Hierarchical time-series forecasting is essential for demand prediction across various industries. While machine learning models have obtained significant accuracy and scalability on such forecasting tasks, the interpretability of their predictions, informed by application, is still largely unexplored. To bridge this gap, we introduce a novel interpretability method for large hierarchical probabilistic time-series forecasting, adapting generic interpretability techniques while addressing challenges associated with hierarchical structures and uncertainty. Our approach offers valuable interpretative insights in response to real-world industrial supply chain scenarios, including 1) the significance of various time-series within the hierarchy and external variables at specific time points, 2) the impact of different variables on forecast uncertainty, and 3) explanations for forecast changes in response to modifications in the training dataset. To evaluate the explainability method, we generate semi-synthetic datasets based on real-world scenarios of explaining hierarchical demands for over ten thousand products at a large chemical company. The experiments showed that our explainability method successfully explained state-of-the-art industrial forecasting methods with significantly higher explainability accuracy. Furthermore, we provide multiple real-world case studies that show the efficacy of our approach in identifying important patterns and explanations that help stakeholders better understand the forecasts. Additionally, our method facilitates the identification of key drivers behind forecasted demand, enabling more informed decision-making and strategic planning. Our approach helps build trust and confidence among users, ultimately leading to better adoption and utilization of hierarchical forecasting models in practice.

Time-series foundation models (TSFMs) have demonstrated strong generalization capabilities across diverse datasets and tasks. However, existing foundation models are typically pre-trained to enhance performance on specific tasks and often struggle to generalize to unseen tasks without fine-tuning. To address this limitation, we propose augmenting TSFMs with In-Context Learning (ICL) capabilities, enabling them to perform test-time inference by dynamically adapting to input-output relationships provided within the context. Our framework, In-Context Time-series Pre-training (ICTP), restructures the original pre-training data to equip the backbone TSFM with ICL capabilities, enabling adaptation to unseen tasks. Experiments demonstrate that ICT improves the performance of state-of-the-art TSFMs by approximately 11.4% on unseen tasks without requiring fine-tuning.

Time-series forecasting (TSF) finds broad applications in real-world scenarios. Due to the dynamic nature of time-series data, it is crucial for TSF models to preserve out-of-distribution (OOD) generalization abilities, as training and test sets represent historical and future data respectively. In this paper, we aim to alleviate the inherent OOD problem in TSF via invariant learning. We identify fundamental challenges of invariant learning for TSF. First, the target variables in TSF may not be sufficiently determined by the input due to unobserved core variables in TSF, breaking the fundamental assumption of invariant learning. Second, time-series datasets lack adequate environment labels, while existing environmental inference methods are not suitable for TSF. To address these challenges, we propose FOIL, a model-agnostic framework that endows time-series forecasting for out-of-distribution generalization via invariant learning. Specifically, FOIL employs a novel surrogate loss to mitigate the impact of unobserved variables. Further, FOIL implements joint optimization by alternately inferring environments effectively with a multi-head network while preserving the temporal adjacency structure and learning invariant representations across inferred environments for OOD generalized TSF. Extensive experiments demonstrate that the proposed FOIL significantly and consistently improves the performance of various TSF models, achieving gains of up to 85%.

Hierarchical time-series forecasting (HTSF) is an important problem for many real-world business applications where the goal is to simultaneously forecast multiple time-series that are related to each other via a hierarchical relation. Recent works, however, do not address two important challenges that are typically observed in many demand forecasting applications at large companies. First, many time-series at lower levels of the hierarchy have high sparsity i.e., they have a significant number of zeros. Most HTSF methods do not address this varying sparsity across the hierarchy. Further, they do not scale well to the large size of the real-world hierarchy typically unseen in benchmarks used in literature. We resolve both these challenges by proposing HAILS, a novel probabilistic hierarchical model that enables accurate and calibrated probabilistic forecasts across the hierarchy by adaptively modeling sparse and dense time-series with different distributional assumptions and reconciling them to adhere to hierarchical constraints. We show the scalability and effectiveness of our methods by evaluating them against real-world demand forecasting datasets. We deploy HAILS at a large chemical manufacturing company for a product demand forecasting application with over ten thousand products and observe a significant 8.5% improvement in forecast accuracy and 23% better improvement for sparse time-series. The enhanced accuracy and scalability make HAILS a valuable tool for improved business planning and customer experience.

