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Deep Learning · Sequential Models, Time series

Xiaodan Chen, Xiucheng Li, Bo Liu, Zhijun Li

Multivariate time series forecasting plays an important role in various applications ranging from meteorology study, traffic management to economics planning. In the past decades, many efforts have been made toward accurate and reliable forecasting methods development under the assumption of intact input data. However, the time series data from real-world scenarios is often partially observed due to device malfunction or costly data acquisition, which can seriously impede the performance of the existing approaches. A naive employment of imputation methods unavoidably involves error accumulation and leads to suboptimal solutions. Motivated by this, we propose a Biased Temporal Convolution Graph Network that jointly captures the temporal dependencies and spatial structure. In particular, we inject bias into the two carefully developed modules, the Multi-Scale Instance PartialTCN and Biased GCN, to account for missing patterns. The experimental results show that our proposed model is able to achieve up to $9.93$\% improvements over the existing methods on five real-world benchmark datasets. Our code is available at: https://github.com/chenxiaodanhit/BiTGraph.

Deep Learning · Sequential Models, Time series

Seunghan Lee, Taeyoung Park, Kibok Lee

Contrastive learning has shown to be effective to learn representations from time series in a self-supervised way.However, contrasting similar time series instances or values from adjacent timestamps within a time series leads to ignore their inherent correlations, which results in deteriorating the quality of learned representations.To address this issue, we propose \textit{SoftCLT}, a simple yet effective soft contrastive learning strategy for time series.This is achieved by introducing instance-wise and temporal contrastive loss with soft assignments ranging from zero to one.Specifically, we define soft assignments for 1) instance-wise contrastive loss by distance between time series on the data space, warping and 2) temporal contrastive loss by the difference of timestamps.SoftCLT is a plug-and-play method for time series contrastive learning that improves the quality of learned representations without bells and whistles.In experiments, we demonstrate that SoftCLT consistently improves the performance in various downstream tasks including classification, semi-supervised learning, transfer learning, and anomaly detection, showing state-of-the-art performance.Code is available at this repository: https://github.com/seunghan96/softclt.

Deep Learning · Sequential Models, Time series

Seunghan Lee, Taeyoung Park, Kibok Lee

Masked time series modeling has recently gained much attention as a self-supervised representation learning strategy for time series.Inspired by masked image modeling in computer vision, recent works first patchify and partially mask out time series, and then train Transformers to capture the dependencies between patches by predicting masked patches from unmasked patches.However, we argue that capturing such patch dependencies might not be an optimal strategy for time series representation learning;rather, learning to embed patches independently results in better time series representations.Specifically, we propose to use 1) the simple patch reconstruction task, which autoencode each patch without looking at other patches, and 2) the simple patch-wise MLP that embeds each patch independently.In addition, we introduce complementary contrastive learning to hierarchically capture adjacent time series information efficiently.Our proposed method improves time series forecasting and classification performance compared to state-of-the-art Transformer-based models, while it is more efficient in terms of the number of parameters and training time.Code is available at this repository: https://github.com/seunghan96/pits.

Deep Learning · Sequential Models, Time series

Arjun Ashok, Étienne Marcotte, Valentina Zantedeschi, Nicolas Chapados, Alexandre Drouin

We introduce a new model for multivariate probabilistic time series prediction, designed to flexibly address a range of tasks including forecasting, interpolation, and their combinations. Building on copula theory, we propose a simplified objective for the recently-introduced transformer-based attentional copulas (TACTiS), wherein the number of distributional parameters now scales linearly with the number of variables instead of factorially. The new objective requires the introduction of a training curriculum, which goes hand-in-hand with necessary changes to the original architecture. We show that the resulting model has significantly better training dynamics and achieves state-of-the-art performance across diverse real-world forecasting tasks, while maintaining the flexibility of prior work, such as seamless handling of unaligned and unevenly-sampled time series. Code is made available at https://github.com/ServiceNow/TACTiS.

