# Photometric redshift - empirical methods (machine learning)

I am currently learning about estimation of photometric redshifts with machine learning methods (or empirical methods in general). These methods use the knowledge about the photometry and the spectroscopic redshift of many galaxies in order to infer a mapping between the photometry and the redshift. Then, based on this mapping, redshifts can be estimated for the photometry of other galaxies.

I've read that for empirical methods it is crucial that the training data (i.e. the data from which the mapping of the photometry to the redshift is inferred) represents the galaxies for which estimated redshifts are desired in the future. I understand that this is crucial, but in what sense does the training data represent a certain distribution and in what sense are other galaxies represented or not represented by this training data? How do I know if a galaxy is well represented by the training data so that I can estimate a redshift for the galaxy?

Would the galaxy have to be from the same region? Does it have to have the same mass? What are the factors to look at, if I want to know whether a galaxy is from the same distribution/is well represented by the training data?

This was too long for a comment, but is not a real answer since I'm not completely sure, but:

My guess is that "representing the galaxies" refers to the "type" of galaxy that you intent to observe, where by "type" I mean e.g. Lyman-break galaxies (Steidel et al. 1996), Lyman $$\alpha$$ emitters (Partridge & Peebles 1967), sub-millimeter galaxies (Blain et al. 2002), (U)LIRGS, etc.

These terms all refer to selection methods (i.e. observational techniques), and hence also to physical differences. The closer the training data are to the observed sample, the better your algorithm will be at linking their redshifts to their photometric properties.

Mass is just one property, there's also e.g. dustiness, star-burstiness, stellar population, age, and others. "Region" is probably less important, but since the clustering of galaxies also affect their properties (e.g. their morphology, Dressler 1980), it could potentially influence the result.

• Huh? Downvoted? Why?
– pela
Jan 13, 2020 at 11:38

Determining the photometric redshift means looking at the light from the galaxy through a limited number of color filters (or bands), and infering the redshift from that data. For instance, the light coming from the galaxy can be measured in the visible light band, the infrared band,... This constitutes the photometry. Then the redshift is determined either by fitting a physical model to the light in each band, or by using machine learning.

With machine learning, the training features consist in the amount of light in each available band, and the training labels are the spectroscopic redshift. If the training data is representative of the real data, that means that for each sample in the real data, there are galaxies in the training data that have similar amounts of light through the different bands.

In short, to know if the data is representative, you have to look at where it is in the feature space.

Would the galaxy have to be from the same region?

From a mathematical perspective, yes, it has to be in a region of the feature space where there are several training samples. However, this does not mean that it is in the same region of the sky! Quite the contrary, there is no reason to believe that galaxies that are nearby in the plane of the sky will have similar light curves.

Does it have to have the same mass?

There is a correlation between galaxy mass and galaxy type. And there is a strong correlation between galaxy type and light emitted. So looking at the mass to know it the dataset is representative shouldn't be awful, but still is no replacement for simply looking at the photometric data.

• Well there is some correlation between galaxy type/morphology and location: Denser environments (e.g. the center of clusters) have an increasingly larger fraction of ellipticals and S0 galaxies, and a corresponding smaller fraction of spirals and irregulars.
– pela
Dec 20, 2019 at 13:40