robust dimensionality reductions

Dimensionality reduction (the basic being PCA) is very sensitive to outliers: A single bad pixel can dominate most objectives and thus create a spurious dimension. One of the best and most classic solutions to this is the robust PCA method, which is presented in a (very long) paper with impressive math and beautiful results. Yesterday Hans-Walter Rix (MPIA) and I coded it up and applied it to ESA Gaia RVS spectra, with extensive (and impressive) help from Claude. It looks very promising, especially in capturing oddities in hot stars. Today I worked out that there should be something similar that takes into account data weights (inverses of squared uncertainties), and I wrote down the algorithm (on paper). We'll see.

O-minus-C inanity

In the exoplanet (and, before that, eclipsing-binary) communities, transit-timing variations are described in terms of a quantity called O−C (pronounced “oh minus sea”), which is the difference between the observed transit time and the “computed” transit time. Right now, Abby Shaum (CUNY) and I are using this terminology in our manuscript about phase variations in coherent pulsators with companions, at the behest of Keaton Bell (CUNY). Okay fine! But O−C has this terrible property, which is that the C part depends on the period or frequency you assume. You can completely change the appearance or morphology of an O−C plot just by slightly tweaking the period. And there is no true period of course! There is just whatever estimates you can make. Which are, in turn, affected by what you use to model the O−C. So it is absolutely awful in every way. Not a stable observable, people! Not even identifiable.

high-order integration schemes

I was working on a white paper on ocean dynamics today and I threw in a sentence about how emulators (like machine-learning replacements for simulations) might be working because they might be effectively learning a high-order integration method. I then threw in a sentence about how, in many applications, high-order integrators are known to be better than low-order integrators. I then went to find a reference and... well, I am not sure I can back that up with a reference! I thought this was common knowledge, but it looks like almost all simulations and integrations are done with low-order integrators. Am I living in a simulation? (A simulation integrated with wimpy first-order integrators?)

coordinate-free reading?

The world is O(3) equivariant. Meaning: The laws of physics don't depend on the orientations of things, nor do they depend on the orientation of your coordinate system. But handwriting—and printed words—are not equivariant: Writing systems have a definite orientation and parity. Indeed, it can be hard to read things when they are reversed in a mirror or at an odd angle. Pick up a paper from your desk and read it. Before you start, you have to orient it. How do you do that?

My answer is: Context. I think you try different orientations until one seems to work for the reading. You can't always tell from a single letter (like an M or a W or an O), but you can tell once a string of a few letters or numbers are visible. Inspired by all this, Villar and I are making this data set (among others) for learning and reasoning tasks:

scope of a paper

Emily J Griffith (Colorado) and I have been working on a two-process (or really few-process) model for the creation of the elements, fit to the abundances measured in the APOGEE survey. Our big conversation this week has been about the scope for our first paper: We have so many results and ideas we don’t know how to cut them into papers. Today we made a tentative scope for paper one: we’ll explain the model, deliver a huge catalog of abundance information, and demonstrate the usefulness for practitioners of Galactic archaeology. Then, later, we can actually do that archaeology!

catalogs rant

Should I write this paper?

Abstract: Observational astronomy projects often produce catalogs—of stars, galaxies, quasars, planet hosts, and so on—for use in other projects. How can we use these catalogs responsibly? The answer to this turns out to be complex; it depends sensitively on how the catalogs were made. In particular, if the catalog entries were obtained by operations on a set of (nearly) independent or separable likelihood functions, the catalog can be used in a much wider set of circumstances than if the catalog entries were obtained by operations on a posterior pdf or on likelihood functions involving important shared parameters or shared data or shared prior information. This is true no matter whether the subsequent analyses of the catalog are Bayesian or frequentist. Importantly, at the present day, many important catalogs are being made from the outputs of MCMC runs or discriminative machine-learning methods (classifications or regressions). These catalogs are very hard or even impossible to use for population studies. I demonstrate these points mathematically, and also with toy examples from comology, stars, and exoplanets. I recommend that catalogs be designed and made with the feasibility of particular end-user investigations as explicit requirements.

citing things

I spent a big part of today working on finishing up a paper with Megan Bedell (Flatiron). My job was to fill in missing references. I'm still not efficient at this, more than 30 years in to my astronomy career.

is it possible to write a conceptual ML paper?

With Schölkopf (MPI-IS) and Villar (JHU) and others I am trying to write a conceptual paper about the structure of machine-learning methods. Physicists love conceptual papers! But the ML literature is all about performance of implemented methods. That makes it hard to write a conceptual paper. Referees expect to see performance that beats SOTA on some problem (at least a toy problem). I'm struggling.

infographics?

I find it hard to admit to myself that I (and collaborators) are considering submitting a manuscript to Nature Communications, which is part of the evil publishing empire (though at least it is Open Access). I have been pretty morally pure on this point for many years. But! It is hard to find publishing venues that are truly interdisciplinary. And many of those venues are bad (pirates even, and I don't mean that in a good way).

If we are going to publish in Nature Communications then we need an infographic or good visuals. Today, Soledad Villar (JHU) and I worked through possible visuals and design ideas for a good infographic. I have to say that I benefitted enormously from the extremely informative and compact visualization that Lily Zhao (Flatiron) made for Excalibur (Figure 1 of this paper).

writing for deadline

I don't like the way computer science works, with conferences and deadlines. I could complain about it for hours. Journals are a thing, people! But anyway, at Dagstuhl last week, Villar, Schölkopf, and I decided to sprint out a paper for the physics-and-ML workshop at NeurIPS this year. Deadline is in two days. Guess what I did with all my research time today?

