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| celerite | |
|---|---|
| Name | celerite |
| Developer | Foreman-Mackey et al. |
| Released | 2017 |
| Programming language | Python, C++ |
| License | MIT |
celerite
celerite is a software library for scalable Gaussian process modeling of one-dimensional time-series data. It provides a specialized kernel class and fast algorithms to evaluate Gaussian process likelihoods and predictions with linear or near-linear scaling. The project has been used extensively in astronomical time-domain studies and in statistical analysis where large irregularly sampled datasets occur.
celerite was introduced to enable efficient Gaussian process inference for time-series encountered in observational programs such as the Kepler spacecraft mission and the Transiting Exoplanet Survey Satellite program. The library targets problems addressed by researchers at institutions like the Institute for Astronomy, University of Hawaii, the Harvard–Smithsonian Center for Astrophysics, and teams associated with the European Space Agency. It complements broader probabilistic tools developed by groups behind NumPy, SciPy, Astropy, and initiatives inspired by methods from the Princeton University statistics community and the University of Washington machine-learning labs.
The core mathematical idea uses kernels representable as a sum of exponentials, enabling a semiseparable or state-space representation of the covariance matrix. This formulation builds on results from linear algebra used in works at Stanford University, Massachusetts Institute of Technology, and theoretical developments discussed in publications from Oxford University and Cambridge University. The kernel family employed relates to damped harmonic oscillators and mixtures of exponential covariances similar to models used by researchers at California Institute of Technology and analytic approaches found in literature associated with Princeton University and the University of California, Berkeley.
celerite implements an algorithm that factorizes the covariance via a specialized Cholesky-like recursion, yielding O(N) or O(NJ^2) performance where J is the number of exponential terms. The implementation leverages numerical libraries such as BLAS and LAPACK routines commonly used in projects from Argonne National Laboratory and code patterns adopted by SciPy and NumPy. The project provides both Python bindings and C++ backends, with build practices familiar to contributors from Google Research and development workflows used by GitHub-hosted scientific repositories and teams at Microsoft Research.
celerite has been applied to modeling stellar variability in datasets from the Kepler spacecraft, transit timing studies for exoplanet programs like HATNet, radial-velocity analyses associated with instruments at European Southern Observatory facilities, and photometric surveys conducted by collaborations linked to the Sloan Digital Sky Survey. Outside astronomy, researchers at Columbia University, University of Toronto, and the Max Planck Institute for Astronomy have used celerite-style kernels for financial time-series, climatological records, and physiological signal processing in studies connected to the National Aeronautics and Space Administration and the National Science Foundation.
celerite's performance advantages stem from its kernel structure; when the data and model conform, it scales far better than general-purpose Gaussian process libraries used in Google or Amazon machine-learning pipelines. Limitations arise when one requires non-exponential kernels, multidimensional inputs, or non-stationary covariance structures as investigated at research centers such as Imperial College London, ETH Zurich, and Carnegie Mellon University. For those problems, alternatives like state-space Kalman implementations from groups at University College London or inducing-point approximations developed by teams at DeepMind and University of Cambridge may be preferred.
Extensive extensions have connected celerite ideas to state-space representations, low-rank approximations, and sparse precision methods explored in literature from Yale University, Rice University, and Johns Hopkins University. Related Gaussian process toolkits include software emerging from the Stan Development Team, the GPy project at University of Sheffield, and libraries inspired by work at Cornell University and University of Oxford. Cross-pollination with variational and kernel-learning approaches from University of Toronto and Carnegie Mellon University has produced hybrid methods combining celerite kernels with inducing-point frameworks.
Typical usage demonstrates fitting quasi-periodic stellar rotation signals in light curves from the Kepler spacecraft and characterizing granulation noise in radial-velocity time series from instruments at the European Southern Observatory. Case studies published by teams affiliated with Harvard University, Princeton University, and the University of California, Santa Cruz illustrate transit modeling, period inference, and noise marginalization. Tutorials and example notebooks are commonly integrated into analysis pipelines alongside Astropy-based reduction flows and reproducible workflows used by collaborations linked to the Space Telescope Science Institute.
Category:Statistical software Category:Astronomy software