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Applications · Time Series

Marco Federici, Patrick Forré, Ryota Tomioka, Bas Veeling

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

Deep Learning · Sequential Models, Time series

Mahan Fathi, Clement Gehring, Jonathan Pilault, David Kanaa, Pierre-Luc Bacon, Ross Goroshin

Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

Applications · Time Series

Xu Zheng, Tianchun Wang, Wei Cheng, Aitian Ma, Haifeng Chen, Mo Sha, Dongsheng Luo

Modern techniques like contrastive learning have been effectively used in many areas, including computer vision, natural language processing, and graph-structured data. Creating positive examples that assist the model in learning robust and discriminative representations is a crucial stage in contrastive learning approaches. Usually, preset human intuition directs the selection of relevant data augmentations. Due to patterns that are easily recognized by humans, this rule of thumb works well in the vision and language domains. However, it is impractical to visually inspect the temporal structures in time series. The diversity of time series augmentations at both the dataset and instance levels makes it difficult to choose meaningful augmentations on the fly. Thus, although prevalent, contrastive learning with data augmentation has been less studied in the time series domain. In this study, we address this gap by analyzing time series data augmentation using information theory and summarizing the most commonly adopted augmentations in a unified format. We then propose a parametric augmentation method, AutoTCL, which can be adaptively employed to support time series representation learning. The proposed approach is encoder-agnostic, allowing it to be seamlessly integrated with different backbone encoders. Experiments on univariate forecasting tasks demonstrate the highly competitive results of our method, with an average 6.5\% reduction in MSE and 4.7\% in MAE over the leading baselines. In classification tasks, AutoTCL achieves a $1.2\%$ increase in average accuracy.

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.

Applications · Time Series

Chenxi Sun, Hongyan Li, Yaliang Li, Shenda Hong

This work summarizes two ways to accomplish Time-Series (TS) tasks in today's Large Language Model (LLM) context: LLM-for-TS (model-centric) designs and trains a fundamental large model, or fine-tunes a pre-trained LLM for TS data; TS-for-LLM (data-centric) converts TS into a model-friendly representation to enable the pre-trained LLM to handle TS data. Given the lack of data, limited resources, semantic context requirements, and so on, this work focuses on TS-for-LLM, where we aim to activate LLM's ability for TS data by designing a TS embedding method suitable for LLM. The proposed method is named TEST. It first tokenizes TS, builds an encoder to embed TS via instance-wise, feature-wise, and text-prototype-aligned contrast, where the TS embedding space is aligned to LLM’s embedding layer space, then creates soft prompts to make LLM more open to that embeddings, and finally implements TS tasks using the frozen LLM. We also demonstrate the feasibility of TS-for-LLM through theory and experiments. Experiments are carried out on TS classification, forecasting, and representation tasks using eight frozen LLMs with various structures and sizes. The results show that the pre-trained LLM with TEST strategy can achieve better or comparable performance than today's SOTA TS models, and offers benefits for few-shot and generalization. By treating LLM as the pattern machine, TEST can endow LLM's ability to process TS data without compromising language ability. We hope that this study will serve as a foundation for future work to support TS+LLM progress.

Deep Learning · Generative Models and Autoencoders

yaxuan zhu, Jianwen Xie, Yingnian Wu, Ruiqi Gao

Training energy-based models (EBMs) on high-dimensional data can be both challenging and time-consuming, and there exists a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To close this gap, inspired by the recent efforts of learning EBMs by maximimizing diffusion recovery likelihood (DRL), we propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs defined on increasingly noisy versons of a dataset, paired with an initializer model for each EBM. At each noise level, the two models are jointly estimated within a cooperative training framework: Samples from the initializer serve as starting points that are refined by a few MCMC sampling steps from the EBM. The EBM is then optimized by maximizing recovery likelihood, while the initializer model is optimized by learning from the difference between the refined samples and the initial samples. In addition, we made several practical designs for EBM training to further improve the sample quality. Combining these advances, we significantly boost the generation performance compared to existing EBM methods on CIFAR-10 and ImageNet 32x32. And we have shown that CDRL has great potential to largely reduce the sampling time. We also demonstrate the effectiveness of our models for several downstream tasks, including classifier-free guided generation, compositional generation, image inpainting and out-of-distribution detection.

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.

