arXiv subjects

Alexander G. Gray

Publications and source records attributed to Alexander G. Gray.

27 records · Page 2Linked to original sources

arXiv2010

Generative and Latent Mean Map Kernels

We introduce two kernels that extend the mean map, which embeds probability measures in Hilbert spaces. The generative mean map kernel (GMMK) is a smooth similarity measure between probabilistic models. The latent mean map kernel (LMMK) generalizes the non-iid formulation of Hilbert space embeddings of empirical distributions in order to incorporate latent variable models. When comparing certain classes of distributions, the GMMK exhibits beneficial regularization and generalization properties not shown for previous generative kernels. We present experiments comparing support vector machine performance using the GMMK and LMMK between hidden Markov models to the performance of other methods on discrete and continuous observation sequence data. The results suggest that, in many cases, the GMMK has generalization error competitive with or better than other methods.

cs.LG↗

arXiv2009

Non-Negative Matrix Factorization, Convexity and Isometry

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex, by using the theory of Completely Positive Factorization. We subsequently explore four novel approaches to finding globally-optimal NMF solutions using various ideas from convex optimization. We then develop a new method, isometric NMF (isoNMF), which preserves non-negativity while also providing an isometric embedding, simultaneously achieving two properties which are helpful for interpretation. Though it results in a more difficult optimization problem, we show experimentally that the resulting method is scalable and even achieves more compact spectra than standard NMF.

cs.AI↗

arXiv2009

Learning Isometric Separation Maps

Maximum Variance Unfolding (MVU) and its variants have been very successful in embedding data-manifolds in lower dimensional spaces, often revealing the true intrinsic dimension. In this paper we show how to also incorporate supervised class information into an MVU-like method without breaking its convexity. We call this method the Isometric Separation Map and we show that the resulting kernel matrix can be used as a binary/multiclass Support Vector Machine-like method in a semi-supervised (transductive) framework. We also show that the method always finds a kernel matrix that linearly separates the training data exactly without projecting them in infinite dimensional spaces. In traditional SVMs we choose a kernel and hope that the data become linearly separable in the kernel space. In this paper we show how the hyperplane can be chosen ad-hoc and the kernel is trained so that data are always linearly separable. Comparisons with Large Margin SVMs show comparable performance.

cs.LG↗

arXiv2009

Eight-Dimensional Mid-Infrared/Optical Bayesian Quasar Selection

We explore the multidimensional, multiwavelength selection of quasars from mid-IR (MIR) plus optical data, specifically from Spitzer-IRAC and the Sloan Digital Sky Survey (SDSS). We apply modern statistical techniques to combined Spitzer MIR and SDSS optical data, allowing up to 8-D color selection of quasars. Using a Bayesian selection method, we catalog 5546 quasar candidates to an 8.0 um depth of 56 uJy over an area of ~24 sq. deg; ~70% of these candidates are not identified by applying the same Bayesian algorithm to 4-color SDSS optical data alone. Our selection recovers 97.7% of known type 1 quasars in this area and greatly improves the effectiveness of identifying 3.5<z<5 quasars. Even using only the two shortest wavelength IRAC bandpasses, it is possible to use our Bayesian techniques to select quasars with 97% completeness and as little as 10% contamination. This sample has a photometric redshift accuracy of 93.6% (Delta Z +/-0.3), remaining roughly constant when the two reddest MIR bands are excluded. While our methods are designed to find type 1 (unobscured) quasars, as many as 1200 of the objects are type 2 (obscured) quasar candidates. Coupling deep optical imaging data with deep mid-IR data could enable selection of quasars in significant numbers past the peak of the quasar luminosity function (QLF) to at least z~4. Such a sample would constrain the shape of the QLF and enable quasar clustering studies over the largest range of redshift and luminosity to date, yielding significant gains in our understanding of quasars and the evolution of galaxies.

astro-ph↗

arXiv2008

Efficient Photometric Selection of Quasars from the Sloan Digital Sky Survey: II. ~1,000,000 Quasars from Data Release Six

We present a catalog of 1,172,157 quasar candidates selected from the photometric imaging data of the Sloan Digital Sky Survey (SDSS). The objects are all point sources to a limiting magnitude of i=21.3 from 8417 sq. deg. of imaging from SDSS Data Release 6 (DR6). This sample extends our previous catalog by using the latest SDSS public release data and probing both UV-excess and high-redshift quasars. While the addition of high-redshift candidates reduces the overall efficiency (quasars:quasar candidates) of the catalog to ~80%, it is expected to contain no fewer than 850,000 bona fide quasars -- ~8 times the number of our previous sample, and ~10 times the size of the largest spectroscopic quasar catalog. Cross-matching between our photometric catalog and spectroscopic quasar catalogs from both the SDSS and 2dF Surveys, yields 88,879 spectroscopically confirmed quasars. For judicious selection of the most robust UV-excess sources (~500,000 objects in all), the efficiency is nearly 97% -- more than sufficient for detailed statistical analyses. The catalog's completeness to type 1 (broad-line) quasars is expected to be no worse than 70%, with most missing objects occurring at z<0.7 and 2.5<z<3.0. In addition to classification information, we provide photometric redshift estimates (typically good to Delta z +/- 0.3 [2 sigma]) and cross-matching with radio, X-ray, and proper motion catalogs. Finally, we consider the catalog's utility for determining the optical luminosity function of quasars and are able to confirm the flattening of the bright-end slope of the quasar luminosity function at z~4 as compared to z~2.

