Today, Lauren Anderson (Flatiron) showed me some awesome visualizations of the color-magnitude distribution (CMD) of stars as a function of position in the Galaxy. There are variations! The question is: What part of the variation is due to dust and what part is due to metallicity (or composition) and what is due to star-formation history (or age)? We don't know how to answer these questions! But one thing we did is take some derivatives of the CMD with respect to position. Is this a sensible thing to do? Could we treat the CMD as data and try to fit it with a latent-variable model? That is, what is the right approach to quantifying and interpreting the CMD variations around the Galaxy?
Andy Casey (Monash) is in town to work on Gaia DR2 and he has been looking at using the radial-velocity uncertainty (which, in the database, is really an empirical scatter across measurements) to identify binary stars. This is a great idea. I was pitching various ways to calibrate this quantity to make it more reliable and then he reminded me that many binaries have tens of km/s semi-amplitudes! Duh. The signal is super-strong. This is a great #GaiaSprint project!
Christina Eilers (MPIA) and I had success today on spectroscopic parallaxes for stars at the top of the red-giant branch: We are now able to predict absolute luminosities (and therefore parallaxes) with almost 10-percent accuracy! That makes them only slightly worse than red-clump stars, and we think there is more information to exploit in the data. Our method is a bit hacky: We are still using spectroscopic quantities from the APOGEE pipelines and not just the spectra themselves, but it should point the way to a cleaner method soon.
Stars Meeting at Flatiron was a great success. One exciting project in progress is that Ruth Angus (Columbia) is finding relationships between exoplanet occurrence and host-star orbital actions! Now the causal part: Is this because of age or abundances or dynamical interactions? Another is that Ben Montet (Chicago) proposed that we find non-transiting hot-jupiter exoplanets by looking at surface rotation: There is at least weak evidence that stars with hot jupiters spin faster—or appear to. That's exciting as another possible indirect planet-detection technique.
Today was the first day of what's looking like it's going to be a very full week! Andy Casey (Monash) arrived in town, to work on binary stars and self-calibration of stellar parameter pipelines. Natalie Hinkel (Vanderbilt) showed up, to also work on self-calibration, in the context of her Hypatia Catalog. Christina Eilers (MPIA) showed up to work on data-driven approaches to estimating parallaxes from spectroscopy, which is a project we are re-booting from last summer. Alex Malz (NYU) dropped by to discuss issues with inferring redshift distributions from biased photometric redshift measurements. Kate Storey-Fisher (NYU) came to talk about mock catalogs for large-scale structure. And I continued conversations with other group members about their #GaiaSprint projects for next week. By the end of the day, Eilers and I were getting parallax predictions at the 20-ish-percent level, but we need to do a factor of two better!
Today Michael Joyce (LPNHE) gave a great talk about analytic and conceptual directions towards understanding nonlinear gravitational growth of structure in the Universe. He focused on the stable-clustering approximation, which dates back to Peebles, is very predictive over a range of scales, and can be used to test simulations. At lunch afterwards, we discussed the great importance of studying gravity analytically, a point made often and well by Roman Scoccimarro (NYU).
Prior to the seminar, Ellie Schwab-Abrams (AMNH) and I discussed self-calibration for pulsar timing arrays, which we think and hope could lead to a new era of gravitational interferometry and enormously increase the sensitivity to long-term gravitational-wave signals. We decided to start by solving the radio-astronomy problem, which has yet to be solved in the literature, because no radio telescope has the problem that the relative velocities of it's elements are unknown!
My data started with two great conversations about imaging and data science. In the first, Marc Gershow (NYU) and Rui Wu (NYU) came to talk to me about their project with fruit-fly larvae (mentioned here). They do a multi-step dimensionality reduction on the (immense amounts of) video data they have and then look for discrete behaviors and discrete changes in behavior. We discussed the possibility that we could re-cast all or parts of this problem as a regression, that would be fast and interpretable. It maps on to a lot of problems we are doing with stars, especially The Cannon and derivatives thereof.
In the second conversation, Mike Blanton (NYU) and Dou Liu (NYU) discussed with me their project to generalize spectro-perfectionism into a method (mentioned here) for combining badly and irregularly sampled imaging. We discussed a certain part of the problem that I was discussing many moons ago with Sam Roweis and Adam Bolton: The method involves a renormalization step, and this renormalization is very sensitive to details. Indeed, when Roweis died, he and I were looking at whether we could replace this step with something that makes more sense. I advised Blanton and Liu to take a calibration approach, where they run not on the flatfield-normalized spectral data, but run on the raw data and the flatfield data and deliver a ratio of results. For now. Until we can figure out the Right Thing To Do (tm).
