The CPM of Wang et al and the transit search methods of Foreman-Mackey et al were developed by us to account for and remove or obviate systematic issues with the Kepler imaging. Last summer, Matthias Samland (MPIA) pointed out that these could be used in direct imaging of exoplanets, which is another place where highly informative things happen in the nuisance space. Today we worked through the math and code that would make a systematics-marginalized search for direct detections of planets in the VLT-SPHERE imaging data. It involves finding a basis of time variations of pixels in the device (pixels, not patches, which is odd and at odds with the standard practice), choosing a prior on these that makes sense, fitting every pixel in the relevant part of the device as sum of variations plus exoplanet, but marginalizing out the former.
On the weekend, Bernhard Schölkopf (Tübingen) showed up in Heidelberg to hang out and talk shop. What an honor and pleasure! We spent time im Garten discussing various things, but he was particularly insightful in the projects we have been doing with Christina Eilers (MPIA) on extending The Cannon to situations where stellar labels (even in the training set) are either noisy or missing. As we described the training and test steps, we drew graphical models and then looked at the inconsistencies of those graphical models—or not really inconsistencies, but limitations. We realized that we couldn't keep the model interpretable (which is a core idea underlying The Cannon) without putting stronger priors on both the label space (the properties of stars) and the coefficient space (the control parameters of the spectral expectation). If we put on these priors, the model ought to get regularized into a sensible place. I think I know how to do this!
He also pointed out that a probabilistic version of The Cannon would look a lot like the GPLVM (Gaussian Process latent-variable model). That means that there might be out-of-the-box code that could conceivably help us. I am slightly suspicious,
because my idea of the priors or regularization in the label domain is so specific, astrophysical, and informative. But it is worth thinking about this.
One of my main research accomplishments today was to work up a project proposal for Yuan-Sen Ting (ANU) and others about finding stars whose spectra suggest that they have (recently) swallowed a lot of rocky material. This was inspired by a few things: The first is that Andy Casey (Monash) can find Li-rich stars in LAMOST just by looking at the residuals away from a fit by The Cannon at the location of Li lines. The second is that Semyeong Oh (Princeton) and various collaborators have found Sun-like stars that look like they have swallowed many Earth masses of rock in their recent pasts, by doing (or having John Brewer of Yale do) detailed chemical abundance work on the spectra. The third is that Yuan-Sen Ting has derivatives of spectral expectations with respect to all elements for LAMOST-like spectra.
At the end of the day, Hans-Walter Rix (MPIA) gave a colloquium on the After-Sloan-IV project, which my loyal reader knows a lot about. I learned things in his talk, however: One is that SDSS-III BOSS has found several broad (ish) lined quasars that shut off between SDSS-I and SDSS-III. One relevant paper is here. Another is that he (with Jonathan Bird of Vandy) has made some beautiful visualizations of the point of doing dense sampling of the giant stars in the Milky Way disk.
At MPIA Galaxy Coffee, Daniel Lenz (JPL) spoke about foregrounds and component separation in CMB and LSS experiments. He emphasized (and I agree completely) that the dominant problem for next-generation ("Stage-4" in the unpleasant terminology of cosmologists) cosmology experiments—be they CMB, LSS, or line intensity mapping—is component separation or foreground inferences. He showed some nice results using generalized linear models of optical data for Milky-Way dust inferences. Afterwards I pitched him my ideas about latent variable models (all vapor ware right now).
Late in the day, Christina Eilers (MPIA) and I met to discuss why our project to fit for both labels and spectral model in a new version of The Cannon didn't work. I have various theories, most of which relate to some unholy mix of the curse of dimensionality (such that optimization of a model is a bad idea) and model wrongness (such that the model is trying to use the freedom it has inappropriately). But I am seriously confused. We worked through all the possible directions and realized that we need to re-group with our full team to decide what to do next. I assigned myself two things: The first is to look at marginalization of The Cannon internals (that is, what marginalizations might be analytic?). The second is to look at the machine-learning literature on the difference between optimizing a model for prediction accuracy as opposed to optimizing it for model accuracy (or likelihood).
