translation, geometry, deep learning, fast GPs

Friday-morning parallel-working session was brief today. I talked to Shiloh Pitt (NYU) about verifying matrix identities using numerical methods. And then we went downstairs for a mini-workshop at NYU CCPP organized by Kyle Cranmer (NYU) and Glennys Farrar (NYU) about physics and data science.

Cranmer led it off with an informal discussion of the different language used by statistics and computer science and applied math and physics. There are lots of words used differently, or that trigger different things. He mentioned “bias” and “correlation” and the uses or meanings of graphs and flowcharts. During the talks more words came up. One subtle one is that data scientists think of a data record as a point in data space (so, say, an image is a point in image space). That isn't always natural for physicists.

Joan Bruna (NYU) gave a nice talk about the geometric properties of deep learning, keying off of the success of convolutional neural networks. He said many interesting and insightful things, but here are a few that stuck with me: The convolutional symmetry at small scales in image space aids the NN in finding a distance metric (or something like that) between images that respects symmetries or structure that is really there. And it does that tractably, or in reasonable time. He claims that any compact symmetry group can be incorporated: That is, he claims that deep learning models can be made to exactly respect any symmetry that has certain properties. That's very exciting for physical applications. Distances between nodes on a graph also represent a geometry; it can be extremely different from geometry on simple manifolds! But the same ideas apply: If there are symmetries, they can be respected by the deep learning algorithms.

Life intervened! But by the end of the day, I made it to Flatiron to see a talk by Dan Foreman-Mackey (Flatiron) about data science, interdisciplinarity, open science, and finding planets around other stars. He gave a lot of credit to his interdisciplinary collaborations. He also mentioned the kinds of translation issues that Cranmer opened with at NYU. On the technical side, he showed his Gaussian-process methods and code and the near-linear scaling that they deliver. As I like to say: If you are doing linear algebra faster than N-squared (and he is, by far) then you can't even represent your matrices. That is, building the matrix itself is already N-squared. After his talk the Flatiron applied mathematicians were in heated arguments about exactly why (in a math sense) his methods are so fast. Foreman-Mackey's code is making possible things in astrophysics that have never been possible before.

betterizing Gaia parallaxes

Because of various bits of bad luck, it was a low-research day today. The one real research thing I got into today was exploring all the nearly-geometric approaches to improving Gaia parallaxes. The idea is: If you are a hard-core astrometrist, you only believe geometric distances. And Gaia measures those! But how can you improve upon Gaia without bringing in additional assumptions about stars, stellar photospheres, stellar evolution, and so on? The answer is that you can't, trivially. However, you can think about approaches that use very minimal additional information, and nothing so dirty and gastrophysical as a stellar model:

You can use joint information of all the stars to improve every individual star! This is what we did in Anderson et al. We assumed that all stars come from a stationary distribution in color and magnitude, but we used a very flexible model for that and trained it entirely on purely geometric information. So it was like an amplification of the geometric information latent in the larger data set, applied to each individual star.

What Dustin Lang (Toronto), Megan Bedell (Flatiron), and I are thinking about is whether we can use stars that appear to move together to make new information. That is, if two stars are co-moving and near each other in an angular sense, they are very likely to be close in radial distance. So we can combine parallax information, and improve both stars. That is a purely geometric method, although it does make (fairly weak) assumptions about the existence of binary stars.

On another thread, Boris Leistedt (NYU) and I are thinking about how to use proper motion to constrain distances. This definitely makes strong assumptions about the Galaxy, but they are very reasonable and testable, and they exist only in the kinematic domain (not the gastrophysical). So that's promising. But it's early days.

To do better than Gaia, you have to make additional assumptions. Duh! But what are the most anodyne and conservative assumptions that we can make that still have the effect of betterizing parallax or distance inferences?

spots, variational inference, bad sci-fi

After the #GaiaDR2 week and all the knock-on consequences, I'm starting to feel a little strung out this week! But I pulled it together for Stars meeting at Flatiron. Brett Morris (UW) was in town, and he talked about the degeneracies between transit depths and star spot statistics and other observables. He is generalizing the star surface model to properly capture those uncertainties. That's important for downstream inferences.

