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Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a…

Period estimation is one of the central topics in astronomical time series analysis, where data is often unevenly sampled. Especially challenging are studies of stellar magnetic cycles, as there the periods looked for are of the order of…

The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a…

One of the main features of interest in analysing the light curves of stars is the underlying periodic behaviour. The corresponding observations are a complex type of time series with unequally spaced time points and are sometimes…

We introduce a new periodicity detection algorithm for binary time series of event onsets, the Gaussian Mixture Periodicity Detection Algorithm (GMPDA). The algorithm approaches the periodicity detection problem to infer the parameters of a…

Detection of a signal hidden by noise within a time series is an important problem in many astronomical searches, i.e. for light curves containing the contributions of periodic/semi-periodic components due to rotating objects and all other…

Radio observations of the neutral hydrogen signal from the Cosmic Dawn and Epoch of Reionisation have helped to provide constraints on the properties of the first stars and galaxies. Since this global 21-cm cosmological signal from the…

The detection of anomalies in multivariate time series data is crucial for various practical applications, including smart power grids, traffic flow forecasting, and industrial process control. However, real-world time series data is…

Detection of periodic patterns of interest within noisy time series data plays a critical role in various tasks, spanning from health monitoring to behavior analysis. Existing learning techniques often rely on labels or clean versions of…

The estimation of periodicity is a fundamental task in many scientific areas of study. Existing methods rely on theoretical assumptions that the observation times have equal or i.i.d. spacings, and that common estimators, such as the…

Aperiodic variability is a characteristic feature of young stars, massive stars, and active galactic nuclei. With the recent proliferation of time domain surveys, it is increasingly essential to develop methods to quantify and analyze…

The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data…

The ability to automatically and robustly self-verify periodicity present in time-series astronomical data is becoming more important as data sets rapidly increase in size. The age of large astronomical surveys has rendered manual…

We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in…

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

The last two decades have seen a major expansion in the availability, size, and precision of time-domain datasets in astronomy. Owing to their unique combination of flexibility, mathematical simplicity and comparative robustness, Gaussian…

Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…

Time series analysis is fundamental to characterizing the variability inherent in multi-wavelength emissions from blazars. However, a major observational challenge lies in the need for well-sampled, temporally uniform data, which is often…

Ongoing and future surveys with repeat imaging in multiple bands are producing (or will produce) time-spaced measurements of brightness, resulting in the identification of large numbers of variable sources in the sky. A large fraction of…