Dagstuhl, day 3

Today was day 3 of Machine Learning for Science: Bridging Data-driven and Mechanistic Modeling at Schloss Dagstuhl.

We had an open discussion about goals for ML in science today. The idea of explainability came up. I liked the comment that explainability (or what counts as explainability) might depend incredibly strongly on field or context. Like it is different in medicine and in astronomy. And, related, the idea of how models are communicated is very context dependent. And maybe very dependent on history. For example, in the future, models might be communicated through APIs rather than scientific papers maybe?

Causation and causal inference was a big theme of the day with Bernhard Schölkopf, Jonas Peters, Bubacar Bah, and Niki Kilbertus all talking about overlapping ideas in causal inference, mechanism inference, differential equation inference, and symbolic regression. Is causation the new framework for machine learning? Many in the room think so.

metallicity and spiral arms

In Milky Way Group Meeting at MPIA today we discussed this paper on spiral structure as observed by Gaia. The paper shows that the spiral arms appear not just in the density of young stars but in their metallicities (at very low amplitude). What does this mean? I think maybe it's just the response of a smoother disk population to a perturbation: If you have a smooth disk with a metallicity gradient in it, and you perturb it, you wind up a spiral in the disk and that spiral appears as a low-amplitude abundance feature, because the spiral involves synchronizing the radial oscillations of stars at different guiding radii (and hence, given the gradient, different abundances). It is easy to work out quantitatively though. Maybe I should do that? Reminds me of what I have been working on with Neige Frankel (CITA), but in the vertical (rather than azimuthal) dynamics.

new paper scope

We had a great meeting today with Kate Storey-Fisher (NYU), Hans-Walter Rix (MPIA), Christina Eilers (MIT), and me to discuss KSF's progress on the ESA Gaia quasar sample. We looked at her large-scale structure results and her jackknifes and discussed paper scope. Options range from a quasar-catalog paper to a selection-function paper to a full cosmological parameter-estimation paper. Of course we decided to do all three! But importantly we decided that this week we would focus on writing a quasar-catalog paper. That's good, and achievable.

do we have the baryon acoustic feature?

Today I posted this tweet (below), which I think explains what happened today! I also gave a talk at MPIA Galaxy Coffee, with Adrian Price-Whelan (Flatiron), about the appearance of stellar parameters in the ESA Gaia XP spectral coefficients.

Seen on @katestoreyfish’s monitor rn. Is that a BARYON ACOUSTIC FEATURE in the @ESAGaia DR3 quasar sample?? #GaiaFete pic.twitter.com/0W0PPJd8H8

— David W Hogg (@davidwhogg) July 28, 2022

discretized vector calculus

On Friday, Will Farr (Flatiron) suggested to me that the work I have been doing (with Soledad Villar) on image-convolution operators with good geometric and group-theoretic properties might be related somehow to discretized differential geometry. It does! I tried to read some impenetrable papers but my main take-away is that I have to understand this field.

me reading?

As my collaborators and friends know, if there is one thing I hate to do, it is spend all day reading the literature. I love and respect the literature! But don't make me actually read it. But today I sucked it up and read some 20-ish papers about characterizing dark-matter halo shapes, to find out if the coordinate-free shape measurements that Kate Storey-Fisher (NYU) and I are measuring are new. I think they are! In almost every paper I read, the word “shape” translated to eigenvalues of the positional variance tensor, or maybe ratios of those. Am I wrong?

refereeing can be very valuable

Christina Eilers (MIT) and I discussed our referee report today, on our paper on re-calibrating abundance ratios as measured by APOGEE to remove log-g-dependent systematics. The referee report came quickly! And it was very useful: The referee found an assumption that we are making that we had not explicitly stated in the paper. And this is important: As my loyal reader knows, I believe that a data-analysis paper is correct only insofar as it is consistent with its explicitly stated (and hopefully tested and justified) assumptions. So if a paper is missing an assumption, it is wrong!

what is gauge symmetry?

After we posted this paper on gauge-equivariant methods for machine learning, we got referee comments that maybe what we are doing isn't gauge. So we spent a lot of time working on gauge! What we are doing can be gauge, but there are additional things to add to make that clear. We are clarifying, but maybe for a next contribution in which we really do full gauge invariance, and things like parallel transport.

finishing the response to referee and adjusting the paper.

As is usual with Publications of the Astronomical Society of the Pacific (great journal!), Soledad Villar and I got a constructive and useful referee report on our fitting paper. We finished our comments and adjustments to the paper today. The referee made an excellent point, which is: Since there are fast Gaussian process codes out there, why ever do interpolation or flexible fitting any other way? Good question! We answered it in the new revision (because sometimes fast GPs don't exist, and sometimes you don't want a stationary process and sometimes you are in a weird geometry or space), which we will update on arXiv soon.

physics-of-sailing literature

I sucked it up and read a bunch of the physics-of-sailing literature today (and on the weekend). Some of the books very correctly attribute the forces on sails and wings to momentum transport. Some of the books very incorrectly attribute them to differences of pressure calculable from Bernoulli effect alone. But in reading it all, I did come to the conclusion that no-one is working in precisely the space we want to work, so I do think there is a (correctly scoped) paper to write. Of course even if there weren't, I couldn't stop myself!