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"Time Series Analysis": models, code, and papers

Adaptive exponential power distribution with moving estimator for nonstationary time series

Mar 23, 2020
Jarek Duda

While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters $\theta$, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating parameters $\theta_T$ for each time $T$ based on the earlier values $(x_t)_{t

* 6 pages, 4 figures 

LSAR: Efficient Leverage Score Sampling Algorithm for the Analysis of Big Time Series Data

Dec 26, 2019
Ali Eshragh, Fred Roosta, Asef Nazari, Michael W. Mahoney

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive (AR) model in big data regimes. We show that the accuracy of approximations lies within $(1+\mathcal{O}(\varepsilon))$ of the true leverage scores with high probability. These theoretical results are subsequently exploited to develop an efficient algorithm, called LSAR, for fitting an appropriate AR model to big time series data. Our proposed algorithm is guaranteed, with high probability, to find the maximum likelihood estimates of the parameters of the underlying true AR model and has a worst case running time that significantly improves those of the state-of-the-art alternatives in big data regimes. Empirical results on large-scale synthetic as well as real data highly support the theoretical results and reveal the efficacy of this new approach.

* 38 pages, 8 figures 

Normalized multivariate time series causality analysis and causal graph reconstruction

Apr 23, 2021
X. San Liang

Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to formulate it from first principles, however, seems to go unnoticed. This study introduces to the community this line of work, with a long-due generalization of the information flow-based bivariate time series causal inference to multivariate series, based on the recent advance in theoretical development. The resulting formula is transparent, and can be implemented as a computationally very efficient algorithm for application. It can be normalized, and tested for statistical significance. Different from the previous work along this line where only information flows are estimated, here an algorithm is also implemented to quantify the influence of a unit to itself. While this forms a challenge in some causal inferences, here it comes naturally, and hence the identification of self-loops in a causal graph is fulfilled automatically as the causalities along edges are inferred. To demonstrate the power of the approach, presented here are two applications in extreme situations. The first is a network of multivariate processes buried in heavy noises (with the noise-to-signal ratio exceeding 100), and the second a network with nearly synchronized chaotic oscillators. In both graphs, confounding processes exist. While it seems to be a huge challenge to reconstruct from given series these causal graphs, an easy application of the algorithm immediately reveals the desideratum. Particularly, the confounding processes have been accurately differentiated. Considering the surge of interest in the community, this study is very timely.

* 17 pages, 2 figures 

Attentive Weakly Supervised land cover mapping for object-based satellite image time series data with spatial interpretation

Apr 30, 2020
Dino Ienco, Yawogan Jean Eudes Gbodjo, Roberto Interdonato, Raffaele Gaetano

Nowadays, modern Earth Observation systems continuously collect massive amounts of satellite information. The unprecedented possibility to acquire high resolution Satellite Image Time Series (SITS) data (series of images with high revisit time period on the same geographical area) is opening new opportunities to monitor the different aspects of the Earth Surface but, at the same time, it is raising up new challenges in term of suitable methods to analyze and exploit such huge amount of rich and complex image data. One of the main task associated to SITS data analysis is related to land cover mapping where satellite data are exploited via learning methods to recover the Earth Surface status aka the corresponding land cover classes. Due to operational constraints, the collected label information, on which machine learning strategies are trained, is often limited in volume and obtained at coarse granularity carrying out inexact and weak knowledge that can affect the whole process. To cope with such issues, in the context of object-based SITS land cover mapping, we propose a new deep learning framework, named TASSEL (aTtentive weAkly Supervised Satellite image time sEries cLassifier), that is able to intelligently exploit the weak supervision provided by the coarse granularity labels. Furthermore, our framework also produces an additional side-information that supports the model interpretability with the aim to make the black box gray. Such side-information allows to associate spatial interpretation to the model decision via visual inspection.

* Under submission to Elsevier journal 

Interpolation-Prediction Networks for Irregularly Sampled Time Series

Sep 13, 2019
Satya Narayan Shukla, Benjamin M. Marlin

In this paper, we present a new deep learning architecture for addressing the problem of supervised learning with sparse and irregularly sampled multivariate time series. The architecture is based on the use of a semi-parametric interpolation network followed by the application of a prediction network. The interpolation network allows for information to be shared across multiple dimensions of a multivariate time series during the interpolation stage, while any standard deep learning model can be used for the prediction network. This work is motivated by the analysis of physiological time series data in electronic health records, which are sparse, irregularly sampled, and multivariate. We investigate the performance of this architecture on both classification and regression tasks, showing that our approach outperforms a range of baseline and recently proposed models.