David Blei (Columbia) graced us with his presence. He categorized inference problems into a nested classification, with Gibbs-like problems in the center and fully implicit (you can do simulations but nothing else) problems on the outside. We have problems across this spectrum. He talked about how variational methods capitalize on optimization advances to deliver posterior approximations; this has limitations, but it is far faster than MCMC in most high-dimensional situations. He talked about many other things as well, and we looked at points of contact for collaborations. We are interested in scaling up things we did in the million-source TGAS to the billion-source Gaia DR2.

Late in the day, Rabbi Dan Ain (Because Jewish) and I did an event with Brian Sheppard (Seton Hall) at Caveat NYC, using the (bad) 80s film Short Circuit as our jumping-off point. It was ill-attended, but seriously fun.

LIGO; GD-1

Right after lunch today, Ben Farr (Oregon) gave a seminar about how gravitational waves are detected by LIGO from a data-analysis perspective. He has been a big part of the team that made the LIGO results so probabilistically righteous! He gave some credit to the injection tests in the system for demonstrating that the Bayesian techniques were the highest-performing methods. He showed results on black-hole spins: He finds that either spins are low in amplitude, or else they tend to be aligned with one another and the orbital plane. That's already a fairly substantial result with 6-ish systems; and there will be many more soon. After his talk we discussed noise modeling.

Late in the day, I had a phone call with Ana Bonaca (Harvard) to discuss next steps after her beautiful paper on GD-1 in Gaia. I pitched a method for simulating dark-matter-subhalo interactions with streams that Kathryn Johnston (Columbia) and I worked out many years ago. We discussed how to make simulations that are realistic enough to be useful now.

halo and Gaia

Lauren Anderson (Flatiron) and I looked at some simple selections of M-type giant stars in the Milky Way halo, to see if we see Sagittarius and other halo structures. They didn't jump out as obviously as I expected! But then we looked back at the Majewski et al paper and saw that their color selection was certainly not trivial! At the suggestion of Hans-Walter Rix (MPIA), we also looked at the Gaia CMD paper and the bimodal halo stars that were shown at the DR2 press conference. I am sure that the Milky Way halo will be full of interesting things! Now let's find them.

Also Megan Bedell (Flatiron) and I discussed our BetterTogether project, which has multiple goals. Her work today is to find planet hosts with comoving companions. One issue is that Kepler has such a low angular resolution, the matching between Kepler and Gaia might be difficult or ambiguous. Something to think about, given that we can't really re-photometer either dataset.

#GaiaDR2 zero-day workshop, day 3

Today was the third and final day of our Gaia DR2 zero-day workshop. My goodness it was a fun week. Many of the participants told me that they would remember this week for the rest of their lives! Now that's not something I hear every day. And the participants here in NYC were very much focused on learning what is in the data, and exploring the data. There was no sense of trying to rush out publications or results. I loved the atmosphere.

In my own research today, I worked with Dustin Lang (Toronto) to understand the SDSS-III spectra that overlap the white-dwarf parts of the UV color–magnitude diagram that David Schiminovich (Columbia) and Lang showed yesterday. It wasn't obviously simple, but I have ideas about making a latent-variable model for it: Predicting spectra from photometry!

In the lunch-time check-in session there were some really impressive results. One was a big model for stellar physical parameters, and extinctions in a two-component model by Eddie Schlafly (LBNL). He pointed out that since Gaia gives distances and colors, it is sensitive to even fully gray extinction. So it provides a new window into extinction. Since his model involves simultaneously modeling stellar multi-band photometry (combined from many missions) along with the intrinsic properties of every star, it got big fast. I think it was at 800,000 parameters today. Optimized! That's pretty good for day three.

