Probabilistic Auto-Encoder

We introduce the Probabilistic Auto-Encoder (PAE), a generative model with a lower dimensional latent space that is based on an Auto-Encoder which is interpreted probabilistically after training using a Normalizing Flow. The PAE combines the advantages of an Auto-Encoder, i.e. it is fast and easy to train and achieves small reconstruction error, with the desired properties of a generative model, such as high sample quality and good performance in downstream tasks. Compared to a VAE and its common variants, the PAE trains faster, reaches lower reconstruction error and achieves state of the art samples without parameter fine-tuning or annealing schemes. We demonstrate that the PAE is further a powerful model for performing the downstream tasks of outlier detection and probabilistic image reconstruction: 1) Starting from the Laplace approximation to the marginal likelihood, we identify a PAE-based outlier detection metric which achieves state of the art results in Out-of-Distribution detection outperforming other likelihood based estimators. 2) Using posterior analysis in the PAE latent space we perform high dimensional data inpainting and denoising with uncertainty quantification.Comment: 11 pages, 6 figures. Code available at https://github.com/VMBoehm/PAE. Updated version with additional references and appendi

RSD measurements from BOSS galaxy power spectrum using the halo perturbation theory model

We present growth of structure constraints from the cosmological analysis of the power spectrum multipoles of SDSS-III BOSS DR12 galaxies. We use the galaxy power spectrum model of Hand et al. (2017), which decomposes the galaxies into halo mass bins, each of which is modeled separately using the relations between halo biases and halo mass. The model combines Eulerian perturbation theory and halo model calibrated on $N$-body simulations to model the halo clustering. In this work, we also generate the covariance matrix by combining the analytic disconnected part with the empirical connected part: we smooth the connected component by selecting a few principal components and show that it achieves good agreement with the mock covariance. Our analysis differs from recent analyses in that we constrain a single parameter $f\sigma_8$ fixing everything else to Planck+BAO prior, thereby reducing the effects of prior volume and mismodeling. We find tight constraints on $f\sigma_8$: $f\sigma_8(z_{\mathrm{eff}}=0.38)=0.489 \pm 0.038$ and $f\sigma_8(z_{\mathrm{eff}}=0.61)=0.455 \pm 0.028$ at $k_{\mathrm{max}} = 0.2\ h$Mpc$^{-1}$, with an overall amplitude error of 5(within 0.3 sigma) of Planck amplitude. We discuss the sensitivity of cosmological parameter estimation to the choice of scale cuts, covariance matrix, and the inclusion of hexadecapole$P_4(k)$. We show that with$k_{\mathrm{max}} = 0.4\ h$Mpc$^{-1}$the constraints improve considerably to an overall 3.2misspecification on MultiDark-PATCHY mocks. Choosing$k_{\mathrm{max}}$ consistently and reliably remains the main challenge of RSD analysis methods.Comment: 21 pages, 13 figure