astro-ph↗

arXiv2006

A high redshift detection of the integrated Sachs-Wolfe effect

We present evidence of a large angle correlation between the cosmic microwave background measured by WMAP and a catalog of photometrically detected quasars from the SDSS. The observed cross correlation is (0.30 +- 0.14) microK at zero lag, with a shape consistent with that expected for correlations arising from the integrated Sachs-Wolfe effect. The photometric redshifts of the quasars are centered at z ~ 1.5, making this the deepest survey in which such a correlation has been observed. Assuming this correlation is due to the ISW effect, this constitutes the earliest evidence yet for dark energy and it can be used to constrain exotic dark energy models.

astro-ph↗

arXiv2005

First Measurement of the Clustering Evolution of Photometrically-Classified Quasars

We present new measurements of the quasar autocorrelation from a sample of \~80,000 photometrically-classified quasars taken from SDSS DR1. We find a best-fit model of $ω(θ) = (0.066\pm^{0.026}_{0.024})θ^{-(0.98\pm0.15)}$ for the angular autocorrelation, consistent with estimates from spectroscopic quasar surveys. We show that only models with little or no evolution in the clustering of quasars in comoving coordinates since z~1.4 can recover a scale-length consistent with local galaxies and Active Galactic Nuclei (AGNs). A model with little evolution of quasar clustering in comoving coordinates is best explained in the current cosmological paradigm by rapid evolution in quasar bias. We show that quasar biasing must have changed from b_Q~3 at a (photometric) redshift of z=2.2 to b_Q~1.2-1.3 by z=0.75. Such a rapid increase with redshift in biasing implies that quasars at z~2 cannot be the progenitors of modern L* objects, rather they must now reside in dense environments, such as clusters. Similarly, the duration of the UVX quasar phase must be short enough to explain why local UVX quasars reside in essentially unbiased structures. Our estimates of b_Q are in good agreement with recent spectroscopic results, which demonstrate the implied evolution in b_Q is consistent with quasars inhabiting halos of similar mass at every redshift. Treating quasar clustering as a function of both redshift and luminosity, we find no evidence for luminosity dependence in quasar clustering, and that redshift evolution thus affects quasar clustering more than changes in quasars' luminosity. We provide a new method for quantifying stellar contamination in photometrically-classified quasar catalogs via the correlation function.

astro-ph↗

arXiv2004

Efficient Photometric Selection of Quasars from the Sloan Digital Sky Survey: 100,000 z<3 Quasars from Data Release One

We present a catalog of 100,563 unresolved, UV-excess (UVX) quasar candidates to g=21 from 2099 deg^2 of the Sloan Digital Sky Survey (SDSS) Data Release One (DR1) imaging data. Existing spectra of 22,737 sources reveals that 22,191 (97.6%) are quasars; accounting for the magnitude dependence of this efficiency, we estimate that 95,502 (95.0%) of the objects in the catalog are quasars. Such a high efficiency is unprecedented in broad-band surveys of quasars. This ``proof-of-concept'' sample is designed to be maximally efficient, but still has 94.7% completeness to unresolved, g<~19.5, UVX quasars from the DR1 quasar catalog. This efficient and complete selection is the result of our application of a probability density type analysis to training sets that describe the 4-D color distribution of stars and spectroscopically confirmed quasars in the SDSS. Specifically, we use a non-parametric Bayesian classification, based on kernel density estimation, to parameterize the color distribution of astronomical sources -- allowing for fast and robust classification. We further supplement the catalog by providing photometric redshifts and matches to FIRST/VLA, ROSAT, and USNO-B sources. Future work needed to extend the this selection algorithm to larger redshifts, fainter magnitudes, and resolved sources is discussed. Finally, we examine some science applications of the catalog, particularly a tentative quasar number counts distribution covering the largest range in magnitude (14.2<g<21.0) ever made within the framework of a single quasar survey.

astro-ph↗

arXiv2004

Multi-Tree Methods for Statistics on Very Large Datasets in Astronomy

Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have dramatically reduced the computational complexity of 1) kernel density estimation (which also extends to nonparametric regression, classification, and clustering), and 2) the n-point correlation function for arbitrary n. These new multi-tree methods typically yield orders of magnitude in speedup over the previous state of the art for similar accuracy, making millions of data points tractable on desktop workstations for the first time.

astro-ph↗