Large pre-trained models have been vital in recent advancements in domains like language and vision, making model training for individual downstream tasks more efficient and provide superior performance. However, tackling time-series analysis tasks usually involves designing and training a separate model from scratch leveraging training data and domain expertise specific to the task. We tackle a significant challenge for pre-training a foundational time-series model from multi-domain time-series datasets: extracting semantically useful tokenized inputs to the model across heterogeneous time-series from different domains. We propose Large Pre-trained Time-series Models (LPTM) that introduces a novel method of adaptive segmentation that automatically identifies optimal dataset-specific segmentation strategy during pre-training. This enables LPTM to perform similar to or better than domain-specific state-of-art model when fine-tuned to different downstream time-series analysis tasks and under zero-shot settings. LPTM achieves superior forecasting and time-series classification results taking up to 40% less data and 50% less training time compared to state-of-art baselines.

Time series data are ubiquitous across a wide range of real-world domains. Whilereal-world time series analysis (TSA) requires human experts to integrate numerical series data with multimodal domain-specific knowledge, most existing TSAmodels rely solely on numerical data, overlooking the significance of information beyond numerical series. This oversight is due to the untapped potentialof textual series data and the absence of a comprehensive, high-quality multimodal dataset. To overcome this obstacle, we introduce Time-MMD, the firstmulti-domain, multimodal time series dataset covering 9 primary data domains.Time-MMD ensures fine-grained modality alignment, eliminates data contamination, and provides high usability. Additionally, we develop MM-TSFlib, thefirst-cut multimodal time-series forecasting (TSF) library, seamlessly pipeliningmultimodal TSF evaluations based on Time-MMD for in-depth analyses. Extensiveexperiments conducted on Time-MMD through MM-TSFlib demonstrate significant performance enhancements by extending unimodal TSF to multimodality,evidenced by over 15% mean squared error reduction in general, and up to 40%in domains with rich textual data. More importantly, our datasets and libraryrevolutionize broader applications, impacts, research topics to advance TSA. Thedataset is available at https://github.com/AdityaLab/Time-MMD.

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have hierarchical relations. Previous works assume rigid consistency over the given hierarchies and do not adapt well to real-world data that show deviation from this assumption. Moreover, recent state-of-art neural probabilistic methods also impose hierarchical relations on point predictions and samples of the predictive distribution. This does not account for full forecast distributions being consistent with the hierarchy and leading to poorly calibrated forecasts. We close both these gaps and propose PROFHiT, a probabilistic hierarchical forecasting model that jointly models forecast distributions over the entire hierarchy. PROFHiT (1) uses a flexible probabilistic Bayesian approach and (2) introduces soft distributional consistency regularization that enables end-to-end learning of the entire forecast distribution leveraging information from the underlying hierarchy. This enables calibrated forecasts as well as adaptation to real-life data with varied hierarchical consistency. PROFHiT provides 41-88% better performance in accuracy and significantly better calibration over a wide range of dataset consistency. Furthermore, PROFHiT adapts to missing data and can provide reliable forecasts even if up to 10% of input time-series data is missing, whereas other methods' performance severely degrades by over 70%

