Gaussian Process regression for astronomical time-series

Aigrain, S.; Foreman-Mackey, Daniel

doi:10.48550/arxiv.2209.08940

Cited by 8 publications

(7 citation statements)

References 79 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This has led previous studies to characterise SLF variability instead in the Fourier domain (Blomme et al 2011;Bowman et al 2019aBowman et al ,b, 2020Dorn-Wallenstein et al 2019, 2020Nazé et al 2021;Elliott et al 2022). However, there are various statistical tools and methodologies, such as GP regression (Rasmussen & Williams 2006;Aigrain & Foreman-Mackey 2022), low-order linear stochastic differential equations (Koen 2005), and continuous-time autoregressive moving average models (Kelly et al 2014), that yield a model for stochastic signals in the time domain based on the statistical properties of time-series data.…”

Section: Methodsmentioning

confidence: 99%

“…A GP regression model is a non-parametric model that describes correlated stochastic variability in a time series by fitting hyperparameters to define a covariance matrix. Each data point in a time series is described as a correlated random variable with a mean and a variance, for which any finite collection of variables has a multi-variate Gaussian distribution (Rasmussen & Williams 2006;Aigrain & Foreman-Mackey 2022). In GP regression, a function is not directly fitted to a data set, but rather hyperparameters are fit to define a covariance matrix.…”

Section: Defining a Gp Kernelmentioning

confidence: 99%

See 1 more Smart Citation

Photometric detection of internal gravity waves in upper main-sequence stars

Bowman

Dorn-Wallenstein

2022

A&A

View full text Add to dashboard Cite

Context. Recent studies of massive stars using high-precision space photometry have revealed that they commonly exhibit stochastic low-frequency (SLF) variability. This has been interpreted as being caused by internal gravity waves (IGWs) excited at the interface of convective and radiative regions within stellar interiors, such as the convective core or sub-surface convection zones, or caused by dynamic turbulence excited in the sub-surface convection zones within the envelopes of main-sequence massive stars. Aims. We aim to compare the properties of SLF variability in massive main-sequence stars observed by the Transiting Exoplanet Survey Satellite (TESS) mission determined by different statistical methods, and confirm the correlation between the morphology of SLF variability and a star's location in the Hertzsprung-Russell (HR) diagram. We also aim to quantify the impact of data quality on the inferred SLF morphologies using both fitting methodologies. Methods. From a sample of 30 previously observed and characterised massive stars observed by TESS, we compare the resultant parameters of SLF variability, in particular the characteristic frequency, obtained from fitting the amplitude spectrum of the light curve with those inferred from fitting the covariance structure of the light curve using the celerite2 Gaussian process (GP) regression software and a damped SHO kernel. Results. We find a difference in the characteristic frequency obtained from the amplitude spectrum fitting and from fitting the covariance structure of the light curve using a GP regression with celerite2 for only a minority of the considered sample. However, the trends among mass, age and the properties of SLF variability previously reported remain unaffected. We also find that the method of GP regression is more efficient in terms of computation time and, on average, more robust against the quality and noise properties of the input time series data in determining the properties of SLF variability. Conclusions. GP regression is a useful and novel methodology to efficiently characterise SLF variability in massive stars compared to previous techniques used in the literature. We conclude that the correlation between a star's SLF variability, in particular the characteristic frequency, and its location in the HR diagram is robust for main-sequence massive stars. There also exists a distribution in the stochasticity of SLF variability in massive stars, which indicates that the coherency of SLF variability is also a function of mass and age in massive stars.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Defining a Gp Kernelmentioning

confidence: 99%

Photometric detection of internal gravity waves in upper main-sequence stars

Bowman

Dorn-Wallenstein

2022

A&A

View full text Add to dashboard Cite

show abstract

“…For those interested in the stochastic behavior of astronomical variability, GP provides a flexible method to model the LC with stochastic processes. The application of GPs for astronomical time series is discussed in a recent review ( see Aigrain & Foreman-Mackey 2022). Considering a data set of y n at coordinates x n , the GP model consists of a mean function μ θ (x) parameterized by θ and a kernel function (covariance function) k α (x n , x m ) parameterized by parameters α (Foreman- Mackey et al 2017).…”

