Time Series

Recent test-time adaptation methods heavily rely on nuanced adjustments of batch normalization (BN) parameters. However, one critical assumption often goes overlooked: that of independently and identically distributed (i.i.d.) test batches with respect to unknown labels. This oversight leads to skewed BN statistics and undermines the reliability of the model under non-i.i.d. scenarios. To tackle this challenge, this paper presents a novel method termed '$\textbf{Un-Mix}$ing $\textbf{T}$est-Time $\textbf{N}$ormalization $\textbf{S}$tatistics' (UnMix-TNS). Our method re-calibrates the statistics for each instance within a test batch by $\textit{mixing}$ it with multiple distinct statistics components, thus inherently simulating the i.i.d. scenario. The core of this method hinges on a distinctive online $\textit{unmixing}$ procedure that continuously updates these statistics components by incorporating the most similar instances from new test batches. Remarkably generic in its design, UnMix-TNS seamlessly integrates with a wide range of leading test-time adaptation methods and pre-trained architectures equipped with BN layers. Empirical evaluations corroborate the robustness of UnMix-TNS under varied scenarios—ranging from single to continual and mixed domain shifts, particularly excelling with temporally correlated test data and corrupted non-i.i.d. real-world streams. This adaptability is maintained even with very small batch sizes or single instances. Our results highlight UnMix-TNS's capacity to markedly enhance stability and performance across various benchmarks. Our code is publicly available at https://github.com/devavratTomar/unmixtns.

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

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.

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.

Test-time adaptation (TTA) aims to adapt a pre-trained model from a source domain to a target domain only using online unlabeled target data during testing, without accessing to the source data or modifying the original training process. Among the various TTA methods, pseudo-labeling has gained popularity. However, the presence of incorrect pseudo-labels can hinder the effectiveness of target domain adaptation. To overcome this challenge, we propose a novel TTA method, called PROtotype GRAph Model based pseudo-label learning (PROGRAM). PROGRAM consists of two key components: (1) Prototype Graph Model (PGM) for reliable pseudo-label generation; (2) Robust Self-Training (RST) for test-time adaptation with noisy pseudo-labels. PGM constructs the graph using prototypes and test samples, facilitating effective message passing among them to generate more reliable pseudo-labels. RST combines the advantages of consistency regularization and pseudo-labeling to achieve robust target domain adaptation in the presence of noisy pseudo-labels. Our proposed PROGRAM can be easily integrated into existing baselines, resulting in consistent improvement. Extensive experiments show that our PROGRAM outperforms the existing TTA methods on multiple domain generalization and image corruption benchmarks.

Bandwidth constraints during signal acquisition frequently impede real-time detection applications. Hyperspectral data is a notable example, whose vast volume compromises real-time hyperspectral detection. To tackle this hurdle, we introduce a novel approach leveraging pre-acquisition modulation to reduce the acquisition volume. This modulation process is governed by a deep learning model, utilizing prior information. Central to our approach is LUM-ViT, a Vision Transformer variant. Uniquely, LUM-ViT incorporates a learnable under-sampling mask tailored for pre-acquisition modulation. To further optimize for optical calculations, we propose a kernel-level weight binarization technique and a three-stage fine-tuning strategy. Our evaluations reveal that, by sampling a mere 10\% of the original image pixels, LUM-ViT maintains the accuracy loss within 1.8\% on the ImageNet classification task. The method sustains near-original accuracy when implemented on real-world optical hardware, demonstrating its practicality. Code will be available at [https://github.com/MaxLLF/LUM-ViT](https://github.com/MaxLLF/LUM-ViT).

