AstroData Hack Week, day 1

On my way to Seattle, I wrote up a two-page document about inferring the velocity distribution when you only get (perhaps noisy, perhaps censored) measurements of v sin i. When I arrived at the AstroData Hack Week, I learned that Foreman-Mackey and Price-Whelan had both come to the same conclusion that this would be a valuable and achievable hack for the week. Price-Whelan and I spent hacking time specifying the project better.

That said, Foreman-Mackey got excited about doing a good job on K2 point-source photometry. We talked out the components of such a model and tried to find the simplest possible version of the project, which Foreman-Mackey wants to approach by building a full, parameterized, physical model of the point-spread function, the spacecraft Euler angles, and the flat-field. Late in the day (at the bar) we found out that our first shot at this model is going badly off the rails: The flat-field and the point-spread function are degenerate (somewhat or totally?) in the naive model we have right now. Simple fixes didn't work.

GRB beaming, classifying stars

Andy Fruchter (STScI) gave the astrophysics seminar, on gamma-ray bursts and their host galaxies. He showed Modjaz's (and others) results on the metallicities of "broad-line type IIc" supernovae, which show that the ones associated with gamma-ray bursts are in much lower-metallicity environments than those not associated. I always react to this result by pointing out that this ought to put a very strong constraint on GRB beaming, because (if there is beaming) there ought to be "off-axis" bursts that we don't see as GRBs, but that we do see as a BLIIc. Both Fruchter and Modjaz claimed that the numbers make the constraint uninteresting, but I am surprised: The result is incredibly strong.

In group meeting, Fadely showed evidence that he can make a generative model of the colors and morphologies (think: angular sizes, or compactnesses) of faint, compact sources in the SDSS imaging data. That is, he can build a flexible model (using the "extreme deconvolution" method) that permits him to predict the compactness of a source given a noisy measurement of its five-band spectral energy distribution. This shows great promise to evolve into a non-parametric, model-free (that is: free of stellar or galaxy models) method for separating stars from galaxies in multi-band imaging. The cool thing is he might be able to create a data-driven star–galaxy classification system without training on any actual star or galaxy labels.

single-example learning

I pitched projects to new graduate students in the Physics and Data Science programs today; hopefully some will stick. Late in the day, I took out new Data Science Fellow Brenden Lake (NYU) for a beer, along with Brian McFee (NYU) and Foreman-Mackey. We discussed many things, but we were blown away by Lake's experiments on single-instance learning: Can a machine learn to identify or generate a class of objects from seeing only a single example? Humans are great at this but machines are not. He showed us comparisons between his best machines and experimental subjects found on the Mechanical Turk. His machines don't do badly!

crazy diversity of stars; cosmological anomalies

At CampHogg group meeting (in the new NYU Center for Data Science space!), Sanderson (Columbia) talked about her work on finding structure through unsupervised clustering methods, and Price-Whelan talked about chaotic orbits and the effect of chaos on the streams in the Milky Way. Dun Wang blew us all away by showing us the amazing diversity of Kepler light-curves that go into his effective model of stellar and telescope variability. Even in a completely random set of a hundred light-curves you get eclipsing binaries, exoplanet transits, multiple-mode coherent pulsations, incoherent pulsations, and lots of other crazy variability. We marveled at the range of things used as "features" in his model.

At lunch (with surprise, secret visitor and Nobel Laureate Brian Schmidt), I had a long conversation with Matt Kleban (NYU), following my conversation from yesterday with D'Amico. We veered onto the question of anomalies: Just as there are anomalies in the CMB, there are probably also anomalies in the large-scale structure, but no-one really knows how to look for them. We should figure out and look! Also, each anomaly known in the CMB should make a prediction for an anomaly visible (or maybe not) in the large-scale structure. That would make for a valuable research program.

searching in the space of observables

In the early morning, Ness and I talked by phone about The Cannon (or maybe The Jump; guess the source of the name!), our method for providing stellar parameter labels to stars without using stellar models. We talked about possibly putting priors in the label space; this might regularize the results towards plausible values when the data are ambiguous. That's for paper 2, not paper 1. She has drafted an email to the APOGEE-2 collaboration about our current status, and we talked about next steps.

In the late morning, I spoke with Guido D'Amico (NYU) about future projects in cosmology that I am interested in thinking about. One class of projects involves searching for new kinds of observables (think: large-scale structure mixed-order statistics and the like) that are tuned to have maximum sensitivity to the cosmological parameters of interest. I feel like there is some kind of data-science-y approach to this, given the incredible simulations currently on the market.

CDS space

Does it count as research when I work on the NYU Center for Data Science space planning? Probably not, but I spent a good fraction of the day analyzing plans and then discussing with the architects working to create schematics for the new space. We want a great diversity of offices, shared spaces (meeting rooms, offices, and carrels), and open space (studio space and lounge and cafe space). We want our space plans to be robust to our uncertainties about how people will want to use the space.

writing

Hidden away in a cabin off the grid, I made writing progress on my project with Ness to make data-driven spectral models, and on my project to use hot planets as clocks for timing experiments. On the latter, I figured out some useful things about expected signal-to-noise and why there is a huge difference between checking local clock rates and looking at global, time-variable timing residuals away from a periodic model.

single transits, group meeting, robot DJs

The day started with a discussion with So Hattori about finding single transits in the Kepler data. We did some research and it seems like there may be no clear sample in the published literature, let alone any planet inference based on them. So we are headed in that direction. In group meeting, Foreman-Mackey told us about his approach to exoplanet search, Goodman told us about his approach to sampling that uses (rather than discards) the rejected likelihood calls (in the limit that they are expensive), and Vakili told us about probabilistic PSF modeling. On the latter, we had requests that he do something more like train and test.

