In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: object A is more similar to object B than it is to C, where comparisons are given by humans. Existing solutions to this prob
lem assume many comparisons are provided to learn a high quality kernel. However, this can be considered unrealistic for many real-world tasks since relative assessments require human input, which is often costly or difficult to obtain. Because of this, only a limited number of these comparisons may be provided. In this work, we explore methods for aiding the process of learning a kernel with the help of auxiliary kernels built from more easily extractable information regarding the relationships among objects. We propose a new kernel learning approach in which the target kernel is defined as a conic combination of auxiliary kernels and a kernel whose elements are learned directly. We formulate a convex optimization to solve for this target kernel that adds only minor overhead to methods that use no auxiliary information. Empirical results show that in the presence of few training relative comparisons, our method can learn kernels that generalize to more out-of-sample comparisons than methods that do not utilize auxiliary information, as well as similar methods that learn metrics over objects.
One of the most pernicious theoretical systematics facing upcoming gravitational lensing surveys is the uncertainty introduced by the effects of baryons on the power spectrum of the convergence field. One method that has been proposed to account for
these effects is to allow several additional parameters (that characterize dark matter halos) to vary and to fit lensing data to these halo parameters concurrently with the standard set of cosmological parameters. We test this method. In particular, we use this technique to model convergence power spectrum predictions from a set of cosmological simulations. We estimate biases in dark energy equation of state parameters that would be incurred if one were to fit the spectra predicted by the simulations either with no model for baryons, or with the proposed method. We show that neglecting baryonic effect leads to biases in dark energy parameters that are several times the statistical errors for a survey like the Dark Energy Survey. The proposed method to correct for baryonic effects renders the residual biases in dark energy equation of state parameters smaller than the statistical errors. These results suggest that this mitigation method may be applied to analyze convergence spectra from a survey like the Dark Energy Survey. For significantly larger surveys, such as will be carried out by the Large Synoptic Survey Telescope, the biases introduced by baryonic effects are much more significant. We show that this mitigation technique significantly reduces the biases for such larger surveys, but that a more effective mitigation strategy will need to be developed in order ensure that the residual biases in these surveys fall below the statistical errors.
Quasar feedback has most likely a substantial but only partially understood impact on the formation of structure in the universe. A potential direct probe of this feedback mechanism is the Sunyaev-Zeldovich effect: energy emitted from quasar heats th
e surrounding intergalactic medium and induce a distortion in the microwave background radiation passing through the region. Here we examine the formation of such hot quasar bubbles using a cosmological hydrodynamic simulation which includes a self-consistent treatment of black hole growth and associated feedback, along with radiative gas cooling and star formation. From this simulation, we construct microwave maps of the resulting Sunyaev-Zeldovich effect around black holes with a range of masses and redshifts. The size of the temperature distortion scales approximately with black hole mass and accretion rate, with a typical amplitude up to a few micro-Kelvin on angular scales around 10 arcseconds. We discuss prospects for the direct detection of this signal with current and future single-dish and interferometric observations, including ALMA and CCAT. These measurements will be challenging, but will allow us to characterize the evolution and growth of supermassive black holes and the role of their energy feedback on galaxy formation.
