Online Tensor Methods for Learning Latent Variable Models

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2) topic modeling, in which we infer hidden topics of text articles. We consider decomposition of moment tensors using stochastic gradient descent. We conduct optimization of multilinear operations in SGD and avoid directly forming the tensors, to save computational and storage costs. We present optimized algorithm in two platforms. Our GPU-based implementation exploits the parallelism of SIMD architectures to allow for maximum speed-up by a careful optimization of storage and data transfer, whereas our CPU-based implementation uses efficient sparse matrix computations and is suitable for large sparse datasets. For the community detection problem, we demonstrate accuracy and computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic modeling problem, we also demonstrate good performance on the New York Times dataset. We compare our results to the state-of-the-art algorithms such as the variational method, and report a gain of accuracy and a gain of several orders of magnitude in the execution time.Comment: JMLR 201

Testing the universality of star formation - I. Multiplicity in nearby star-forming regions

We have collated multiplicity data for five clusters (Taurus, Chamaeleon I, Ophiuchus, IC348, and the Orion Nebula Cluster). We have applied the same mass ratio (flux ratios of delta K <= 2.5) and primary mass cuts (~0.1-3.0 Msun) to each cluster and therefore have directly comparable binary statistics for all five clusters in the separation range 62-620 au, and for Taurus, Chamaeleon I, and Ophiuchus in the range 18-830 au. We find that the trend of decreasing binary fraction with cluster density is solely due to the high binary fraction of Taurus, the other clusters show no obvious trend over a factor of nearly 20 in density. With N-body simulations we attempt to find a set of initial conditions that are able to reproduce the density, morphology and binary fractions of all five clusters. Only an initially clumpy (fractal) distribution with an initial total binary fraction of 73 per cent (17 per cent in the range 62-620 au) is able to reproduce all of the observations (albeit not very satisfactorily). Therefore, if star formation is universal the initial conditions must be clumpy and with a high (but not 100 per cent) binary fraction. This could suggest that most stars, including M-dwarfs, form in binaries.Comment: Accepted for publication in MNRAS, 19 pages, 22 figure

Dynamical Mass Measurements of Contaminated Galaxy Clusters Using Machine Learning

We study dynamical mass measurements of galaxy clusters contaminated by interlopers and show that a modern machine learning (ML) algorithm can predict masses by better than a factor of two compared to a standard scaling relation approach. We create two mock catalogs from Multidark's publicly available $N$-body MDPL1 simulation, one with perfect galaxy cluster membership information and the other where a simple cylindrical cut around the cluster center allows interlopers to contaminate the clusters. In the standard approach, we use a power-law scaling relation to infer cluster mass from galaxy line-of-sight (LOS) velocity dispersion. Assuming perfect membership knowledge, this unrealistic case produces a wide fractional mass error distribution, with a width of $\Delta\epsilon\approx0.87$. Interlopers introduce additional scatter, significantly widening the error distribution further ($\Delta\epsilon\approx2.13$). We employ the support distribution machine (SDM) class of algorithms to learn from distributions of data to predict single values. Applied to distributions of galaxy observables such as LOS velocity and projected distance from the cluster center, SDM yields better than a factor-of-two improvement ($\Delta\epsilon\approx0.67$) for the contaminated case. Remarkably, SDM applied to contaminated clusters is better able to recover masses than even the scaling relation approach applied to uncontaminated clusters. We show that the SDM method more accurately reproduces the cluster mass function, making it a valuable tool for employing cluster observations to evaluate cosmological models.Comment: 18 pages, 12 figures, accepted for publication at Ap

The Search for Low-mass Companions of B Stars in the Carina Nebula Cluster Trumpler 16

