Gaussian process in astronomy and astrophysics

How it is used

Astronomy data arrives in gaps. A telescope sees a star or a galaxy only when the weather, the season and the queue allow, so a record of changing brightness over time (a light curve) is a scatter of points, not a continuous line. A gaussian process is a way of describing all the smooth curves that could plausibly pass through those points, and of saying how confident one can be at each moment in between. The astronomer chooses a kernel, a rule for how strongly two measurements separated by some gap should resemble each other, and the data then fixes the rest. In the examples here, gaussian processes interpolate supernova light curves across time and across colour bands, and smooth counts of stars into continuous maps of the Milky Way's disc.

The output is often not the final answer but an input to something else. One study turns each exploding star's irregular observations into a regular grid of brightness and uncertainty, a kind of image that a neural network can then classify. Another uses interpolated curves to line up a newly seen supernova with ones already catalogued, so the two can be compared at matching moments. A third takes published gaussian process maps of stellar density and feeds them into a physical calculation of the mass of the galactic disc. In each case the method supplies a continuous, uncertainty-aware version of patchy observations.

Why researchers use it

The alternative is to assume a shape. One could fit a template curve, or a polynomial, or a physical model with a handful of adjustable numbers. That works when the shape is known, and misleads when it is not. A gaussian process asks far less: it assumes only that nearby points should be similar, with the kernel setting how quickly similarity fades. This matters in astronomy because many sources vary in ways that are not well described by any simple formula, and because an honest error bar is often as important as the central value. Cosmology and galactic dynamics both propagate measurement uncertainty through long chains of inference, so a method that carries uncertainty forward is worth the extra cost.

In the record

Limits

The modesty is partly an illusion: the kernel and its length scales are assumptions, and in these studies they are often set by hand or from the spacing of the data rather than learned. Choose them badly and the curve will oversmooth a real feature or invent wiggles in noise, while still reporting tidy error bars. The method also says nothing about physics, so an interpolated curve can run through regions no star could occupy. Cost grows steeply with the number of points, and where gaussian process output is fitted with an analytic function afterwards, the uncertainty it carefully tracked can be quietly discarded.

Written by AIxSci: the background from general knowledge, the examples from checked records.

Related

• Gaussian process: the idea, across every field
• AI in astronomy and astrophysics

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