Social Aspects · Accountability, Transparency and Interpretability

Krzysztof Kacprzyk, Tennison Liu, Mihaela van der Schaar

Transparent machine learning (ML) models are essential for ensuring interpretability and trustworthiness in decision-making systems, particularly in high-stakes domains such as healthcare, finance, and criminal justice. While transparent machine learning models have been proposed for classification and regression, time series forecasting presents some unique challenges for ensuring transparency. In particular, currently used bottom-up approaches that focus on the values of the time series at specific time points (usually regularly spaced) do not provide a holistic understanding of the entire time series. This limits the applicability of ML in many critical areas. To open up these domains for ML, we propose a top-down framework of bi-level transparency, which involves understanding the higher-level trends and the lower-level properties of the predicted time series. Applying this framework, we develop TIMEVIEW, a transparent ML model for time series forecasting based on static features, complemented with an interactive visualization tool. Through a series of experiments, we demonstrate the efficacy and interpretability of our approach, paving the way for more transparent and reliable applications of ML in various domains.

Applications · Language, Speech and Dialog

Qi Yan, Raihan Seraj, Jiawei He, Lili Meng, Tristan Sylvain

Machine-based prediction of real-world events is garnering attention due to its potential for informed decision-making. Whereas traditional forecasting predominantly hinges on structured data like time-series, recent breakthroughs in language models enable predictions using unstructured text. In particular, (Zou et al., 2022) unveils AutoCast, a new benchmark that employs news articles for answering forecasting queries. Nevertheless, existing methods still trail behind human performance. The cornerstone of accurate forecasting, we argue, lies in identifying a concise, yet rich subset of news snippets from a vast corpus. With this motivation, we introduce AutoCast++, a zero-shot ranking-based context retrieval system, tailored to sift through expansive news document collections for event forecasting. Our approach first re-ranks articles based on zero-shot question-passage relevance, honing in on semantically pertinent news. Following this, the chosen articles are subjected to zero-shot summarization to attain succinct context. Leveraging a pre-trained language model, we conduct both the relevance evaluation and article summarization without needing domain-specific training. Notably, recent articles can sometimes be at odds with preceding ones due to new facts or unanticipated incidents, leading to fluctuating temporal dynamics. To tackle this, our re-ranking mechanism gives preference to more recent articles, and we further regularize the multi-passage representation learning to align with human forecaster responses made on different dates. Empirical results underscore marked improvements across multiple metrics, improving the performance for multiple-choice questions (MCQ) by 48% and true/false (TF) questions by up to 8%. Code is available at https://github.com/BorealisAI/Autocast-plus-plus.

Deep Learning · Generative Models and Autoencoders

Joey Bose, Tara Akhound-Sadegh, Guillaume Huguet, Kilian FATRAS, Jarrid Rector-Brooks, Chenghao Liu, Andrei Nica, Maksym Korablyov, Michael Bronstein, Alexander Tong

The computational design of novel protein structures has the potential to impact numerous scientific disciplines greatly. Toward this goal, we introduce \foldflow, a series of novel generative models of increasing modeling power based on the flow-matching paradigm over $3\mathrm{D}$ rigid motions---i.e. the group $\mathrm{SE(3)}$---enabling accurate modeling of protein backbones. We first introduce $\text{FoldFlow-Base}$, a simulation-free approach to learning deterministic continuous-time dynamics and matching invariant target distributions on $\mathrm{SE(3)}$. We next accelerate training by incorporating Riemannian optimal transport to create $\text{FoldFlow-OT}$, leading to the construction of both more simple and stable flows. Finally, we design \foldflowsfm, coupling both Riemannian OT and simulation-free training to learn stochastic continuous-time dynamics over $\mathrm{SE(3)}$. Our family of $\text{FoldFlow}$, generative models offers several key advantages over previous approaches to the generative modeling of proteins: they are more stable and faster to train than diffusion-based approaches, and our models enjoy the ability to map any invariant source distribution to any invariant target distribution over $\mathrm{SE(3)}$. Empirically, we validate $\text{FoldFlow}$, on protein backbone generation of up to $300$ amino acids leading to high-quality designable, diverse, and novel samples.

Applications · Time Series

Luke Darlow, Qiwen Deng, Ahmed Hassan, Martin Asenov, Rajkarn Singh, Artjom Joosen, Adam Barker, Amos Storkey

