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In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…

Methodology · Statistics 2014-03-18 Michael Vogt , Holger Dette

A time series represents a set of observations collected over time. Typically, these observations are captured with a uniform sampling frequency (e.g. daily). When data points are observed in uneven time intervals the time series is…

Machine Learning · Computer Science 2022-01-03 Pedro Costa , Vitor Cerqueira , João Vinagre

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…

Methodology · Statistics 2015-04-03 Michael Vogt , Holger Dette

The era of information explosion had prompted the accumulation of a tremendous amount of time-series data, including stationary and non-stationary time-series data. State-of-the-art algorithms have achieved a decent performance in dealing…

Machine Learning · Computer Science 2021-11-23 Xipei Wang , Haoyu Zhang , Yuanbo Zhang , Meng Wang , Jiarui Song , Tin Lai , Matloob Khushi

We present Synergy Aware Forgetting Ensemble (SAFE), a method to adapt large models on a diverse collection of data while minimizing the expected cost to remove the influence of training samples from the trained model. This process, also…

Machine Learning · Computer Science 2023-08-23 Yonatan Dukler , Benjamin Bowman , Alessandro Achille , Aditya Golatkar , Ashwin Swaminathan , Stefano Soatto

We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…

Molecular Networks · Quantitative Biology 2015-06-03 Nils B. Becker , Rosalind J. Allen , Pieter Rein ten Wolde

We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…

Machine Learning · Statistics 2019-12-06 David Tolpin

Deep Neural Networks have spearheaded remarkable advancements in time series forecasting (TSF), one of the major tasks in time series modeling. Nonetheless, the non-stationarity of time series undermines the reliability of pre-trained…

Machine Learning · Computer Science 2025-01-10 HyunGi Kim , Siwon Kim , Jisoo Mok , Sungroh Yoon

Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…

Methodology · Statistics 2020-04-02 Tomáš Rubín , Victor M. Panaretos

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time…

Instrumentation and Methods for Astrophysics · Physics 2015-06-05 Jeffrey D. Scargle , Jay P. Norris , Brad Jackson , James Chiang

Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over…

Machine Learning · Computer Science 2023-11-27 Yong Liu , Haixu Wu , Jianmin Wang , Mingsheng Long

Sequence modeling faces challenges in capturing long-range dependencies across diverse tasks. Recent linear and transformer-based forecasters have shown superior performance in time series forecasting. However, they are constrained by their…

Machine Learning · Computer Science 2024-11-25 Bong Gyun Kang , Dongjun Lee , HyunGi Kim , DoHyun Chung , Sungroh Yoon

Time series anomaly detection plays a critical role in automated monitoring systems. Most previous deep learning efforts related to time series anomaly detection were based on recurrent neural networks (RNN). In this paper, we propose a…

Machine Learning · Computer Science 2019-06-03 Tailai Wen , Roy Keyes

An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a…

Statistics Theory · Mathematics 2016-07-19 Philip Preuß , Kemal Sen , Holger Dette

Time series anomaly detection is an important process for system monitoring and model switching, among other applications in cyber-physical systems. In this document, we present a fast subspace method for time series anomaly detection, with…

Systems and Control · Electrical Eng. & Systems 2022-05-23 Fredy Vides , Esteban Segura , Carlos Vargas-Agüero

When dealing with time series with complex non-stationarities, low retrospective regret on individual realizations is a more appropriate goal than low prospective risk in expectation. Online learning algorithms provide powerful guarantees…

Machine Learning · Statistics 2011-06-30 Cosma Rohilla Shalizi , Abigail Z. Jacobs , Kristina Lisa Klinkner , Aaron Clauset

In this work, a novel approach for the construction and training of time series models is presented that deals with the problem of learning on large time series with non-equispaced observations, which at the same time may possess features…

Machine Learning · Computer Science 2020-11-25 Charilaos Mylonas , Eleni Chatzi

Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…

Signal Processing · Electrical Eng. & Systems 2021-06-23 Daniel E. Shea , Rajiv Giridharagopal , David S. Ginger , Steven L. Brunton , J. Nathan Kutz

Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…

Machine Learning · Statistics 2019-01-15 Felipe Tobar

Non-stationarity is an intrinsic property of real-world time series and plays a crucial role in time series forecasting. Previous studies primarily adopt instance normalization to attenuate the non-stationarity of original series for better…

Machine Learning · Computer Science 2025-03-05 Tianyu Jia , Zongxia Xie , Yanru Sun , Dilfira Kudrat , Qinghua Hu