Deep Learning · Sequential Models, Time series

Siqiao Xue, Xiaoming Shi, Zhixuan Chu, Yan Wang, Hongyan Hao, Fan Zhou, caigao jiang, Chen Pan, James Zhang, Qingsong Wen 等

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts. The code and data are available at \url{https://github.com/ant-research/EasyTemporalPointProcess}.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Joseph Early, Gavin Cheung, Kurt Cutajar, Hanting Xie, Jas Kandola, Niall Twomey

Conventional Time Series Classification (TSC) methods are often black boxes that obscure inherent interpretation of their decision-making processes. In this work, we leverage Multiple Instance Learning (MIL) to overcome this issue, and propose a new framework called MILLET: Multiple Instance Learning for Locally Explainable Time series classification. We apply MILLET to existing deep learning TSC models and show how they become inherently interpretable without compromising (and in some cases, even improving) predictive performance. We evaluate MILLET on 85 UCR TSC datasets and also present a novel synthetic dataset that is specially designed to facilitate interpretability evaluation. On these datasets, we show MILLET produces sparse explanations quickly that are of higher quality than other well-known interpretability methods. To the best of our knowledge, our work with MILLET is the first to develop general MIL methods for TSC and apply them to an extensive variety of domains.

Deep Learning · Sequential Models, Time series

Joonhun Lee, Myeongho Jeon, Myungjoo Kang, Kyunghyun Park

We propose Feature-aligned N-BEATS as a domain-generalized time series forecasting model. It is a nontrivial extension of N-BEATS with doubly residual stacking principle (Oreshkin et al. [45]) into a representation learning framework. In particular, it revolves around marginal feature probability measures induced by the intricate composition of residual and feature extracting operators of N-BEATS in each stack and aligns them stack-wise via an approximate of an optimal transport distance referred to as the Sinkhorn divergence. The training loss consists of an empirical risk minimization from multiple source domains, i.e., forecasting loss, and an alignment loss calculated with the Sinkhorn divergence, which allows the model to learn invariant features stack-wise across multiple source data sequences while retaining N-BEATS’s interpretable design and forecasting power. Comprehensive experimental evaluations with ablation studies are provided and the corresponding results demonstrate the proposed model’s forecasting and generalization capabilities.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Lifan Zhao, Yanyan Shen

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.4% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

Applications · Time Series

Xuan Zhang, Jacob Helwig, Yuchao Lin, Yaochen Xie, Cong Fu, Stephan Wojtowytsch, Shuiwang Ji

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model’s performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Miscellaneous Aspects of Machine Learning · Everything Else

Haowei Lin, Yijia Shao, Weinan Qian, Ningxin Pan, Yiduo Guo, Bing Liu

Class incremental learning (CIL) is a challenging setting of continual learning, which learns a series of tasks sequentially. Each task consists of a set of unique classes. The key feature of CIL is that no task identifier (or task-id) is provided at test time. Predicting the task-id for each test sample is a challenging problem. An emerging theory-guided approach (called TIL+OOD) is to train a task-specific model for each task in a shared network for all tasks based on a task-incremental learning (TIL) method to deal with catastrophic forgetting. The model for each task is an out-of-distribution (OOD) detector rather than a conventional classifier. The OOD detector can perform both within-task (in-distribution (IND)) class prediction and OOD detection. The OOD detection capability is the key to task-id prediction during inference. However, this paper argues that using a traditional OOD detector for task-id prediction is sub-optimal because additional information (e.g., the replay data and the learned tasks) available in CIL can be exploited to design a better and principled method for task-id prediction. We call the new method TPL (Task-id Prediction based on Likelihood Ratio). TPL markedly outperforms strong CIL baselines and has negligible catastrophic forgetting. The code of TPL is publicly available at https://github.com/linhaowei1/TPL.

Yu-Hsuan Wu, Jerry Hu, Weijian Li, Bo-Yu Chen, Han Liu

We present **STanHop-Net** (**S**parse **Tan**dem **Hop**field **Net**work) for multivariate time series prediction with memory-enhanced capabilities. At the heart of our approach is **STanHop**, a novel Hopfield-based neural network block, which sparsely learns and stores both temporal and cross-series representations in a data-dependent fashion. In essence, STanHop sequentially learns temporal representation and cross-series representation using two tandem sparse Hopfield layers. Additionally, STanHop incorporates two external memory modules: **Plug-and-Play** and **Tune-and-Play** for train-less and task-aware memory enhancements, respectively. They allow StanHop-Net to swiftly respond to sudden events. Methodologically, we construct the STanHop-Net by stacking STanHop blocks in a hierarchical fashion, enabling multi-resolution feature extraction with resolution-specific sparsity. Theoretically, we introduce a unified construction (**Generalized Sparse Modern Hopfield Model**) for both dense and sparse modern Hopfield models and show that it endows a tighter memory retrieval error compared to the dense counterpart without sacrificing memory capacity. Empirically, we validate the efficacy of STanHop-Net on many settings: time series prediction, fast test-time adaptation, and strongly correlated time series prediction.

