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Evaluating robustness under temporal distribution shift remains an open challenge. Existing metrics quantify the average decline in performance, but fail to capture how models adapt to evolving data. As a result, temporal degradation is…

Machine Learning · Computer Science 2026-04-09 Lorenzo Iovine , Giacomo Ziffer , Emanuele Della Valle

Heteroscedasticity -- where the variance of a variable changes with other variables -- is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and…

Machine Learning · Statistics 2026-05-28 Yoichi Chikahara

Multiple metrics have been developed to detect causality relations between data describing the elements constituting complex systems, all of them considering their evolution through time. Here we propose a metric able to detect causality…

Data Analysis, Statistics and Probability · Physics 2016-05-20 Massimiliano Zanin

In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).…

Data Analysis, Statistics and Probability · Physics 2012-07-26 O. Melchert

Temporal event data are collected across a broad range of domains, and a variety of visual analytics techniques have been developed to empower analysts working with this form of data. These techniques generally display aggregate statistics…

Human-Computer Interaction · Computer Science 2019-11-13 David Gotz , Jonathan Zhang , Wenyuan Wang , Joshua Shrestha , David Borland

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…

Data Analysis, Statistics and Probability · Physics 2015-05-20 Lucas Lacasa , Raul Toral

Existing Python libraries and tools lack the ability to efficiently compute statistical test results for large datasets in the presence of missing values. This presents an issue as soon as constraints on runtime and memory availability…

Mathematical Software · Computer Science 2025-05-02 Fabian Woller , Lis Arend , Christian Fuchsberger , Markus List , David B. Blumenthal

In this paper, we develop a novel logic-based approach to detecting high-level temporally extended events from timestamped data and background knowledge. Our framework employs logical rules to capture existence and termination conditions…

Artificial Intelligence · Computer Science 2026-04-24 Yvon K. Awuklu , Meghyn Bienvenu , Katsumi Inoue , Vianney Jouhet , Fleur Mougin

In this paper we describe a method to discover frequent behavioral patterns in event logs. We express these patterns as \emph{local process models}. Local process model mining can be positioned in-between process discovery and episode /…

Databases · Computer Science 2017-05-17 Niek Tax , Natalia Sidorova , Reinder Haakma , Wil M. P. van der Aalst

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…

Data Analysis, Statistics and Probability · Physics 2022-12-14 Martin Heßler , Oliver Kamps

Here we present our Python toolbox "MR. Estimator" to reliably estimate the intrinsic timescale from electrophysiologal recordings of heavily subsampled systems. Originally intended for the analysis of time series from neuronal spiking…

Neurons and Cognition · Quantitative Biology 2021-05-11 F. P. Spitzner , J. Dehning , J. Wilting , A. Hagemann , J. P. Neto , J. Zierenberg , V. Priesemann

The use of observational time series data to assess the impact of multi-time point interventions is becoming increasingly common as more health and activity data are collected and digitized via wearables, social media, and electronic health…

Methodology · Statistics 2020-12-01 Roy Adams , Suchi Saria , Michael Rosenblum

In the last years there has been a considerable increase in the availability of continuous sensor measurements in a wide range of application domains, such as Location-Based Services (LBS), medical monitoring systems, manufacturing plants…

Databases · Computer Science 2015-03-20 Michele Dallachiesa , Besmira Nushi , Katsiaryna Mirylenka , Themis Palpanas

Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…

Fluid Dynamics · Physics 2017-09-12 A. Rupe , J. P. Crutchfield , K. Kashinath , Prabhat

Previously we have developed the concept of the dynamic pathosome, which suggests that individual patterns of phenotype development, i.e., phenotypic trajectories, contain more information than is commonly appreciated and that a phenotype's…

Quantitative Methods · Quantitative Biology 2021-03-25 Peter Lenart , Daniela Kuruczova , Lubomir Kukla , Martin Scheringer , Julie Bienertova Vasku

Longitudinal and time-to-event data are often analyzed in biomarker research to study the association between the longitudinal biomarker measurements and the event-time outcome, in which the longitudinal information contributes to the…

Methodology · Statistics 2025-09-09 Minzee Kim , Joel A. Dubin

Comprehensive characterization of non-Poissonian, bursty temporal patterns observed in various natural and social processes is crucial to understand the underlying mechanisms behind such temporal patterns. Among them bursty event sequences…

Data Analysis, Statistics and Probability · Physics 2020-07-24 Hang-Hyun Jo , Takayuki Hiraoka , Mikko Kivelä

Given an extensive, semi-infinite collection of multivariate coevolving data sequences (e.g., sensor/web activity streams) whose observations influence each other, how can we discover the time-changing cause-and-effect relationships in…

Machine Learning · Computer Science 2026-02-19 Naoki Chihara , Yasuko Matsubara , Ren Fujiwara , Yasushi Sakurai

A large fraction of data generated via human activities such as online purchases, health records, spatial mobility etc. can be represented as a sequence of events over a continuous-time. Learning deep learning models over these…

Machine Learning · Computer Science 2022-08-29 Vinayak Gupta , Srikanta Bedathur , Sourangshu Bhattacharya , Abir De

Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation.…

Machine Learning · Computer Science 2026-04-29 Muhammad Hasan Ferdous , Md Osman Gani