[I was on vacation for a few days.]
I spent a tiny bit of time on my vacation working on fixing the wrong parts of section 7 of my paper with Bovy and Lang on fitting a line to data. I am close to a new wording I am happy with, and with corrected equations. I then realized that there are a mess of old issues to look at; I might do that too before I re-post it to arXiv.
Today was the last day of the 2017 Heidelberg Gaia Sprint. Every participant prepared a single slide in a shared slide deck (available here), and had 120 seconds to present their results. Look at the slides for the full story, but it was really impressive! A few highlights for me were:
Rix and Fouesneau used common proper motions to match Gaia DR1 TGAS stars to much-fainter PanSTARRS companions, and found hundreds of white dwarf binaries, with a clear, complete white-dwarf sequence. Hawkins was able to separate red clump stars from other RGB stars with a data-driven spectral classifier, and to interpret it. Ting found similar, but working just with the spectral labels fit to spectra with physical models. El-Badry showed that stars he finds are binaries, spectroscopically (and he can find them even if the velocity differences vanish) are above the main sequence in the color—magnitude diagram.
Beaton showed that an old statistical-parallax calibration of RR Lyrae stars by Kollmeier turns out to be strongly confirmed in the TGAS data. Birky built a beautiful one-dimensional model of M-dwarf spectra in APOGEE using only a single label, which is literature spectral classifications. Burggraaff has a possible vertical-direction moving group coming through our local position in the Milky Way disk. Coronado found that she can calibrate main-sequence star luminosities using spectral labels to almost the quality of other standard candles. Rybizki made progress towards an empirical set of supernova yields, starting with APOGEE abundances and (poor) stellar ages.
And, as I have mentioned before, Casey showed that we might be able to do asteroseismology with Gaia, and Anderson made incredible maps of the Milky-Way disk (and animations of slices thereof!).
Today Lauren Anderson (Flatiron) and Adrian Price-Whelan (Princeton) made beautiful visualizations of Anderson's 20-million star catalog with distances, built by training a model on the TGAS Catalog and applying it to plausibly-red-clump stars in the billion-star catalog from Gaia. I give an example below, which shows two thin slices of the Milky Way, one through the Sun, and one through the Galactic Center (but blotted out by local dust).
Andy Casey (Monash) got our asteroseismology project working with real data! He sub-sampled some Kepler light curves down to something like Gaia end-of-mission cadence, and then applied the Stephen Feeney (Flatiron) likelihood function. Again, it has peaks at reasonable asteroseismic parameters, near the KASC published values. We are slowly developing some intuitions about what parameters are well constrained and where.
After four days of hacking on The Cannon but with probabilistic (noisy and missing) labels, Christina Eilers (MPIA) and I gave up: We worked out the bugs, got the optimizer working, and realized that our issues are fundamentally conceptual: When you have a bad model for your data (that is, a model that is ruled out strongly by the data), there can be conflicts between model accuracy and prediction accuracy. We have hit one of those conflicts. We need to re-group on this one.
Today we got amazing success with an incredibly simple (read: dumb-ass) project for making precise maps of the Milky Way: Lauren Anderson (Flatiron) and I built a data-driven model of dust extinction, using the red-clump stars in the TGAS sample that we deconvolved last month. We then applied this dust inference to every single star in the full billion-star catalog (requiring 2MASS photometry), and selected stars whose dust-corrected color is consistent with being a RC star. That is, we assumed that every star with the correct de-reddened color is a RC star. RC stars are standard candles, so then we could map the entire MW disk. The maps are precise, but contaminated. So much structure visible. Adrian Price-Whelan (Princeton) says we are seeing a flaring disk!