Lifeng Shen, Weiyu Chen, James Kwok

The diffusion model has been successfully used in many computer vision applications, such as text-guided image generation and image-to-image translation. Recently, there have been attempts on extending the diffusion model for time series data. However, these extensions are fairly straightforward and do not utilize the unique properties of time series data. As different patterns are usually exhibited at multiple scales of a time series, we in this paper leverage this multi-resolution temporal structure and propose the multi-resolution diffusion model (mr-Diff). By using the seasonal-trend decomposition, we sequentially extract fine-to-coarse trends from the time series for forward diffusion. The denoising process then proceeds in an easy-to-hard non-autoregressive manner. The coarsest trend is generated first. Finer details are progressively added, using the predicted coarser trends as condition variables. Experimental results on nine real-world time series datasets demonstrate that mr-Diff outperforms state-of-the-art time series diffusion models. It is also better than or comparable across a wide variety of advanced time series prediction models.

Deep Learning · Sequential Models, Time series

Irina Rish, Kartik Ahuja, Mohammad Javad Darvishi Bayazi, Pooneh Mousavi, Guillaume Dumas, Jean-Christophe Gagnon-Audet

Deep learning models often fail to generalize well under distribution shifts. Understanding and overcoming these failures have led to a new research field on Out-of-Distribution (OOD) generalization. Despite being extensively studied for static computer vision tasks, OOD generalization has been severely underexplored for time series tasks. To shine a light on this gap, we present WOODS: 10 challenging time series benchmarks covering a diverse range of data modalities, such as videos, brain recordings, and smart device sensory signals. We revise the existing OOD generalization algorithms for time series tasks and evaluate them using our systematic framework. Our experiments show a large room for improvement for empirical risk minimization and OOD generalization algorithms on our datasets, thus underscoring the new challenges posed by time series tasks.

Deep Learning · Sequential Models, Time series

Yi Heng Lim, Qi Zhu, Joshua Selfridge, Muhammad Firmansyah

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature.For many years this bottleneck has persisted, as many thought sequential models could not be parallelized.We challenge this long-held belief with our parallel algorithm that accelerates GPU evaluation of sequential models by up to 3 orders of magnitude faster without compromising output accuracy.The algorithm does not need any special structure in the sequential models' architecture, making it applicable to a wide range of architectures.Using our method, training sequential models can be more than 10 times faster than the common sequential method without any meaningful difference in the training results.Leveraging this accelerated training, we discovered the efficacy of the Gated Recurrent Unit in a long time series classification problem with 17k time samples.By overcoming the training bottleneck, our work serves as the first step to unlock the potential of non-linear sequential models for long sequence problems.

Deep Learning · Sequential Models, Time series

Giovanni De Felice, Andrea Cini, Daniele Zambon, Vladimir Gusev, Cesare Alippi

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

Deep Learning · Sequential Models, Time series

Xihaier Luo, Wei Xu, Balasubramanya T. Nadiga, Yihui Ren, Shinjae Yoo

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequenty arises in many scientific domains. In practice, the process generating the data is often not known to sufficient accuracy. Therefore, there is a growing interest in the deep neural network route to the problem. In this work, we present a novel approach that learns a continuous representation of the field using implicit neural representations (INR). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the technique of separation of variables, the method learns relevant basis functions from sparsely sampled irregular data points to thus develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a state of the art climate model and on a second dataset that comprises of ultra-high resolution satellite-based sea surface temperature field. [Website for the Project: Both data and code are accessible.](https://xihaier.github.io/ICLR-2024-MMGN/)

Deep Learning · Sequential Models, Time series

Zhijian Xu, Ailing Zeng, Qiang Xu

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain, achieving performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks. Notably, FITS accomplishes this with a svelte profile of just about $10k$ parameters, making it ideally suited for edge devices and paving the way for a wide range of applications. The code is available for review at: \url{https://anonymous.4open.science/r/FITS}.

