent dynamics modeling complex long-term dependencies. Moreover, conditional normalizing flows are incorporated in our emission model, enabling the adaptation to a broad class of underlying data distributions. We further propose a Monte Carlo Objective that employs an efficient variational proposal distribution, which fuses the filtering and the dynamic prior information, to approximate the posterior state with proper particles. Our results demonstrate the competitiveness of forecasting performance of our proposed model comparing with other state-of-the-art SSMs.