Another beautiful set of results at the check-in were visualizations of tidal features: Sarah Pearson (Columbia) visualized the tidal tails of Palomar 5, hoping to find them extend further than ever before. Chervin Laporte (UVic) visualized the anti-center stream and made the case that all of its kinematic properties are consistent with it being a tidal arm coming off the Milky Way from an interaction (with Sagittarius, I guess?). The morphology of the anti-center stream really is sharp, like a fold caustic.

In more general data-understanding categories, Sergey Koposov (CMU) scanned through proper-motion space, showing us low-parallax (that is, non-close) stars in different proper-motion bins. That highlighted a lot of streams, clusters, and anisotropies. And Andy Cassey (Monash) showed us how good (or bad) astrometric excess variance (and also radial-velocity excess variance) is at detecting binary stars. The answer is: Promising, but not calibrated usefully yet. In an ideal world we would build a self-calibrated model of what causes the variance and then use the residuals to detect binarity.

There were many more impressive things today, about the nearby volume, about comoving stars, about detailed chemical abundances, about the GD-1 stream (and possible progenitor!), and about kinematics of the disk and kinematics of the bar; too many things to mention here. Thank you, Gaia Collaboration.

#GaiaDR2 zero-day workshop, day 2

It was a little harder to get up this morning after yesterday's 13-hour day, but I still made it in early for the second day of the Gaia DR2 zero-day workshop. We had about 70 yesterday and still maybe 50 today; the room was at capacity and we had people all over the 3rd floor of the (very generous) Flatiron Institute.

Dustin Lang (Toronto) coined the name "BetterTogether" for a project that Megan Bedell (Flatiron) and I started to find all the comoving pairs that can be confidently identified in the data. This kind of work isn't new: Semyeong Oh (Princeton) had big impact with her comoving-pair work in Gaia DR1. But what's new is the idea of using the co-moving-ness to betterize the parallaxes of both stars, and in particular the less luminous (and hence noisier) star. So pairs that are WD-MS or MS-RGB are most valuable! This project builds conceptually on work I did with Morgan Fouesneau (MPIA) and Hans-Walter Rix (MPIA) in the TGAS–PanSTARRS overlap.

The issue is that you can't trivially look at every pair in a 1.3-billion-star catalog. There are 1e18 pairs! And even deciding not to look at a pair takes time. So Lang started to build us a very nice data structure for doing the two-point work while Bedell looked at the restricted sample that matches the Kepler targets.

In the mid-day check-in, some really impressive things were shown. Lang and David Schiminovich (Columbia) showed a set of UV color–magnitude diagrams that literally caused the audience to gasp. Stars look so different in the UV! And there are stars where there “shouldn't be”, because of binarity or chromospheric activity or something. So much structure! Kohei Hattori (Michigan) showed a hyper-velocity star that looks like it was launched from the disk towards the Galactic Center. Tim Morton (Princeton) showed that the Gaia stellar radii are good enough to bring out the radius gap in Kepler exoplanets. Ana Bonaca (Harvard) and Adrian Price-Whelan (Princeton) showed that the gaps in the GD-1 stellar stream are really there, and also had hints of kinematic offsets that might indicate dark-matter substructure!

On a more astrophysical note, Kareem El-Badry (Berkeley) spent yesterday and today becoming an expert on white-dwarf physics and was able to give a reasonable, quantitative explanation of the (exquisite, surprising) morphology of the white-dwarf part of the color-magnitude diagram, including a generative model! He finds that even if the IMF and star-formation history are monotonic, the white-dwarf mass distribution is not, because of wiggly initial-mass–final-mass relations. That gets much (but not all, I'm interested to note) of the multi-modal structure in the diagram.

#GaiaDR2 zero-day workshop, day 1

Today was Gaia DR2. My day started at 05:00 for the press release, and ended at 18:00 with the champagne toast we lifted to the entire Gaia DPAC, who have actually changed the world. Amazing things happened during the day, way too much to report on in this forum. So I will just tell you what I was paying close attention to today.