Gaia Sprint continued today with Christina Eilers (MPIA) and I puzzling over the behavior of her code that is an extension of The Cannon to the case in which there are label uncertainties on the training-set stars. The behavior of the code is odd: As we give the code less freedom, the model of the stellar spectra gets better but the prediction gets worse. Makes no sense! The optimization is huge, and it relies on hand-typed analytic derivatives (I know, I know!), so we don't know whether we have conceptual issues or bugs.
Meanwhile, Andy Casey (Monash) and Ana Bonaca (Harvard) got excited about doing asteroseismology with the sparse photometric light curves that will be produced by Gaia. In particular, Casey got Stephen Feeney's (Flatiron) fake-data generator and likelihood function code (made for TESS-like data) working for Gaia-like data. He finds peaks in the likelihood function! Which means that maybe we can do asteroseismology without taking a Fourier Transform. His results, however, challenged both of our intuitions about the information about nu-max and delta-nu that ought to reside in any data stream. Inspired by all this, Bonaca and Donatas Narbutis (Lithuania) looked up large HST programs on stellar clusters and showed that it is plausible that we could do asteroseismology in HST too!
In other news, Mariangela Lisanti (Princeton) worked through recent results on dynamical friction in an ultralight-scalar dark-matter model (where the dark matter has a de Broglie wavelength that is kpc in scale!) and has plausible evidence that the timing argument (for the masses of local-group objects) might rule out or constrain ULS dark matter. And Anthony Brown (Leiden) and Olivier Burggraaff (Leiden) showed me an update of Jo Bovy and my (2009) extreme-deconvolution model of the local MW disk velocity field, and they find some structure in the vertical direction, which is cool and intriguing.
Today was the first day of the 2017 Heidelberg Gaia Sprint. It was the first day of the meeting but nonetheless an impressive day of accomplishments. The day started with a pitch session in which each of the 47 participants was given one slide and 120 seconds to say who they are and what they want to do or learn at the Sprint. These pitch slides are here.
After the pitch, my projects launched well: Jessica Birky (UCSD) was able to get the new version of The Cannon created by Christina Eilers (MPIA) working and started to get some seemingly valuable spectral models out of the M-dwarf spectra in APOGEE. Lauren Anderson (Flatiron) set up and trained a data-driven (empirical) model for the extinction of red stars, based on the Gaia and 2MASS photometry.
Perhaps the most impressive accomplishment of the day is that Morgan Fouesneau (MPIA) and Hans-Walter Rix (MPIA) matched stars between Gaia TGAS and the new GPS1 catalog that puts proper motions onto all PanSTARRS stars. They find co-moving stars where the brighter is in TGAS and the fainter is in GPS1. These pairs are extremely numerous. Many are main-sequence pairs but many pair a main-sequence star in TGAS with a white dwarf in GPS1. These pairs identify white dwarfs but also potentially put cooling ages onto both stars in the pair. The white-dwarf sequence they find is beautiful. Exciting!
Jessica Birky (UCSD) and I met with Wolfgang Brandner (MPIA) and Derek Homeier (MPIA) to discuss M-dwarf spectra. Homeier has just finished a study of a few dozen M-dwarfs in APOGEE with the PHOENIX models. We are going to find out whether this set of stars will constitute an adequate training set for The Cannon. It is very weighted to a small temperature range, so it might not have enough coverage for us. We learned a huge amount in our meeting, like whether rotation might affect us (or be detectable), whether binaries might be common in our sample, and whether we might be able to use photometry (or photometry plus astrometry) to get effective temperatures. The conversation was very wide ranging and I learned a huge amount.
Today, at MPIA Milky Way Group Meeting, I presented my thinking about Stephen Feeney (Flatiron), Ana Bonaca (Harvard), and my project on doing asteroseismology without the Fourier Transform. I am so excited about the (remote, perhaps) possibility that Gaia might be able to measure delta-nu and nu-max for many stars! Possible #GaiaSprint project?