We have developed lists of likely B3--A0 stars (called "late B" stars) in the young cluster Trumpler 16. The following criteria were used: location within 3' of Eta Car, an appropriate V and B-V combination, and proper motion (where available). Color and magnitude cuts have been made assuming an E(B-V) =0.55 mag +/- 0.1, which is a good approximation close to the center of Trumpler 16. These lists have been cross-correlated with X-ray sources found in the Chandra Carina Complex Project (CCCP). Previous studies have shown that only very rarely (if at all) do late main sequence B stars produce X-rays. We present evidence that the X-ray detected sources are binaries with low-mass companions, since stars less massive than 1.4 Msun are strong X-ray sources at the age of the cluster. Both the median X-ray energies and X-ray luminosities of these sources are in good agreement with values for typical low-mass coronal X-ray sources. We find that 39% of the late B stars based on a list with proper motions have low-mass companions. Similarly, 32% of a sample without proper motions have low-mass companions. We discuss the X-ray detection completeness. These results on low-mass companions of intermediate mass stars are complementary to spectroscopic and interferometric results, and probe new parameter space of low mass companions at all separations. They do not support a steeply rising distribution of mass ratios to low masses for intermediate-mass (5 Msun) primaries, such as would be found by random pairing from the Initial Mass Function.Comment: Accepted for the ApJS Special Issue on the Chandra Carina Complex Project (CCCP), scheduled for publication in May 2011. All 16 CCCP Special Issue papers are available at http://cochise.astro.psu.edu/Carina_public/special_issue.html through 2011 at leas

Testing Newtonian Gravity with AAOmega: Mass-to-Light Profiles of Four Globular Clusters

Testing Newtonian gravity in the weak-acceleration regime is vital to our understanding of the nature of the gravitational interaction. It has recently been claimed that the velocity dispersion profiles of several globular clusters flatten out at large radii, reminiscent of galaxy rotation curves, even though globular clusters are thought to contain little or no dark matter. We investigate this claim, using AAOmega observations of four globular clusters, namely M22, M30, M53 and M68. M30, one such cluster that has had this claim made for its velocity dispersion, was included for comparison with previous studies. We find no statistically significant flattening of the velocity dispersion at large radii for any of our target clusters and therefore we infer the observed dynamics do not require that globular clusters are dark matter dominated, or a modification of gravity. Furthermore, by applying a simple dynamical model we determine the radial mass-to-light profiles for each cluster. The isothermal rotations of each cluster are also measured, with M22 exhibiting clear rotation, M68 possible rotation and M30 and M53 lacking any rotation, within the uncertainties.Comment: 7 pages, 4 figures and two tables. Accepted by MNRA

CLASH-VLT: The stellar mass function and stellar mass density profile of the z=0.44 cluster of galaxies MACS J1206.2-0847

Context. The study of the galaxy stellar mass function (SMF) in relation to the galaxy environment and the stellar mass density profile, rho(r), is a powerful tool to constrain models of galaxy evolution. Aims. We determine the SMF of the z=0.44 cluster of galaxies MACS J1206.2-0847 separately for passive and star-forming (SF) galaxies, in different regions of the cluster, from the center out to approximately 2 virial radii. We also determine rho(r) to compare it to the number density and total mass density profiles. Methods. We use the dataset from the CLASH-VLT survey. Stellar masses are obtained by SED fitting on 5-band photometric data obtained at the Subaru telescope. We identify 1363 cluster members down to a stellar mass of 10^9.5 Msolar. Results. The whole cluster SMF is well fitted by a double Schechter function. The SMFs of cluster SF and passive galaxies are statistically different. The SMF of the SF cluster galaxies does not depend on the environment. The SMF of the passive population has a significantly smaller slope (in absolute value) in the innermost (<0.50 Mpc), highest density cluster region, than in more external, lower density regions. The number ratio of giant/subgiant galaxies is maximum in this innermost region and minimum in the adjacent region, but then gently increases again toward the cluster outskirts. This is also reflected in a decreasing radial trend of the average stellar mass per cluster galaxy. On the other hand, the stellar mass fraction, i.e., the ratio of stellar to total cluster mass, does not show any significant radial trend. Conclusions. Our results appear consistent with a scenario in which SF galaxies evolve into passive galaxies due to density-dependent environmental processes, and eventually get destroyed very near the cluster center to become part of a diffuse intracluster medium.Comment: A&A accepted, 15 pages, 13 figure