Ana Bonaca (Harvard) and Adrian Price-Whelan (Princeton) looked to see if they could see the long, cold stellar stream GD-1. They found it, and it is in the data at immense signal-to-noise. It is still subtle though, reminding us that finding brand-new streams in the data will still be a challenging project. Their map of the stream confirms the gaps we thought we saw many years ago, and there might even be hints of kinematic distortions at the edges of those gaps. If any of that turns out to be real, we might be able to directly measure substructure in the stream.

Megan Bedell (Flatiron) did the match between Gaia and Kepler and made basic visualizations. These already revealed something interesting: Although there are very few planets around blue subdwarfs (and no, I have no idea what they are, but blue stars below the main sequence), the fraction of blue subdwarfs that host planets looks like it is way too high. What could this mean? Perhaps even more interesting: The planet orbital periods are too short for the planets to have survived the stellar evolution up the red-giant branch and back down again, so there is an astrophysical mystery there too.

In the Gaia DR2 press conference, the team attributed complexity in the white-dwarf color-magnitude diagram (and check it out, it is beautiful!) to different compositions (or maybe surface compositions) of the white dwarfs in the different stripes or modes in the diagram. Kareem El-Badry (Berkeley) did some digging in the white-dwarf world and finds that this is not a good explanation for the differences, or at least not a complete explanation. He thinks there must be some complexity to the mass distribution of white dwarfs, unless the cooling models have serious issues. And he also thinks that the diagram is not showing lots of white-dwarf–white-dwarf binaries, but also not showing zero of them!

There were some reporters at the event. I thought this story by Lee Billings (Scientific American) captured a lot of the spirit of the day!

not ready for LSST!

Fed Bianco (NYU) gave a great astro seminar today at NYU about the LSST project. She focused on time-domain and transient aspects, but did a good job of discussing the methods for making objective trade-offs in the cadence and survey-strategy space. Arguments broke out about filters and about data access. That was interesting and valuable. The project is amazingly ambitious, especially as regards data analysis and permitting and enabling non-trivial computational work by outsiders.

ready for DR2

Today I spent all my research time on details in preparation for Gaia DR2, which happens on Wednesday. Unfortunately, my preparation wasn't exactly research: I was working on building access, catering details, room arrangement, invitations, and encouragement. We have some forty people (not all of them astronomers) converging on Flatiron to work together on the new data.

One thing has become absolutely clear over the last few weeks, in part because of hard things some people have said to me, about themselves and about others and about perceptions: Our goal this week is to have fun. And learn. It isn't to be first on things. It is to learn things we couldn't have known before. The idea is to cooperate, to share, and to support the global Gaia community. I think we have been doing that for years now (I sure hope we have), but it is worth re-stating daily, especially when there is a lot of anticipation and excitement and, frankly, anxiety, about the upcoming data release.

Here's to 1.6 BILLION stars. In less than 36 hours.

finished a single-author paper!

In parallel-working session this morning, I finished and prepared for submission (to arXiv) my paper on a likelihood function for Bayesian data analyses with the Gaia data.

fiber robots; gravitational waves

At lunch, Mike Blanton (NYU) and I discussed operational matters for SDSS-V. One thing we discussed was how to have different cadences for different types of stars, when we have a huge field of view and finite target densities for each stellar type. His view is that we should re-formulate the question in terms of sky patches, and set cadences for particular sky patches, and then observe the stars inside those patches as makes sense given the patch cadences. We also asked how to formulate this problem in terms of a scalar objective function or cost function, which is essential if we are going to let loose with optimizers.

The other thing we talked about is positioning a dense set of fibers. There are configurational constraints on the path that the fiber robots can take if they are going to avoid collisions and conflicts. Can we resolve these? And what engineering literature do we look to for the best or standard solutions to problems of this type. I am sure there is a huge literature, because it connects to all sorts of things like milling machines and warehousing and things like that. But I need keywords. I promised to deliver some to the SDSS-V Collaboration.

