local linear regressions

For some reason, even though I dislike deep learning, I love local linear regressions. My friends tell me that RELU networks are locally linear, so I am really just a hypocrite. Anyway, today Adrian Price-Whelan and I built a regression in which we find nearest neighbors (among the training-set objects) in the space of ESA Gaia DR3 Bp/Rp spectral coefficients and, among those neighbors, we fit a locally linear model to predict the parallax of the test object. Technically we use a clever trick called the ”schmag“ but which should probably be called the reduced parallax, in which we correct the parallax into the inverse of the square root of the luminosity. Why? It's so we can use the parallax errors fairly, and include training-set objects with negative parallaxes.

Hill I will die on: If you cut your sample to high SNR parallaxes or positive parallaxes, you will bias any regressions you do to predict parallaxes or distances or distance moduli!

Gaia Hike, day 5

Today was day 5 of the Gaia Hike. Jason Hunt and I looked at a file of kinematic information prepared by Adrian Price-Whelan (Flatiron) to look at the possibility that the Milky Way has a low-amplitude counter-rotating disk of stars. We found nothing. This was in contrast to what Claudia Bielecki and Federico Sestito were finding—with a similar file created by George Kordopatis. By the time I had to leave the meeting, we hadn't resolved the discrepancy. It's interesting either way!

Gaia Hike, day 4

On day 4 of the Gaia Hike, Neige Frankel (CITA) and I tried to look for the signature of the Snail (the vertical phase spiral in the Milky Way stellar kinematics) in metallicity. It's visible in the Gaia Collaboration chemical cartography paper. But it's not trivial to find it. We got a tiny hint of it using RVS metallicities, and we resolved to try some more tomorrow. We also figured out that it should be there even if the Snail is a late production of a late interaction: Abundance gradients FTW.

Gaia Hike, day 3

Today was the literal hike day of the Gaia Hike. I couldn't go, for uninteresting technical reasons. So instead I spent my time preparing hack projects for those who are looking for straightforward hack ideas and want to learn. I got stuck many times and Adrian Price-Whelan (Flatiron) helped me un-stick. I guess straightforward isn't straightforward! Anyway, I produced this document which contains hack ideas. It is just a start, just a stub, but maybe it will be useful?

Gaia Hike, day 2

Today was day two of the Gaia Hike at UBC. The results of yesterday's discussions and hacking were discussed in the morning and then we moved to tutorials about how to use the ESA Gaia data responsibly. From my own personal perspective, the highlight was a big tutorial from George Seabroke (UCL) on the high-resolution RVS spectra. His presentation went through all the properties and issues with the data, including things like overlapping spectra on the focal plane. It was really impressive, incredibly useful, extremely detailed, and an amazing representation of how complex and challenging a mission like Gaia is. Congratulations to the entire DPAC for pulling this off!

Gaia Hike, day 1

Today was the first day of the Gaia Hike hosted at UBC and led by Neige Frankel (CITA). The day started with business cards (short intro talks from everyone), followed by an attempt to find common themes across participants. Once the themes were identified, we split into groups to talk about what we might do this week with the ESA Gaia DR3 data. I ended up in a mapping and visualization group, which was fun, and (of course!) we closed out the day hacking on a piece of the data on stellar parameters, trying to figure out why the stellar parameters don't look exactly as we expect.

coordinate freedom?

I spent the weekend recovering from the Gaia Fete. During my recovery day, I worked on very long-term projects. For example, I spent some time working on how to express the following issue in my work (with Villar) on exact symmetries:

The mathematics and computer-science communities call these exact symmetries “equivariances” and they are imagining that the data or the laws of physics are precisely equivariant in the sense that if you (say) rotate all the inputs, you get a rotated output. But this is not the main reason that we write the laws of physics in terms of exact symmetries! We write the laws of physics in terms of invariants because we want our laws of physics to be coordinate free. This is required even when the laws aren't equivariant! But I have trouble making this distinction clearly, since the mathematical implementations of the two symmetries are identical. There's some cool philosophy here: Does coordinate freedom enforce symmetries? What would it even look like for the laws of physics to be asymmetric but coordinate free?