Section: Gp Methodsmentioning

confidence: 99%

Gaussian Process Modeling Blazar Multiwavelength Variability: Indirectly Resolving Jet Structure

Zhang¹,

Yan²,

Zhang³

2023

ApJ

View full text Add to dashboard Cite

Blazar jet structure can be indirectly resolved by analyzing the multiwavelength variability. In this work, we analyze the long-term variability of blazars in radio, optical, and X-ray energies with the Gaussian process (GP) method. The multiwavelength variability can be successfully characterized by the damped-random walk model. The nonthermal optical characteristic timescales of 38 blazars are statistically consistent with the γ-ray characteristic timescales of 22 blazars. For three individual sources (3C 273, PKS 1510-089, and BL Lac), the nonthermal optical, X-ray, and γ-ray characteristic timescales are also consistent within the measured 95% errors, but the radio timescale of 3C 273 is too large to be constrained by the decade-long light curve. The synchrotron and inverse-Compton emissions have the same power spectral density, suggesting that the long-term jet variability is irrelevant to the emission mechanism. In the plot of the rest-frame timescale versus black hole mass, the optical-γ-ray timescales of the jet variability occupy almost the same space with the timescales of accretion disk emission from normal quasars, which may imply that the long-term variabilities of the jet and accretion disk are driven by the same physical process. It is suggested that the nonthermal optical-X-ray and γ-ray emissions are produced in the same region, while the radio core, which can be resolved by very long baseline interferometry, locates at a far more distant region from the black hole. Our study suggests a new methodology for comparing thermal and nonthermal emissions, which is achieved by using the standard GP method.

show abstract

“…For example, JAX may offer speedups attributable to Just In Time (JIT) compilation, at the expense of a more rigid functional programming style. Access to scalable GP implementations may be another deciding factor (Aigrain & Foreman-Mackey 2022).…”

Section: Pytorch and The Autodiff Ecosystemmentioning

confidence: 99%

An Interpretable Machine-learning Framework for Modeling High-resolution Spectroscopic Data*

Gully-Santiago

Morley

2022

ApJ

View full text Add to dashboard Cite

Comparison of échelle spectra to synthetic models has become a computational statistics challenge, with over 10,000 individual spectral lines affecting a typical cool star échelle spectrum. Telluric artifacts, imperfect line lists, inexact continuum placement, and inflexible models frustrate the scientific promise of these information-rich data sets. Here we debut an interpretable machine-learning framework blasé that addresses these and other challenges. The semiempirical approach can be viewed as “transfer learning”—first pretraining models on noise-free precomputed synthetic spectral models, then learning the corrections to line depths and widths from whole-spectrum fitting to an observed spectrum. The auto-differentiable model employs back-propagation, the fundamental algorithm empowering modern deep learning and neural networks. Here, however, the 40,000+ parameters symbolize physically interpretable line profile properties such as amplitude, width, location, and shape, plus radial velocity and rotational broadening. This hybrid data-/model-driven framework allows joint modeling of stellar and telluric lines simultaneously, a potentially transformative step forward for mitigating the deleterious telluric contamination in the near-infrared. The blasé approach acts as both a deconvolution tool and semiempirical model. The general-purpose scaffolding may be extensible to many scientific applications, including precision radial velocities, Doppler imaging, chemical abundances for Galactic archeology, line veiling, magnetic fields, and remote sensing. Its sparse-matrix architecture and GPU acceleration make blasé fast. The open-source PyTorch-based code blase includes tutorials, Application Programming Interface documentation, and more. We show how the tool fits into the existing Python spectroscopy ecosystem, demonstrate a range of astrophysical applications, and discuss limitations and future extensions.

show abstract

Gaussian Process regression for astronomical time-series

Cited by 8 publications

References 79 publications

Photometric detection of internal gravity waves in upper main-sequence stars

Photometric detection of internal gravity waves in upper main-sequence stars

Gaussian Process Modeling Blazar Multiwavelength Variability: Indirectly Resolving Jet Structure

An Interpretable Machine-learning Framework for Modeling High-resolution Spectroscopic Data*

Contact Info

Product

Resources

About