I spent the day at a workshop at UMD on the connections between (what I would call) data science and (what the community calls) multi-messenger astrophysics. Multi-messenger means that there is information coming not just from photons, but maybe also neutrinos, or cosmic rays, or (importantly these days) gravitational waves. The idea is for a group of people to build a white paper that makes the case for joint programs between data-intensive research and MMA research. I spent some of my capital at the meeting arguing that we should make sure we focus on the whole scientific process, that includes not just discovery of transient events but also continuous-wave sources, sub-threshold populations, and all the machinery we need for inference and modeling as well. The future of data science is putting immensely complicated physical simulations inside the inference loop (which might be an optimization process or a sampling process). I learned a lot, both about MMA and about the NSF, who proposed that we hold the meeting: They use this kind of input in making high-level funding decisions. That is, programmatic decisions. By the end of the day we had 30 pages of text. In one day!
My morning started with a great call with Ana Bonaca (Harvard): She can make a very simple simulation of a cold stream that creates a gap in the stream and a spur of stars off the stream from the gap, looking extremely similar to the features found by her and Price-Whelan in the GD-1 stream in Gaia. We are looking at doing a little perturbative physics and building an atlas of possible stream features, in different physical regimes. We discussed a bit the first set of figures. Part of the point of the project is to work out all the dimensionless numbers that put stream interactions (with, say, dark-matter substructures) into different calculational regimes.
Today we had the first-ever Astronomical Data Group Meeting. The rules are: You must bring a plot, and you get a time period of (1 hr)/N where N is the number of people in the room to get feedback. It was fun: All of the plots (even Foreman-Mackey's) related to the Gaia DR2 data. I asked the crew whether the stars below the main sequence in the Gaia color–magnitude diagram are very low in metallicity? And if so, shouldn't we take spectra? Anderson thinks maybe they are just issues with crowded fields. That is, issues in the data. Problems with chasing outliers!
After that I had long sessions with Ellie Schwab-Abrams (CUNY), and Jonathan Bird (Vanderbilt). Schwab-Abrams and I are trying to convert my question about self-calibrating gravitational-wave pulsar-timing arrays into the equivalent question about self-calibrating radio telescopes. It is very similar! But we have to take into account the 6-space position not the 3-space position, and we also have to deal with light travel time issues that we can't control with delay lines! But the payoff is immense: I naively expect a factor of more than a billion increase in sensitivity of the arrays if we can do it. Yes I said billion. I hope I'm right.
Bird is finishing his paper on the age–velocity relationship in the disk. We went over discussion points. I recommended explicitly challenging the assumptions and saying what we think would happen if we relaxed them, both in terms of the results and in terms of model complexity. My problem (as it often is in projects) is that I care about the method much more than the astrophysical results.
Jonathan Bird (Vandy) is in town for two days, to finish a paper on heating in the Milky Way disk. The model is a hierarchical probabilistic model that generates the ages and vertical velocities of all the red-clump stars in a big part of the APOGEE data, where the ages come from C and N abundances from Ness and the velocities come from APOGEE and Gaia. He gets very precise answers! But there are deviations between the data and the model in the space of the data, and we debated how important these are to our conclusions.
Lauren Anderson (Flatiron) decided today that she has to down-select from many Gaia DR2 projects to one single Gaia DR2 project. Good idea! And in discussing this with her, I realized that I also needed to do this. We didn't get to final decisions.
Too many things today for one blog post! So just a rapid-fire list. Matt Buckley (Rutgers) and Adrian Price-Whelan (Princeton) and I discussed whether we could, in practice, measure phase-space six-volumes given a point-set in Gaia or a future data set. It isn't clear, so we started by designing some extremely simple simulations to test.
Price-Whelan and I discussed our myspace project to find the nonlinear transformation of the phase-space data near the Sun to make the phase-space structure as compact or informative as possible. We have a plan for implementation of the data-science side of the project, but we have no idea whether anything we find will be interpretable!
We had our first Stars Meeting under the new rules that we established last week. The objectives are, more-or-less: We want the presenters to be less prepared and we want the audience to be more engaged. We created some rules or guidelines to help achieve these objectives. And the meeting went well! Among other things that happened in this meeting, Price-Whelan showed a forming star cluster he found in the Milky Way halo, possibly connected to the Magellanic gas stream, and John Brewer (Yale) showed micro-tellurics (tiny atmospheric absorption lines) found in some of the very first R=150,000 EXPRES spectra.
On that last point: Brewer found these tellurics by observing a B star, which has no narrow lines (and almost no lines at all), so the narrow absorption lines must be intervening. Megan Bedell (Flatiron) has a data-driven method for finding tellurics even in very featured, narrow-lined spectra, by exploiting the causal structure: Star lines move with the star, atmosphere lines move with the atmosphere! She confirms at least qualitatively, at least some of Brewer's lines. I expect that we have some nice points to make in the comparison.
Oh, and: Unmodeled telluric absorption might be the limiting systematic in exoplanet RV surveys, right now or in the near future.
My day was made low-research by the realization on waking that NASA ADAP proposals are due on Thursday, and not next week as I had, perhaps self-servingly, believed. That blew most of my day. Only research highlight was giving an informal talk at the NYU Center for Data Science, where I gave the crowd some idea of why and where we do data science in astronomy.