Before me, Kareem El-Badry (Berkeley) talked about how wrong your inferences about stars can be when you model the spectrum without considering binarity. This maps on to a lot of things I discuss with Tim Morton (Princeton) in the area of exoplanet science. Also Yuan-Sen Ting (ANU) spoke about using t-SNE to look for clustering of stars in chemical space.
I spent the early morning writing up a safe-for-methodologists (think: statisticians, mathematicians, and computer scientists) description of The Cannon's likelihood function, when the stellar labels themselves are poorly known (really the project of Christina Eilers here at MPIA). I did this because Jonathan Weare (Chicago) has proposed that he can probably sample the full posterior. I hope that is true! It would be a probabilistic tour de force.
Lauren Anderson (Flatiron) showed up at MPIA today to discuss #GaiaSprint projects and our next projects more generally. We discussed a possible project in which we try to use the TGAS data to infer the relationships between extinction and intrinsic color for red-giant stars, and then use those relationships in the billion-star catalog to predict parallaxes for DR2 (and also learn the dust map and the spatial distribution of stars in the Milky Way).
Stephen Feeney (Flatiron) sent me plots today that suggest that we can measure asteroseismic nu-max and delta-nu for a red-giant star without ever taking the Fourier Transform of the data. Right now, there are still many issues: This is still fake data, which is always cheating. The sampler (despite being nested and all) gets stuck in poor modes (and this problem is exceedingly multimodal). But when we inspect the sampling after the fact, the good answer beats the bad answers in likelihood by a huge ratio, which suggests that we might be able to do asteroseismology at pretty low signal-to-noise too. We need to move to real data (from Kepler).
Because of concern that (in our stellar-stream project) we aren't marginalizing out all our unknowns yet—and maybe that is making things look more informative than they are—Ana Bonaca (Harvard) stared today on including the progenitor position in our Fisher-matrix (Cramér-Rao) analysis of all stellar streams. We also have concerns about the rigidity of the gravitational potential model (which is a toy model, in keeping with the traditions of the field!). We discussed also marginalizing out some kind of perturbation expansion around that toy model. This would permit us to both be more conservative, and also criticize the precisions obtained with these toy models.
Jessica Birky (UCSD) looked at chi-square differences (in spectral space) between APOGEE spectra of low-temperature stars without good labels and two known M-type stars, one giant and one dwarf. This separated all the cool stars in APOGEE easily into two classes. Nice! We are sanity-checking the answers. We are still far, however, from having a good training set to fire into The Cannon.
So many projects! I love my summers in Heidelberg. I spent time working through the figures that would support a paper on M-dwarf stars with The Cannon with Jessica Birky (UCSD) today. She has run The Cannon on a tiny training set of M-dwarf stars in the APOGEE data, and it seems to work (despite the size and quality of our training set). We are diagnosing whether it all makes sense now.
With Christina Eilers (MPIA), Hans-Walter Rix (MPIA) and I discussed the amazing fact that she can optimize (a more sophisticated version of) The Cannon on all internal parameters and all stellar labels in a single shot; this is a hundred-thousand-parameter non-linear least-square fit! It seems to be working but there are oddities to follow up. She is dealing with the point that many stars have bad, missing, or noisy labels.
With Kareem El-Badry (Berkeley), Rix and I worked through the math of going from an SB2 catalog (that is, a catalog of stars known to be binary because their spectra are better fit by superpositions of pairs of stars than by single stars) through to a population inference about the binary population. This project meshes well with the plans that Adrian Price-Whelan (Columbia) and I have for the summer.
With Ana Bonaca (Harvard), I discussed further marginalizations in her project to determine the information content in stellar streams. She finds that the potential form and the progenitor phase-space information are very informative; that is, if we relax those to give more freedom, we expect to find that the streams are less constraining of the Galactic potential. We discussed ways to test this in the next few days.