Deep neural networks (DNNs) have achieved enormous success in a wide range of domains, such as computer vision, natural language processing and scientific areas. However, one key bottleneck of DNNs is that they are ignorant about the uncertainties in their predictions. They can produce wildly wrong predictions without realizing, and can even be confident about their mistakes. Such mistakes can cause misguided decisions-sometimes catastrophic in critical applications, ranging from self-driving cars to cyber security to automatic medical diagnosis. In this tutorial, we present recent advancements in uncertainty quantification for DNNs and their applications across various domains. We first provide an overview of the motivation behind uncertainty quantification, different sources of uncertainty, and evaluation metrics. Then, we delve into several representative uncertainty quantification methods for predictive models, including ensembles, Bayesian neural networks, conformal prediction, and others. We go on to discuss how uncertainty can be utilized for label-efficient learning, continual learning, robust decision-making, and experimental design. Furthermore, we showcase examples of uncertainty-aware DNNs in various domains, such as health, robotics, and scientific machine learning. Finally, we summarize open challenges and future directions in this area.

The recent COVID-19 pandemic has reinforced the importance of epidemic forecasting to equip decision makers in multiple domains, ranging from public health to economics. However, forecasting the epidemic progression remains a non-trivial task as the spread of diseases is subject to multiple confounding factors spanning human behavior, pathogen dynamics and environmental conditions, etc. Research interest has been fueled by the increased availability of rich data sources capturing previously unseen facets of the epidemic spread and initiatives from government public health and funding agencies like forecasting challenges and funding calls. This has resulted in recent works covering many aspects of epidemic forecasting. Data-centered solutions have specifically shown potential by leveraging non-traditional data sources as well as recent innovations in AI and machine learning. This tutorial will explore various data-driven methodological and practical advancements. First, we will enumerate epidemiological datasets and novel data streams capturing various factors like symptomatic online surveys, retail and commerce, mobility and genomics data. Next, we discuss methods and modeling paradigms with a focus on the recent data-driven statistical and deep-learning based methods as well as novel class of hybrid models that combine domain knowledge of mechanistic models with the effectiveness and flexibility of statistical approaches. We also discuss experiences and challenges that arise in real-world deployment of these forecasting systems including decision-making informed by forecasts. Finally, we highlight some open problems found across the forecasting pipeline.

Probabilistic time-series forecasting enables reliable decision making across many domains. Most forecasting problems have diverse sources of data containing multiple modalities and structures. Leveraging information from these data sources for accurate and well-calibrated forecasts is an important but challenging problem. Most previous works on multi-view time-series forecasting aggregate features from each data view by simple summation or concatenation and do not explicitly model uncertainty for each data view. We propose a general probabilistic multi-view forecasting framework CAMul, which can learn representations and uncertainty from diverse data sources. It integrates the information and uncertainty from each data view in a dynamic context-specific manner, assigning more importance to useful views to model a well-calibrated forecast distribution. We use CAMul for multiple domains with varied sources and modalities and show that CAMul outperforms other state-of-art probabilistic forecasting models by over 25% in accuracy and calibration.

Accurate and trustworthy epidemic forecasting is an important problem for public health planning and disease mitigation. Most existing epidemic forecasting models disregard uncertainty quantification, resulting in mis-calibrated predictions. Recent works in deep neural models for uncertainty-aware time-series forecasting also have several limitations; e.g., it is difficult to specify proper priors in Bayesian NNs, while methods like deep ensembling can be computationally expensive. In this paper, we propose to use neural functional processes to fill this gap. We model epidemic time-series with a probabilistic generative process and propose a functional neural process model called EpiFNP, which directly models the probability distribution of the forecast value in a non-parametric way. In EpiFNP, we use a dynamic stochastic correlation graph to model the correlations between sequences, and design different stochastic latent variables to capture functional uncertainty from different perspectives. Our experiments in a real-time flu forecasting setting show that EpiFNP significantly outperforms state-of-the-art models in both accuracy and calibration metrics, up to 2.5x in accuracy and 2.4x in calibration. Additionally, as EpiFNP learns the relations between the current season and similar patterns of historical seasons, it enables interpretable forecasts. Beyond epidemic forecasting, EpiFNP can be of independent interest for advancing uncertainty quantification in deep sequential models for predictive analytics.