A fraction of the group had lunch with Brian McFee (NYU), the new Data Science Fellow. McFee works on music, from a data analysis perspective. His past research was on song selection and augmenting or replacing collaborative filtering. His present research is on beat matching. So with the two put together he might have a full robot DJ. I have work for that robot!

calibration and search

A phone call between Wang, Foreman-Mackey, Schölkopf, and me started the day, and a conversation between Foreman-Mackey and me ended the day, both on the subject of modeling the structured noise in the Kepler data and the impact of such methods on exoplanet search. In the morning conversation, we discussed the relative value of using other stars as predictors for the target star (because co-variability of stars encodes telescope variability) compared to using the target star itself, but shifted in time (because the past and future behavior of the star can predict the present state of the star). Wang has a good system for exploring this at the pixel level. We gave him some final tasks before we reduce our scope and write a paper about it.

In the afternoon conversation, we looked at Foreman-Mackey's heuristic "information criteria" that he is using for exoplanet search in the Kepler data. By the end of the day, his search scalar included such interesting components as the following: Each proposed exoplanet period and phase is compared not just to a null model, but to a model in which there is a periodic signal but with time-varying amplitude (which would be a false positive). Each peak in the search scalar is vetoed if it shares transits with other, higher peaks (to rule out period aliasing and transit–artifact pairings). A function of period is subtracted out, to model the baseline created by noise (which is a non-trivial function of period). Everything looks promising for exoplanet candidate generation.

psf interpolation

Vakili and I spoke about his probabilistic interpolation of the point-spread function in imaging using Gaussian Processes and a basis derived from principal components. The LSST atmospheric PSF looks very stable, according to Vakili's image simulations (which use the LSST code), so I asked for shorter exposures to see more variability. We talked about the point that there might be PSF variations that are fast in time but slow in focal-plane position (from the atmosphere) and others that might be slow in time but fast in focal-plane position (from the optics) and maybe hybrid situations (if, say, the optics have some low-dimensional but fast variability). All these things could be captured by a sophisticated model.

exoplanet search

Back when we were in Tübingen, Foreman-Mackey promised Schölkopf that he would find some new exoplanets by September 1. That's today! He failed, although he has some very impressive results recovering some known systems that are supposed to be hard to find. That is, it looks like existing systems are found at higher significance for us than for other groups, so we ought to be able to find some lower-significance systems. The key technology (we think) is our insanely flexible noise model for stellar (and Kepler) variability, that uses a Gaussian process not just of time, but of hundreds of other-star lightcurves. Foreman-Mackey and I talked extensively about this today, but we are still many days away from discoveries. We are bound to announce our discoveries on twitter (tm). Bound in the sense of "obligated". Let's see if we have the fortitude to do that!

detecting clock drifts

I continued working on "hot Jupiters as clocks", building a system to find clock drifts. I find that the precision with which a drift is detected is slightly less than I found for the precision of the clock phase or offset; this makes sense, because any drift model has multiple parameters. It took me a while to get good sampling to work (with emcee, and a sensible burn-in schedule) but it now seems to. I can now start searching for signals. Heather Knutson (Caltech) gave me a couple of suggestions.

exoclocks: period and phase precision

It is back to the non-research grind now, but that didn't stop me from stealing a couple hours to work on Foreman-Mackey and my "stellar clocks" project. My question was: How precisely can you phase up or measure the time using a transiting hot Jupiter. That is, how good is a hot Jupiter as a clock? If good, we could use it for all kinds of fun things.

I started with fake data. As my loyal reader knows, I am against using fake data; all it provides is a functional test of your code! But over the years I have come around: After all, it provides a functional test of your code! It also permits you to check your results with absolutely known input assumptions; that is, it provides sanity checking on your estimates of (in this case) the precision you expect.

I find, with extremely optimistic assumptions (about the period, depth, duration, ingress time, gravitational dynamics, and, of course, photon noise), that a high-quality transiting hot Jupiter in Kepler normal-cadence data could, over the lifetime of the now-over Kepler mission, provide a time standard that is good to a few tenths of a second. This agrees with the order-of-magnitude calculation I had made myself earlier and suggests that we might be able to do some timing experiments.

words on a plane

While in transit back to NYC, I worked on writing more about Ness and my quadratic-in-tags model for stellar spectra in our manuscript, and she got the quadratic model to work from end to end. It looks extremely promising.

data science, data-driven models

Today was my last day in Heidelberg for 2014. Sad day! I spent most of my research time working with Ness on our data-driven models of stars. We got the code to go from first-order (linear) linear fitting to second-order (quadratic) linear fitting, and vowed that we would never go to third order! We will use a Gaussian Process before we do that. We discussed outliers—both outlier stars and outlier pixels—and how to deal with them while still retaining computational tractability, good probability of convergence to a good optimum (or good sampling prospects), and the likelihood principle. We don't have a good solution yet, although I have ideas in my old document on fitting a line. We also discussed next steps on the path to paper 1, including especially making figures that demonstrate the properties and qualities of the individual-wavelength least-square fits we are doing.

At the end of the day, I was noticing that this project is a perfect example of the new discipline of "Data Science", about which I am supposed to have opinions: It was an idea we both had, but I didn't know enough about the spectroscopy, and Ness didn't know enough about the methods available. Neither of us could have done this project without the collaboration (nor without significant amounts of computation).