It is challenging to scale time series forecasting models such that they forecast accurately for multiple distinct domains and datasets, all with potentially different underlying collection procedures (e.g., sample resolution), patterns (e.g., periodicity), and prediction requirements (e.g., reconstruction vs. forecasting). We call this general task universal forecasting. Existing methods usually assume that input data is regularly sampled, and they forecast to pre-determined horizons, resulting in failure to generalise outside of the scope of their training. We propose the DAM -- a neural model that takes randomly sampled histories and outputs an adjustable basis composition as a continuous function of time for forecasting to non-fixed horizons. It involves three key components: (1) a flexible approach for using randomly sampled histories from a long-tail distribution, that enables an efficient global perspective of the underlying temporal dynamics while retaining focus on the recent history; (2) a transformer backbone that is trained on these actively sampled histories to produce, as representational output, (3) the basis coefficients of a continuous function of time. We show that a single univariate DAM, trained on 25 time series datasets, either outperformed or closely matched existing SoTA models at multivariate long-term forecasting across 18 datasets, including 8 held-out for zero-shot transfer, even though these models were trained to specialise for each dataset-horizon combination. This single DAM excels at zero-shot transfer and very-long-term forecasting, performs well at imputation, is interpretable via basis function composition and attention, can be tuned for different inference-cost requirements, is robust to missing and irregularly sampled data by design.

Miscellaneous Aspects of Machine Learning · Causality

YUXIAO CHENG, Ziqian Wang, Tingxiong Xiao, Qin Zhong, Jinli Suo, Kunlun He

Time-series causal discovery (TSCD) is a fundamental problem of machine learning. However, existing synthetic datasets cannot properly evaluate or predict the algorithms' performance on real data. This study introduces the CausalTime pipeline to generate time-series that highly resemble the real data and with ground truth causal graphs for quantitative performance evaluation. The pipeline starts from real observations in a specific scenario and produces a matching benchmark dataset. Firstly, we harness deep neural networks along with normalizing flow to accurately capture realistic dynamics. Secondly, we extract hypothesized causal graphs by performing importance analysis on the neural network or leveraging prior knowledge. Thirdly, we derive the ground truth causal graphs by splitting the causal model into causal term, residual term, and noise term. Lastly, using the fitted network and the derived causal graph, we generate corresponding versatile time-series proper for algorithm assessment. In the experiments, we validate the fidelity of the generated data through qualitative and quantitative experiments, followed by a benchmarking of existing TSCD algorithms using these generated datasets. CausalTime offers a feasible solution to evaluating TSCD algorithms in real applications and can be generalized to a wide range of fields. For easy use of the proposed approach, we also provide a user-friendly website, hosted on www.causaltime.cc.

Oren Mangoubi, Nisheeth Vishnoi

We consider the problem of sampling from a logconcave distribution $\pi(\theta) \propto e^{-f(\theta)}$ constrained to a polytope $K:=${$\theta \in \mathbb{R}^d: A\theta \leq b$}, where $A\in \mathbb{R}^{m\times d}$ and $b \in \mathbb{R}^m$. The fastest-known algorithm for the setting when $f$ is $O(1)$-Lipschitz or $O(1)$-smooth runs in roughly $O(md \times md^{\omega -1})$ arithmetic operations, where the $md^{\omega -1}$ term arises because each Markov chain step requires computing a matrix inversion and determinant ($\omega \approx 2.37$ is the matrix multiplication constant). We present a nearly-optimal implementation of this Markov chain with per-step complexity that is roughly the number of non-zero entries of $A$ while the number of Markov chain steps remains the same. The key technical ingredients are 1) to show that the matrices that arise in this Dikin walk change slowly, 2) to deploy efficient linear solvers which can leverage this slow change to speed up matrix inversion by using information computed in previous steps, and 3) to speed up the computation of the determinantal term in the Metropolis filter step via a randomized Taylor series-based estimator. This result directly improves the runtime for applications that involve sampling from Gibbs distributions constrained to polytopes that arise in Bayesian statistics and private optimization.

Social Aspects · Accountability, Transparency and Interpretability

Zichuan Liu, Yingying ZHANG, Tianchun Wang, Zefan Wang, Dongsheng Luo, Mengnan Du, Min Wu, Yi Wang, Chunlin Chen, Lunting Fan 等

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}.

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}.

Applications · Time Series

Peng Chen, Yingying ZHANG, Yunyao Cheng, Yang Shu, Yihang Wang, Qingsong Wen, Bin Yang, Chenjuan Guo

Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with adaptive pathways. It integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale Transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics of the input, improving the accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. The code is made available at https://github.com/decisionintelligence/pathformer.

Applications · Time Series

xue wang, Tian Zhou, Qingsong Wen, Jinyang Gao, Bolin Ding, Rong Jin

Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., **C**hannel **A**ligned **R**obust Blen**d** Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository: https://github.com/wxie9/CARD.

Probabilistic Methods · Variational Inference

Lorenz Richter, Julius Berner

Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on previous work, we identify these approaches as special cases of a generalized Schrödinger bridge problem, seeking a stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called \textit{log-variance loss}, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.