Deep Learning/Sequential Models, Time series

Kun Yi, Qi Zhang, Wei Fan, Shoujin Wang, Pengyang Wang, Hui He, Ning An, Defu Lian, Longbing Cao, Zhendong Niu

Time series forecasting has played the key role in different industrial, including finance, traffic, energy, and healthcare domains. While existing literatures have designed many sophisticated architectures based on RNNs, GNNs, or Transformers, another kind of approaches based on multi-layer perceptrons (MLPs) are proposed with simple structure, low complexity, and superior performance. However, most MLP-based forecasting methods suffer from the point-wise mappings and information bottleneck, which largely hinders the forecasting performance. To overcome this problem, we explore a novel direction of applying MLPs in the frequency domain for time series forecasting. We investigate the learned patterns of frequency-domain MLPs and discover their two inherent characteristic benefiting forecasting, (i) global view: frequency spectrum makes MLPs own a complete view for signals and learn global dependencies more easily, and (ii) energy compaction: frequency-domain MLPs concentrate on smaller key part of frequency components with compact signal energy. Then, we propose FreTS, a simple yet effective architecture built upon Frequency-domain MLPs for Time Series forecasting. FreTS mainly involves two stages, (i) Domain Conversion, that transforms time-domain signals into complex numbers of frequency domain; (ii) Frequency Learning, that performs our redesigned MLPs for the learning of real and imaginary part of frequency components. The above stages operated on both inter-series and intra-series scales further contribute to channel-wise and time-wise dependency learning. Extensive experiments on 13 real-world benchmarks (including 7 benchmarks for short-term forecasting and 6 benchmarks for long-term forecasting) demonstrate our consistent superiority over state-of-the-art methods. Code is available at this repository: https://github.com/aikunyi/FreTS.

Probabilistic Methods/Bayesian Models and Methods

Mingxuan Zhang, Yan Sun, Faming Liang

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research has focused on problems where the observations are independent and identically distributed (i.i.d.), and there has been little work on the problems where the observations are dependent, such as time series data and sequential data in natural language processing. This paper aims to address this gap by studying the theory for sparse deep learning with dependent data. We show that sparse recurrent neural networks (RNNs) can be consistently estimated, and their predictions are asymptotically normally distributed under appropriate assumptions, enabling the prediction uncertainty to be correctly quantified. Our numerical results show that sparse deep learning outperforms state-of-the-art methods, such as conformal predictions, in prediction uncertainty quantification for time series data. Furthermore, our results indicate that the proposed method can consistently identify the autoregressive order for time series data and outperform existing methods in large-scale model compression. Our proposed method has important practical implications in fields such as finance, healthcare, and energy, where both accurate point estimates and prediction uncertainty quantification are of concern.

Deep Learning/Sequential Models, Time series

Tanya Marwah, Ashwini Pokle, J. Zico Kolter, Zachary Lipton, Jianfeng Lu, Andrej Risteski

Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and outputs its solution. However, the architectural design space, especially given structural knowledge of the PDE family of interest, is still poorly understood. We seek to remedy this gap by studying the benefits of weight-tied neural network architectures for steady-state PDEs. To achieve this, we first demonstrate that the solution of most steady-state PDEs can be expressed as a fixed point of a non-linear operator. Motivated by this observation, we propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE as the infinite-depth fixed point of an implicit operator layer using a black-box root solver and differentiates analytically through this fixed point resulting in $\mathcal{O}(1)$ training memory. Our experiments indicate that FNO-DEQ-based architectures outperform FNO-based baselines with $4\times$ the number of parameters in predicting the solution to steady-state PDEs such as Darcy Flow and steady-state incompressible Navier-Stokes. Finally, we show FNO-DEQ is more robust when trained with datasets with more noisy observations than the FNO-based baselines, demonstrating the benefits of using appropriate inductive biases in architectural design for different neural network based PDE solvers. Further, we show a universal approximation result that demonstrates that FNO-DEQ can approximate the solution to any steady-state PDE that can be written as a fixed point equation.