Today Dou Liu (NYU) gave a presentation of his thesis research as part of his candidacy exam. His first project has been to adapt the ideas in spectro-perfectionism from the spectral domain to the spatial domain to combine irregular, dithered imaging. He is applying this to integral-field spectroscopic data in MaNGA, which is part of SDSS-IV. He showed that he can get better angular resolution than the standard data-analysis methods, which are generally radial-basis-function interpolations of the data. One of his goals is to produce generally useful tools. Another is to re-process all of the MaNGA data. A great contribution, betterizing existing data that have already been hugely productive.
I had the great pleasure of being on the oral qualifying exam for Rui Wu (NYU), who is looking at the behavior and neural computation of fruit-fly larvae. She told us about her research so far (in preparation for her PhD project), in which she has built a fully data-driven model of larval behavior, classifying multiple different behaviors in an unsupervised model. She can also show that behavioral changes are correlated with changes to larval stimulus. She did all this by dimensionality-reducing video data with a set of clever techniques.
I learned an immense amount in her seminar. One is that they can genetically modify the larvae so that their olfactory senses can be stimulated with light! That's crazy but makes for better experimental techniques. Another is that they can read from individual neurons simultaneously with monitoring large-scale behavior. The fly is a model neural system that does complex things but with very few neurons, so there is a hope of reverse engineering the full computation. A truly out-there idea is that if the computation and behavior is understood, the larvae could be controlled or driven like an engineering system.
At lunch I gave the Flatiron CCA a taste of the science going on with Gaia DR2 in a short lunch talk. And before that I prepared my slides. All that counts as research by my rules.
My research highlight of the day, however, was a conversation with Neige Frankel (MPIA) about her probabilistic model for radial migration in the Milky Way disk. She doesn't have a good quantitative model for the selection function for her data, so she doesn't want her model to generate the three-space positions of the stars in her sample. At the same time, the structural parameters of the Milky Way disk are important. So she wants a model for the stellar properties, conditioned on the stellar positions. There are two ways to do this. The first is to write a graphical model where arrows only come from (and never go to) the stellar positions. We did that, but Frankel doesn't like that option, because the model only has simple analytic form when the arrows go to the positions.
The other option is to use the factorization formula p(a, b) = p(a|b) p(b). The stellar positions can be moved from the left side of the vertical bar to the right side by dividing by a pdf for the positions. We wrote that down, drew the relevant graphical models, and discussed changes to her text. She has beautiful results, TBA.
Now that Gaia DR2 has happened, we still organize parallel-working time at Flatiron for people to get together and hack on their Gaia projects. I worked on two things in this meeting today. In the first, I wrote to Floor van Leeuwen (Cambridge) about his Hipparcos data, because I learned last week that he released individual-visit astrometry for every star (hooray!), and that the visit astrometry has never really been comprehensively searched for arbitrary binary stars. I'm not sure I will do this! It's hard. But a project along these lines would be a great preparation for future Gaia data.
My second project in Gaia workshop was to talk out something with Adrian Price-Whelan (Princeton) that connects to things I have been talking about with Rix and others: In a very, very local sample (very near the Sun), the stars in velocity-space show a lot of informative structure. That is, some disk orbits are over-populated, and some under-populated. As you grow the region around the Sun, the structure in velocity space gets fuzzier, because the local velocity structure is a function of local position. Rix's view (which is sensible) is that we should look at this structure not in velocity space but in action space. That's a good idea! But if the structure is caused by non-axisymmetry in the disk, the actions computed in an axisymmetric potential won't be the clearest space. Let's find that space using the data themselves, and then interpret the transformation from more naive coordinates in terms of the dynamics. Price-Whelan and I came up with a first-step project, and an objective function to optimize. It looks do-able.
I dealt with non-research things today! But late in the day, I got in some Gaia DR2 visualization time with Lauren Anderson (Flatiron)> She can in-real-time manipulate the entirety of DR2 (>1 billion stars) in a Jupyter notebook using vaex, which was designed (beautifully) for this purpose. We looked at halo substructure. I'm sure I'm seeing things in the halo, but how to know?
In the morning, Lauren Anderson (Flatiron) and I discussed Gaia DR2 projects. First we talked about things we could do with David Blei (Columbia) and his group, who have variational methods for extremely large inferences of the types we would like to do. We drew some graphical models (and posted them on twitter). Then we looked at halo red giants selected by parallax and color. Sagittarius shows up beautifully, and now it is time to start to look at other features. The data are incredibly rich.
Alberto Sirlin (NYU) gave the brown-bag talk, on the neutron lifetime. He showed that the neutron lifetime and a certain coupling are related, and showed that measurements of each, and their combination, are consistent, for at least some measurements. There are interesting puzzles though: Some kinds of lifetime measurements disagree with other kinds, and there was a step change in the coupling measurements in 2002-ish. So there are hints of new physics, but also a consistent no-new-physics story. He also showed that the simplest new-physics scenarios are not sensible. The neutron lifetime is important for many things, but especially big-bang nucleosynthesis.
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.
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?
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.
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.