With Stephen Feeney (Flatiron) and Daniel Mortlock (Imperial) I discussed the possibility of writing a paper about the Lutz-Kelker correction (don't do it!) and posterior probabilistic catalogs (don't make them!) and what scope it might have. We tentatively decided to try to put something together.
With Matthias Samland (MPIA) and Jeroen Bouwman (MPIA) I discussed their ideas to move the CPM (which we used to de-trend Kepler and K2 light curves) to the domain of direct detection of exoplanets with coronographs. This is a great idea! We discussed the way to choose predictor pixels, and the form that the likelihood takes when you marginalize out the superposition of predictor pixels. This is a very promising software direction for future coronograph missions. But we noticed that many projects and observing runs might be data-limited: People take hundreds of photon-limited exposures instead of thousands of read-noise-limited exposures. I think that's a mistake: No current results are, in the end, photon-noise limited! We put Samland onto looking at the subspace in which the pixel variations live.
I love my job!
I spent the day at Potsdam, to participate (and give a talk) in the Wempe Award ceremony; the prize went to Alice Quillen (Rochester), who has done dynamical theory on a huge range of scales and in a huge range of contexts. I spoke about how data-driven models of stars might make it possible to precisely test Quillen's predictions. After my talk I had a long session with Ivan Minchev (AIP), Christina Chiappini (AIP), and Friedrich Anders (AIP) about work on stellar chemical abundances in the disk. They are trying to understand whether the alpha-rich disk itself splits into multiple populations or is just one. We discussed the possibility that any explanation of the alpha-to-Fe vs Fe-to-H plot ought to make predictions for other galaxies. Right now theoretical expectations are soft, both because star formation is not right in the cosmological models, and because nucleosynthetic yields are not right in the chemical evolution models. We also discussed Anders's use of t-SNE for dimensionality reduction and how we might test its properties (the properties of t-SNE, that is).
In my science time today, I worked with Ana Bonaca (Harvard) on her computation of derivatives—of stellar stream properties with respect to potential parameters. This is all part of our information-theoretic project on stellar streams. We are taking the derivatives numerically, which is challenging to get right, and we have had many conversations about step sizes and how to choose them. We made (what I hope are) final choices today: They involve computing the derivative at different step sizes, comparing each of those derivatives to those computed at nearby step sizes, and finding the smallest step size at which converged or consistent derivatives are being computed. Adaptive and automatic! But a pain to get working right.
Numerical context: If you take derivatives with step sizes that are too small, you get killed by numerical noise. If you take derivatives with step sizes that are too large, the changes aren't purely linear in the stepped parameter. The Goldilocks step size is not trivial to find.
Today was my first day at MPIA. I worked with Hans-Walter Rix (MPIA) and Christina Eilers (MPIA) on her new version of The Cannon, which simultaneously optimizes the model and the labels, with label uncertainties. It is a risky business for a number of reasons, one of which is that maximum likelihood has all the problems we know, and another of which is that optimization is hard. She has taken all the relevant derivatives (analytically), but is stuck on initialization. We came up with some tricks for improving her initialization; this problem has enormous numbers of local optima!
We also spoke with Kareem El-Badry (Berkeley) about a project he is doing with Rix to find binary stars among the LAMOST spectra. Here the problem is that the binaries will not be resolved spectrally or spatially, so it is up to seeing that the one-d spectrum is better explained by two stars (at the same distance and metallicity) than one. He is finding (not surprisingly) that because the spectral models are not quite accurate enough, a mixture of two stars is almost always better than a single star fit. So he decided today to try implementing (his own, bespoke, version of) The Cannon. Then the model will (at least) be accurate in the spectral domain, which is what he needs.
I got started on a new project with Jessica Birky (UCSD) who is here at MPIA to work with me on M-dwarf spectra in the APOGEE project. Our first job is to find a training set of M dwarfs that have APOGEE spectra but also known temperatures and metallicities. That isn't trivial.