At the end of the day, Vicky Kalogera (Northwestern) gave a great talk about gravitational wave observing. Her group has been essential in converting the theory of gravitational-wave sources into practical schemes for performing principled probabilistic inferences on the data. She said, in her talk, that in the process she has become an observer, but she only observes in the gravitational-wave sector! And it is really true: She referred consistently in her talk to astronomers as “electromagnetic observers”. I love that! But really, the LIGO results are incredible, and Kalogera deserves a lot of credit for them.

a non-parametric model of the MW acceleration field

At Stars group meeting, I spoke about Ana Bonaca and my new paper looking at the information content of cold stellar streams in the Milky-Way halo. It is a huge document, with lots of results, but my absolute favorite is this: As we make the potential model for the Milky Way more flexible, each stream constrains each potential parameter less well. This is the issue with information studies: They depend strongly on the model flexibility! But something cool happens in the limit of very flexible potential model: Each stream appears to end up constraining the local acceleration field, local to the current position (not past position) of the stream. This has lots of consequences: One is that if this is true, we can just model each stream independently, in a flexible potential, and then interpolate the acceleration constraints they deliver with a flexible or non-parametric model as an interpolator! That would make stream fitting more tractable than it is now, not less (and most other ideas we have are computationally impossible at present).

In the discussion, Vasily Belokurov (Cambridge) suggested that we might get more information—and more global information—if we modeled the density of stars along the stream. He is reacting to the point that the Bonaca stream model is a stream-track model, not a full six-dimensional distribution function. Belokurov might be right; we should add something like this to the paper.

After I spoke, Jackie Faherty (AMNH) got us really excited about what Gaia has done and will do for nearby moving groups of young stars (like open clusters). She believes that several of the “connected components” in the Oh et al paper are new, previously undiscovered young clusters, and that Gaia DR2 might find hundreds of new members, going down the main sequence! That's amazing. I hope it's true.

chemistry in protoplanetary disks

My research highlight today was a great talk by Ilse Cleeves (Harvard) about ALMA observations of the dust and molecular gas in proto-planetary disks. She showed that you can see chemical gradients in the disks, including rings and lines of formation of molecules. Much of what's visible is on the outer surfaces of the disk, which is illuminated by the young, accreting star, because the interior parts of the disk are optically thick. Because the chemical models are heavy and imperfect, I proposed looking at latent-variable models to describe the observed molecular abundances; maybe there are interesting features to be found even without relying on physical or chemical models?

The most remarkable thing she showed is time-domain chemical results: She can see chemical changes in real time as the disk responds to (presumably) stellar flares on day-ish time-scales! We discussed methods for distinguishing different kinds of events that might be triggering the chemical changes. Expect denser time sampling in the future; it's ALMA proposal-writing season!

Technically, my favorite part of Cleeves's work is that she does all of her model-fitting and hypothesis comparing in the visibilities. That is, she doesn't make an image from the interferometric data and then model it: She takes her models to the Fourier domain and compares to the raw data. That's classy.

Gaia writing, neutrino masses

In a remarkable turn of events, I finished writing a paper today! More specifically, I finished what I would call the “zeroth draft” of my paper (or really just short note) on the Gaia likelihood function. I checked in with Hans-Walter Rix (MPIA) and he encouraged me to take it through some revisions and submit it to arXiv. We shall see if I make it.

At lunch-time, the NYU CCPP Brown Bag talk was by Derek Inman (NYU) on neutrino masses. He explained what's known from oscillation experiments, from beta-decay experiments, and from cosmology. The laboratory bounds put lower limits on the neutrino masses, and the cosmological bounds put upper limits. The cosmological bounds are very strong, but they are also very dependent on having a very good cosmogonic model. That is, they are not even close to being model-independent. He did a nice job explaining how the flavor eigentstates relate to the propagation eigenstates, and the mass hierarchies. It is a nice set of problems.