The Overlooked Potential of Generalized Linear Models in Astronomy - I: Binomial Regression

Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -- the first in a series aimed at illustrating the power of these methods in astronomical applications -- we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity $\approx 1.3 \times 10^{-4} Z_{\bigodot}$, an increase of $1.2 \times 10^{-2}$ in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.Comment: 20 pages, 10 figures, 3 tables, accepted for publication in Astronomy and Computin

Radio Galaxy Zoo: Knowledge Transfer Using Rotationally Invariant Self-Organising Maps

With the advent of large scale surveys the manual analysis and classification of individual radio source morphologies is rendered impossible as existing approaches do not scale. The analysis of complex morphological features in the spatial domain is a particularly important task. Here we discuss the challenges of transferring crowdsourced labels obtained from the Radio Galaxy Zoo project and introduce a proper transfer mechanism via quantile random forest regression. By using parallelized rotation and flipping invariant Kohonen-maps, image cubes of Radio Galaxy Zoo selected galaxies formed from the FIRST radio continuum and WISE infrared all sky surveys are first projected down to a two-dimensional embedding in an unsupervised way. This embedding can be seen as a discretised space of shapes with the coordinates reflecting morphological features as expressed by the automatically derived prototypes. We find that these prototypes have reconstructed physically meaningful processes across two channel images at radio and infrared wavelengths in an unsupervised manner. In the second step, images are compared with those prototypes to create a heat-map, which is the morphological fingerprint of each object and the basis for transferring the user generated labels. These heat-maps have reduced the feature space by a factor of 248 and are able to be used as the basis for subsequent ML methods. Using an ensemble of decision trees we achieve upwards of 85.7% and 80.7% accuracy when predicting the number of components and peaks in an image, respectively, using these heat-maps. We also question the currently used discrete classification schema and introduce a continuous scale that better reflects the uncertainty in transition between two classes, caused by sensitivity and resolution limits

An HST Snapshot Survey of Proto-Planetary Nebulae Candidates: Two Types of Axisymmetric Reflection Nebulosities

We report the results from an optical imaging survey of proto-planetary nebula candidates using the HST. We exploited the high resolving power and wide dynamic range of HST and detected nebulosities in 21 of 27 sources. All detected reflection nebulosities show elongation, and the nebula morphology bifurcates depending on the degree of the central star obscuration. The Star-Obvious Low-level-Elongated (SOLE) nebulae show a bright central star embedded in a faint, extended nebulosity, whereas the DUst-Prominent Longitudinally-EXtended (DUPLEX) nebulae have remarkable bipolar structure with a completely or partially obscured central star. The intrinsic axisymmetry of these proto-planetary nebula reflection nebulosities demonstrates that the axisymmetry frequently found in planetary nebulae predates the proto-planetary nebula phase, confirming previous independent results. We suggest that axisymmetry in proto-planetary nebulae is created by an equatorially enhanced superwind at the end of the asymptotic giant branch phase. We discuss that the apparent morphological dichotomy is caused by a difference in the optical thickness of the circumstellar dust/gas shell with a differing equator-to-pole density contrast. Moreover, we show that SOLE and DUPLEX nebulae are physically distinct types of proto-planetary nebulae, with a suggestion that higher mass progenitor AGB stars are more likely to become DUPLEX proto-planetary nebulae.Comment: 27 pages (w/ aaspp4.sty), 6 e/ps figures, 4 tables (w/ apjpt4.sty). Data images are available via ADIL (http://imagelib.ncsa.uiuc.edu/document/99.TU.01) To be published in Ap

Using machine learning to study the kinematics of cold gas in galaxies

Next generation interferometers, such as the Square Kilometre Array, are set to obtain vast quantities of information about the kinematics of cold gas in galaxies. Given the volume of data produced by such facilities astronomers will need fast, reliable, tools to informatively filter and classify incoming data in real time. In this paper, we use machine learning techniques with a hydrodynamical simulation training set to predict the kinematic behaviour of cold gas in galaxies and test these models on both simulated and real interferometric data. Using the power of a convolutional autoencoder we embed kinematic features, unattainable by the human eye or standard tools, into a 3D space and discriminate between disturbed and regularly rotating cold gas structures. Our simple binary classifier predicts the circularity of noiseless, simulated, galaxies with a recall of 85% and performs as expected on observational CO and H i velocity maps, with a heuristic accuracy of 95%. The model output exhibits predictable behaviour when varying the level of noise added to the input data and we are able to explain the roles of all dimensions of our mapped space. Our models also allow fast predictions of input galaxies’ position angles with a 1σ uncertainty range of ±17° to ±23° (for galaxies with inclinations of 82.5° to 32.5°, respectively), which may be useful for initial parametrization in kinematic modelling samplers. Machine learning models, such as the one outlined in this paper, may be adapted for SKA science usage in the near future