Dr Tomer Yavetz

Today Tomer Yavetz (Columbia) defended his PhD, which was in part about the dynamics of stellar streams, and in part about macroscopically quantum-mechanical dark matter. The dissertation was great. The stellar-stream part was about stream morphologies induced by dynamical separatrices in phase space: If the stars on a stream are on orbits that span a separatrix, all heck breaks loose. The part of the thesis on this was very pedagogical and insightful about theoretical dynamics. The dark-matter part was about fast computation of steady-states using orbitals and the WKB approximation. Beautiful physics and math! But my favorite part of the thesis was the introduction, in which Yavetz discusses the point that dynamics—even though we can't see stellar orbits—does have directly observable consequences, like the aforementioned streams and their morphologies (and also Saturn's rings and the gaps in the asteroid belt and the velocity substructure in the Milky Way disk). After the defense we talked about re-framing dynamics around this idea of observability. Congratulations, and it has been a pleasure!

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.

discovering quantum physics, automatically?

I have been working on making machine-learning methods dimensionless (in the sense of units). In this context, a question arises: Is it possible to learn that there is a missing dimensional input to a physics problem, using machine learning? Soledad Villar (JHU) and I ignored some of our required work today and wrote some code to explore this problem, using as a toy example the Planck Law example we explained in this paper. We found that maybe you can discover a missing dimensional constant? We have lots more to do to decide what we really have.

making a mock Gaia quasar sample

I had conversations today with both Hans-Walter Rix (MPIA) and Kate Storey-Fisher (NYU) about the upcoming ESA Gaia quasar sample. We are trying to make somewhat realistic mocks to test the size of the sample, the computational complexity of things we want to do, the expected signal-to-noise of various cosmological signals, and the expected amplitude and spatial structure of the Gaia selection function. We have strategies that involve making clean samples with a lognormal mock, and making realistic samples (but which have no clustering) using the Gaia EDR3 photometric sample (matched to NASA WISE).

making Fourier fitting super fast

At the request of Conor Sayres (UW), I have been looking at distortion patterns in the SDSS-V Focal Viewing Camera (FVC), which is the part of the system that looks at whether the focal-plane fiber robots are where they need to be. The distortions are extremely bad; they are large in amplitude and vary on extremely small scales on the focal plane. So I have to fit an extremely flexible model. Here are my comments:

First, you should use mixtures of sines and cosines for problems like this. Not polynomials! Why? Because sines and cosines do not blow up at the edges.

Second, you should punk fast Fourier transform (FFT) codes to speed up your regressions. I wrote code to do this, which wraps the finufft best-in-class non-uniform FFT code in scipy.sparse linear-algebra code. This wrapping makes the FFT operators into linear-algebra operators and permits me to do solve() operations. That move (wrapping FFT in linear algebra) sped up my code by factors of many!

coordinate freedom vs equivariance, again

With Soledad Villar (JHU) and others I have been discussing making generalizations (or restrictions?) of image convolution operators to make machine learning respect more symmetries. One kind of generalization is going to 3-d images, and another is making the weights in the convolution filters geometric objects, like vectors, pseudovectors, and tensors. Then we developed a group-averaging technique to make these geometric filters equivariant. And now we are considering products and contractions of these geometric objects to make universally approximating function spaces. I don't love the word “equivariant” here: In my view the symmetries are coordinate freedoms, not relations between inputs and outputs. But the machine-learning world has spoken.

accretion and mathematical physics

In the CCPP brown-bag today, Andrei Gruzinov (NYU) went through the full mathematical-physics argument of Bondi (from the 1950s) that leads to the Bondi formula for accretion from a stationary, thermal gas onto a point mass. He also talked about a generalization of the Bondi argument that he developed this year (permitting the gas to be moving relative to the point mass) and also a bevy of reasons, both theoretical and observational, that the Bondi solution never actually applies ever in practice! Haha, but beautiful stuff.

generalized flat-relative extraction

I asked, in the Astronomical Data Group meeting at Flatiron, about the method of spectral 2D-to-1D extraction known as flat-relative optimal extraction. It's genius, and simple, but it makes strong assumptions about the spectrograph. I asked how we might improve it. And I think I maybe have a plan. The idea (which was thrown out by Megan Bedell) is to make the spectral representation something continuous, and evaluate it individually at every pixel, not just once per column of the detector. This should improve extraction. And it is relevant to the NASA proposal I am writing with Matt Daunt.