Related papers: Transformation cost spectrum for irregularly sampl…
Consider a supercritical birth and death process where the children acquire mutations. We study the mutation rates along the ancestral lineages in a sample of size $n$ from the population at time $T$. The mutation rate is time-inhomogenous…
Time series forecasting with limited data is a challenging yet critical task. While transformers have achieved outstanding performances in time series forecasting, they often require many training samples due to the large number of…
This paper proposes a simple yet highly accurate prediction-correction algorithm, SHARP, for unconstrained time-varying optimization problems. Its prediction is based on an extrapolation derived from the Lagrange interpolation of past…
This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…
It is quite common that the structure of a time series changes abruptly. Identifying these change points and describing the model structure in the segments between these change points is of interest. In this paper, time series data is…
A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length,…
Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to…
Conformal prediction is a powerful post-hoc framework for uncertainty quantification that provides distribution-free coverage guarantees. However, these guarantees crucially rely on the assumption of exchangeability. This assumption is…
Irregularly sampled time series are ubiquitous, presenting significant challenges for analysis due to missing values. Despite existing methods address imputation, they predominantly focus on leveraging intra-series information, neglecting…
Comparing time series is essential in various tasks such as clustering and classification. While elastic distance measures that allow warping provide a robust quantitative comparison, a qualitative comparison on top of them is missing.…
A method is presented for investigating the periodic signal content of time series in which a number of signals is present, such as arising from the observation of multiperiodic oscillating stars in observational asteroseismology. Standard…
In this work, we introduce a novel approach for determining a joint sparse spectrum from several non-uniformly sampled data sets, where each data set is assumed to have its own, possibly disjoint, and only partially known, sampling times.…
As a new method for detecting change-points in high-resolution time series, we apply Maximum Mean Discrepancy to the distributions of ordinal patterns in different parts of a time series. The main advantage of this approach is its…
Performance estimation aims at estimating the loss that a predictive model will incur on unseen data. These procedures are part of the pipeline in every machine learning project and are used for assessing the overall generalisation ability…
Methods for detecting structural changes, or change points, in time series data are widely used in many fields of science and engineering. This chapter sketches some basic methods for the analysis of structural changes in time series data.…
Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of…
The aim of this paper is to shed light on the analysis of non-stationary time series by means of the method of diffusion entropy. For this purpose, we first study the case when infinitely many time series, as different realizations of the…
The Synchrosqueezing transform is a time-frequency analysis method that can decompose complex signals into time-varying oscillatory components. It is a form of time-frequency reassignment that is both sparse and invertible, allowing for the…
The world is not static: This causes real-world time series to change over time through external, and potentially disruptive, events such as macroeconomic cycles or the COVID-19 pandemic. We present an adaptive sampling strategy that…
On a high-frequency scale the time series are not homogeneous, therefore standard correlation measures can not be directly applied to the raw data. There are two ways to deal with this problem. The time series can be homogenised through an…