Recently, Transformer-based and MLP-based models have emerged rapidly and won dominance in time series analysis. In contrast, convolution is losing steam in time series tasks nowadays for inferior performance. This paper studies the open question of how to better use convolution in time series analysis and makes efforts to bring convolution back to the arena of time series analysis. To this end, we modernize the traditional TCN and conduct time series related modifications to make it more suitable for time series tasks. As the outcome, we propose ModernTCN and successfully solve this open question through a seldom-explored way in time series community. As a pure convolution structure, ModernTCN still achieves the consistent state-of-the-art performance on five mainstream time series analysis tasks while maintaining the efficiency advantage of convolution-based models, therefore providing a better balance of efficiency and performance than state-of-the-art Transformer-based and MLP-based models. Our study further reveals that, compared with previous convolution-based models, our ModernTCN has much larger effective receptive fields (ERFs), therefore can better unleash the potential of convolution in time series analysis. Code is available at this repository: https://github.com/luodhhh/ModernTCN.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

We introduce SocioDojo, an open-ended lifelong learning environment for developing ready-to-deploy autonomous agents capable of performing human-like analysis and decision-making on societal topics such as economics, finance, politics, and culture. It consists of (1) information sources from news, social media, reports, etc., (2) a knowledge base built from books, journals, and encyclopedias, plus a toolbox of Internet and knowledge graph search interfaces, (3) 30K high-quality time series in finance, economy, society, and polls, which support a novel task called "hyperportfolio", that can reliably and scalably evaluate societal analysis and decision-making power of agents, inspired by portfolio optimization with time series as assets to "invest". We also propose a novel Analyst-Assistant-Actuator architecture for the hyperportfolio task, and a Hypothesis & Proof prompting for producing in-depth analyses on input news, articles, etc. to assist decision-making. We perform experiments and ablation studies to explore the factors that impact performance. The results show that our proposed method achieves improvements of 32.4% and 30.4% compared to the state-of-the-art method in the two experimental settings.

Transformers have gained widespread usage in multivariate time series (MTS) forecasting, delivering impressive performance. Nonetheless, these existing transformer-based methods often neglect an essential aspect: the incorporation of uncertainty into the predicted series, which holds significant value in decision-making. In this paper, we introduce a Transformer-Modulated Diffusion Model (TMDM), uniting conditional diffusion generative process with transformers into a unified framework to enable precise distribution forecasting for MTS. TMDM harnesses the power of transformers to extract essential insights from historical time series data. This information is then utilized as prior knowledge, capturing covariate-dependence in both the forward and reverse processes within the diffusion model. Furthermore, we seamlessly integrate well-designed transformer-based forecasting methods into TMDM to enhance its overall performance. Additionally, we introduce two novel metrics for evaluating uncertainty estimation performance. Through extensive experiments on six datasets using four evaluation metrics, we establish the effectiveness of TMDM in probabilistic MTS forecasting.

Explaining multivariate time series is a compound challenge, as it requires identifying important locations in the time series and matching complex temporal patterns. Although previous saliency-based methods addressed the challenges, their perturbation may not alleviate the distribution shift issue, which is inevitable especially in heterogeneous samples. We present ContraLSP, a locally sparse model that introduces counterfactual samples to build uninformative perturbations but keeps distribution using contrastive learning. Furthermore, we incorporate sample-specific sparse gates to generate more binary-skewed and smooth masks, which easily integrate temporal trends and select the salient features parsimoniously. Empirical studies on both synthetic and real-world datasets show that ContraLSP outperforms state-of-the-art models, demonstrating a substantial improvement in explanation quality for time series data. The source code is available at \url{https://github.com/zichuan-liu/ContraLSP}.

Periodic patterns are a fundamental characteristic of time series in natural world, with significant implications for a range of disciplines, from economics to cloud systems. However, the current literature on periodicity detection faces two key challenges: limited robustness in real-world scenarios and a lack of memory to leverage previously observed time series to accelerate and improve inference on new data. To overcome these obstacles, this paper presents AmortizedPeriod, an innovative approach to periodicity identification based on amortized variational inference that integrates Bayesian statistics and deep learning. Through the Bayesian generative process, our method flexibly captures the dependencies of the periods, trends, noise, and outliers in time series, while also considering missing data and irregular periods in a robust manner. In addition, it utilizes the evidence lower bound of the log-likelihood of the observed time series as the loss function to train a deep attention inference network, facilitating knowledge transfer from the seen time series (and their labels) to unseen ones. Experimental results show that AmortizedPeriod surpasses the state-of-the-art methods by a large margin of 28.5% on average in terms of micro $F_1$-score, with at least 55% less inference time.

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.

