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Register a new userSemi-parametric $gamma$-ray modeling with Gaussian processes and variational inference
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Siddharth Mishra-Sharma
Publication date
2020
fields
Physics
and research's language is
English
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Mismodeling the uncertain, diffuse emission of Galactic origin can seriously bias the characterization of astrophysical gamma-ray data, particularly in the region of the Inner Milky Way where such emission can make up over 80% of the photon counts observed at ~GeV energies. We introduce a novel class of methods that use Gaussian processes and variational inference to build flexible background and signal models for gamma-ray analyses with the goal of enabling a more robust interpretation of the make-up of the gamma-ray sky, particularly focusing on characterizing potential signals of dark matter in the Galactic Center with data from the Fermi telescope.
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Our paper reviews the planned space-based gamma-ray telescope GAMMA-400 and evaluates in details its opportunities in the field of dark matter (DM) indirect searches. We estimated GAMMA-400 mean sensitivity to the diphoton DM annihilation cross section in the Galactic center for DM particle masses in the range of 1-500 GeV. We obtained the sensitivity gain at least by 1.2-1.5 times (depending on DM particle mass) with respect to the expected constraints from 12 years of observations by Fermi-LAT for the case of Einasto DM density profile. The joint analysis of the data from both telescopes may yield the gain up to 1.8-2.3 times. Thus the sensitivity reaches the level of annihilation cross section $langle sigma v rangle_{gammagamma}(m_chi=100~mbox{GeV})approx 10^{-28}$ cm$^3$/s. This will allow us to test the hypothesized narrow lines predicted by specific DM models, particularly the recently proposed pseudo-Goldstone boson DM model. We also considered the decaying DM - in this case the joint analysis may yield the sensitivity gain up to 1.1-2.0 times reaching the level of DM lifetime $tau_{gamma u}(m_chi=100~mbox{GeV}) approx 2cdot 10^{29}$ s. We estimated the GAMMA-400 sensitivity to axion-like particle (ALP) parameters by a potential observation of the supernova explosion in the Local Group. This is very sensitive probe of ALPs reaching the level of ALP-photon coupling constant $g_{agamma} sim 10^{-13}~mbox{GeV}^{-1}$ for ALP masses $m_a lesssim 1$ neV. We also calculated the sensitivity to ALPs by constraining the modulations in the spectra of the Galactic gamma-ray pulsars due to possible ALP-photon conversion. GAMMA-400 is expected to be more sensitive than the CAST helioscope for ALP masses $m_a approx (1-10)$ neV reaching $g_{agamma}^{min} approx 2cdot 10^{-11}~mbox{GeV}^{-1}$. Other potentially interesting targets and candidates are briefly considered too.
A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. Unfortunately, the deterministic approximation methods yield a biased posterior belief while the stochastic one is computationally costly. This paper presents an implicit posterior variational inference (IPVI) framework for DGPs that can ideally recover an unbiased posterior belief and still preserve time efficiency. Inspired by generative adversarial networks, our IPVI framework achieves this by casting the DGP inference problem as a two-player game in which a Nash equilibrium, interestingly, coincides with an unbiased posterior belief. This consequently inspires us to devise a best-response dynamics algorithm to search for a Nash equilibrium (i.e., an unbiased posterior belief). Empirical evaluation shows that IPVI outperforms the state-of-the-art approximation methods for DGPs.
We analyze the possibility that the HESS gamma-ray source at the Galactic Center could be explained as the secondary flux produced by annihilation of TeV Dark Matter (TeVDM) particles with locally enhanced density, in a region spatially compatible with the HESS observations themselves. We study the inner 100 pc considering (i) the extrapolation of several density profiles from state-of-the-art N-body + Hydrodynamics simulations of Milky Way-like galaxies, (ii) the DM spike induced by the black hole, and (iii) the DM particles scattering off by bulge stars. We show that in some cases the DM spike may provide the enhancement in the flux required to explain the cut-off in the HESS J1745-290 gamma-ray spectra as TeVDM. In other cases, it may helps to describe the spatial tail reported by HESS II at angular scales < 0.54 degrees towards Sgr A.
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in $N$) cost of matrix operations used in exact inference. Many solutions have been proposed that rely on $M ll N$ inducing variables to form an approximation at a cost of $mathcal{O}(NM^2)$. While the computational cost appears linear in $N$, the true complexity depends on how $M$ must scale with $N$ to ensure a certain quality of the approximation. In this work, we investigate upper and lower bounds on how $M$ needs to grow with $N$ to ensure high quality approximations. We show that we can make the KL-divergence between the approximate model and the exact posterior arbitrarily small for a Gaussian-noise regression model with $Mll N$. Specifically, for the popular squared exponential kernel and $D$-dimensional Gaussian distributed covariates, $M=mathcal{O}((log N)^D)$ suffice and a method with an overall computational cost of $mathcal{O}(N(log N)^{2D}(loglog N)^2)$ can be used to perform inference.
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $beta$-H{o}lder class with an exponentially decreasing tail, which does not need to be sub-Gaussian. We obtain posterior convergence rates of the regression coefficient and the error density, which are nearly optimal and adaptive to the unknown sparsity level. Furthermore, we derive the semi-parametric Bernstein-von Mises (BvM) theorem to characterize asymptotic shape of the marginal posterior for regression coefficients. Under the sub-Gaussianity assumption on the true score function, strong model selection consistency for regression coefficients are also obtained, which eventually asserts the frequentists validity of credible sets.
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