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Mamba has recently emerged as a promising alternative to Transformers, offering near-linear complexity in processing sequential data. However, while channels in time series (TS) data have no specific order in general, recent studies have adopted Mamba to capture channel dependencies (CD) in TS, introducing a sequential order bias. To address this issue, we propose SOR-Mamba, a TS forecasting method that 1) incorporates a regularization strategy to minimize the discrepancy between two embedding vectors generated from data with reversed channel orders, thereby enhancing robustness to channel order, and 2) eliminates the 1D-convolution originally designed to capture local information in sequential data. Furthermore, we introduce channel correlation modeling (CCM), a pretraining task aimed at preserving correlations between channels from the data space to the latent space in order to enhance the ability to capture CD. Extensive experiments demonstrate the efficacy of the proposed method across standard and transfer learning scenarios. Code is available at https://github.com/seunghan96/SOR-Mamba., Comment: NeurIPS Workshop on Time Series in the Age of Large Models, 2024

Recent advancements in foundation models have been successfully extended to the time series (TS) domain, facilitated by the emergence of large-scale TS datasets. However, previous efforts have primarily focused on designing model architectures to address explicit heterogeneity among datasets such as various numbers of channels, while often overlooking implicit heterogeneity such as varying dependencies between channels. In this work, we introduce the concept of partial channel dependence (PCD), which enables a more sophisticated adjustment of channel dependencies based on dataset-specific information. To achieve PCD, we propose a channel mask that captures the relationships between channels within a dataset using two key components: 1) a correlation matrix that encodes relative dependencies between channels, and 2) domain parameters that learn the absolute dependencies specific to each dataset, refining the correlation matrix. We validate the effectiveness of PCD across four tasks in TS including forecasting, classification, imputation, and anomaly detection, under diverse settings, including few-shot and zero-shot scenarios with both TS foundation models and single-task models. Code is available at https://github.com/seunghan96/CM., Comment: NeurIPS Workshop on Time Series in the Age of Large Models, 2024. Oral presentation

Advances in diffusion models for generative artificial intelligence have recently propagated to the time series (TS) domain, demonstrating state-of-the-art performance on various tasks. However, prior works on TS diffusion models often borrow the framework of existing works proposed in other domains without considering the characteristics of TS data, leading to suboptimal performance. In this work, we propose Adaptive Noise schedule for Time series diffusion models (ANT), which automatically predetermines proper noise schedules for given TS datasets based on their statistics representing non-stationarity. Our intuition is that an optimal noise schedule should satisfy the following desiderata: 1) It linearly reduces the non-stationarity of TS data so that all diffusion steps are equally meaningful, 2) the data is corrupted to the random noise at the final step, and 3) the number of steps is sufficiently large. The proposed method is practical for use in that it eliminates the necessity of finding the optimal noise schedule with a small additional cost to compute the statistics for given datasets, which can be done offline before training. We validate the effectiveness of our method across various tasks, including TS forecasting, refinement, and generation, on datasets from diverse domains. Code is available at this repository: https://github.com/seunghan96/ANT., Comment: NeurIPS 2024

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/inference time. Code is available at this repository: https://github.com/seunghan96/pits., Comment: ICLR 2024

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 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 the distance between time series on the data space, 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., Comment: ICLR 2024 Spotlight

In the analysis of binary longitudinal data, it is of interest to model a dynamic relationship between a response and covariates as a function of time, while also investigating similar patterns of time-dependent interactions. We present a novel generalized varying-coefficient model that accounts for within-subject variability and simultaneously clusters varying-coefficient functions, without restricting the number of clusters nor overfitting the data. In the analysis of a heterogeneous series of binary data, the model extracts population-level fixed effects, cluster-level varying effects, and subject-level random effects. Various simulation studies show the validity and utility of the proposed method to correctly specify cluster-specific varying-coefficients when the number of clusters is unknown. The proposed method is applied to a heterogeneous series of binary data in the German Socioeconomic Panel (GSOEP) study, where we identify three major clusters demonstrating the different varying effects of socioeconomic predictors as a function of age on the working status.

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be excluded from the model while simultaneously determining whether nonzero additive components should be represented as linear or non-linear components in the final model. In this paper, we propose a Bayesian model selection method that is facilitated by a carefully specified class of models, including the choice of a prior distribution and the nonparametric model used for the nonlinear additive components. We employ a series of latent variables that determine the effect of each variable among the three possibilities (no effect, linear effect, and nonlinear effect) and that simultaneously determine the knots of each spline for a suitable penalization of smooth functions. The use of a pseudo-prior distribution along with a collapsing scheme enables us to deploy well-behaved Markov chain Monte Carlo samplers, both for model selection and for fitting the preferred model. Our method and algorithm are deployed on a suite of numerical studies and are applied to a nutritional epidemiology study. The numerical results show that the proposed methodology outperforms previously available methods in terms of effective sample sizes of the Markov chain samplers and the overall misclassification rates.

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties., Comment: 61 pages double spaced, 8 figures, accepted for publication in ApJ

The detection and quantification of narrow emission lines in X-ray spectra is a challenging statistical task. The Poisson nature of the photon counts leads to local random fluctuations in the observed spectrum that often results in excess emission in a narrow band of energy resembling a weak narrow line. From a formal statistical perspective, this leads to a (sometimes highly) multimodal likelihood. Many standard statistical procedures are based on (asymptotic) Gaussian approximations to the likelihood and simply cannot be used in such settings. Bayesian methods offer a more direct paradigm for accounting for such complicated likelihood functions but even here multimodal likelihoods pose significant computational challenges. The new Markov chain Monte Carlo (MCMC) methods developed in 2008 by van Dyk and Park, however, are able to fully explore the complex posterior distribution of the location of a narrow line, and thus provide valid statistical inference. Even with these computational tools, standard statistical quantities such as means and standard deviations cannot adequately summarize inference and standard testing procedures cannot be used to test for emission lines. In this paper, we use new efficient MCMC algorithms to fit the location of narrow emission lines, we develop new statistical strategies for summarizing highly multimodal distributions and quantifying valid statistical inference, and we extend the method of posterior predictive p-values proposed by Protassov et al. (2002) to test for the presence of narrow emission lines in X-ray spectra. We illustrate and validate our methods using simulation studies and apply them to the Chandra observations of the high redshift quasar PG1634+706., Comment: 43 pages, 11 figures; accepted for publication in ApJ

A commonly used measure to summarize the nature of a photon spectrum is the so-called Hardness Ratio, which compares the number of counts observed in different passbands. The hardness ratio is especially useful to distinguish between and categorize weak sources as a proxy for detailed spectral fitting. However, in this regime classical methods of error propagation fail, and the estimates of spectral hardness become unreliable. Here we develop a rigorous statistical treatment of hardness ratios that properly deals with detected photons as independent Poisson random variables and correctly deals with the non-Gaussian nature of the error propagation. The method is Bayesian in nature, and thus can be generalized to carry out a multitude of source-population--based analyses. We verify our method with simulation studies, and compare it with the classical method. We apply this method to real world examples, such as the identification of candidate quiescent Low-mass X-ray binaries in globular clusters, and tracking the time evolution of a flare on a low-mass star., Comment: 43 pages, 10 figures, 3 tables; submitted to ApJ