Medical applications of machine learning (ML) have experienced a surge in popularity in recent years. Given the abundance of available data from electronic health records, the intensive care unit (ICU) is a natural habitat for ML. Models have been proposed to address numerous ICU prediction tasks like the early detection of complications. While authors frequently report state-of-the-art performance, it is challenging to verify claims of superiority. Datasets and code are not always published, and cohort definitions, preprocessing pipelines, and training setups are difficult to reproduce. This work introduces Yet Another ICU Benchmark (YAIB), a modular framework that allows researchers to define reproducible and comparable clinical ML experiments; we offer an end-to-end solution from cohort definition to model evaluation. The framework natively supports most open-access ICU datasets (MIMIC III/IV, eICU, HiRID, AUMCdb) and is easily adaptable to future ICU datasets. Combined with a transparent preprocessing pipeline and extensible training code for multiple ML and deep learning models, YAIB enables unified model development, transfer, and evaluation. Our benchmark comes with five predefined established prediction tasks (mortality, acute kidney injury, sepsis, kidney function, and length of stay) developed in collaboration with clinicians. Adding further tasks is straightforward by design. Using YAIB, we demonstrate that the choice of dataset, cohort definition, and preprocessing have a major impact on the prediction performance — often more so than model class — indicating an urgent need for YAIB as a holistic benchmarking tool. We provide our work to the clinical ML community to accelerate method development and enable real-world clinical implementations.

Accurate uncertainty measurement is a key step in building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification framework popular for its ease of implementation, finite-sample coverage guarantees, and generality for underlying prediction algorithms. However, existing conformal prediction approaches for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose the Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite-sample validity guarantee. On four synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and efficient confidence intervals for multi-step prediction tasks than existing techniques. Our code is open-sourced at https://github.com/Rose-STL-Lab/CopulaCPTS.

We introduce Transformer-VQ, a decoder-only transformer computing softmax-based dense self-attention in linear time. Transformer-VQ's efficient attention is enabled by vector-quantized keys and a novel caching mechanism. In our large-scale experiments, Transformer-VQ is shown highly competitive in quality, obtaining 0.99 bpb on Enwik8, 26.6 ppl on PG-19, and 3.16 bpb on ImageNet64. In addition, the optimized implementation of Transformer-VQ is over 3x faster than a comparable quadratic-time transformer at sequence length 8k, is over 12x faster at 32k, and can scale to 131k with similar throughput. Code available: \url{https://github.com/transformer-vq/transformer_vq}

Long-term forecasting presents unique challenges due to the time and memory complexity of handling long sequences. Existing methods, which rely on sliding windows to process long sequences, struggle to effectively capture long-term variations that are partially caught within the short window (i.e., outer-window variations). In this paper, we introduce a novel approach that overcomes this limitation by employing contrastive learning and enhanced decomposition architecture, specifically designed to focus on long-term variations. To this end, our contrastive loss incorporates global autocorrelation held in the whole time series, which facilitates the construction of positive and negative pairs in a self-supervised manner. When combined with our decomposition networks, our constrative learning significantly improves long-term forecasting performance. Extensive experiments demonstrate that our approach outperforms 14 baseline models on well-established nine long-term benchmarks, especially in challenging scenarios that require a significantly long output for forecasting. This paper not only presents a novel direction for long-term forecasting but also offers a more reliable method for effectively integrating long-term variations into time-series representation learning.

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.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model---not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

Time series forecasting is an important and forefront task whose techniques have been applied to electricity forecasting, trajectory prediction, labor planning, etc. However, most of time series forecasting techniques assume that the training data is clean without anomalies. This assumption is unrealistic since the collected time series data can be contaminated in practice. The forecasting model will be inferior if it is directly trained by time series with anomalies. Thus it is essential to develop methods to automatically learn a robust forecasting model from the contaminated data. In this paper, we first statistically define three types of anomalies, then theoretically and experimentally analyze the loss robustness and sample robustness when these anomalies exist. Based on our analyses, we propose a simple and efficient algorithm to learn a robust forecasting model. Extensive experiments show that our method is highly robust and outperforms all existing approaches. The code is available at https://github.com/haochenglouis/RobustTSF.