* International Conference on Learning Representations. arXiv admin note: substantial text overlap with arXiv:1812.00531 

Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis

Mar 15, 2022
Yuya Ohmichi, Kohmi Takahashi, Kazuyuki Nakakita

Time-series data, such as unsteady pressure-sensitive paint (PSP) measurement data, may contain a significant amount of random noise. Thus, in this study, we investigated a noise-reduction method that combines multivariate singular spectrum analysis (MSSA) with low-dimensional data representation. MSSA is a state-space reconstruction technique that utilizes time-delay embedding, and the low-dimensional representation is achieved by projecting data onto the singular value decomposition (SVD) basis. The noise-reduction performance of the proposed method for unsteady PSP data, i.e., the projected MSSA, is compared with that of the truncated SVD method, one of the most employed noise-reduction methods. The result shows that the projected MSSA exhibits better performance in reducing random noise than the truncated SVD method. Additionally, in contrast to that of the truncated SVD method, the performance of the projected MSSA is less sensitive to the truncation rank. Furthermore, the projected MSSA achieves denoising effectively by extracting smooth trajectories in a state space from noisy input data. Expectedly, the projected MSSA will be effective for reducing random noise in not only PSP measurement data, but also various high-dimensional time-series data.

* 15 pages, 12 figures 

Benchmarking adversarial attacks and defenses for time-series data

Aug 30, 2020
Shoaib Ahmed Siddiqui, Andreas Dengel, Sheraz Ahmed

The adversarial vulnerability of deep networks has spurred the interest of researchers worldwide. Unsurprisingly, like images, adversarial examples also translate to time-series data as they are an inherent weakness of the model itself rather than the modality. Several attempts have been made to defend against these adversarial attacks, particularly for the visual modality. In this paper, we perform detailed benchmarking of well-proven adversarial defense methodologies on time-series data. We restrict ourselves to the $L_{\infty}$ threat model. We also explore the trade-off between smoothness and clean accuracy for regularization-based defenses to better understand the trade-offs that they offer. Our analysis shows that the explored adversarial defenses offer robustness against both strong white-box as well as black-box attacks. This paves the way for future research in the direction of adversarial attacks and defenses, particularly for time-series data.


Online Time Series Anomaly Detection with State Space Gaussian Processes

Jan 18, 2022
Christian Bock, François-Xavier Aubet, Jan Gasthaus, Andrey Kan, Ming Chen, Laurent Callot

We propose r-ssGPFA, an unsupervised online anomaly detection model for uni- and multivariate time series building on the efficient state space formulation of Gaussian processes. For high-dimensional time series, we propose an extension of Gaussian process factor analysis to identify the common latent processes of the time series, allowing us to detect anomalies efficiently in an interpretable manner. We gain explainability while speeding up computations by imposing an orthogonality constraint on the mapping from the latent to the observed. Our model's robustness is improved by using a simple heuristic to skip Kalman updates when encountering anomalous observations. We investigate the behaviour of our model on synthetic data and show on standard benchmark datasets that our method is competitive with state-of-the-art methods while being computationally cheaper.


Robust Anomaly Detection for Time-series Data

Feb 06, 2022
Min Hu, Yi Wang, Xiaowei Feng, Shengchen Zhou, Zhaoyu Wu, Yuan Qin

Time-series anomaly detection plays a vital role in monitoring complex operation conditions. However, the detection accuracy of existing approaches is heavily influenced by pattern distribution, existence of multiple normal patterns, dynamical features representation, and parameter settings. For the purpose of improving the robustness and guaranteeing the accuracy, this research combined the strengths of negative selection, unthresholded recurrence plots, and an extreme learning machine autoencoder and then proposed robust anomaly detection for time-series data (RADTD), which can automatically learn dynamical features in time series and recognize anomalies with low label dependency and high robustness. Yahoo benchmark datasets and three tunneling engineering simulation experiments were used to evaluate the performance of RADTD. The experiments showed that in benchmark datasets RADTD possessed higher accuracy and robustness than recurrence qualification analysis and extreme learning machine autoencoder, respectively, and that RADTD accurately detected the occurrence of tunneling settlement accidents, indicating its remarkable performance in accuracy and robustness.

* 18 pages, 12 figures, 6 tables