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Oct 29

An Efficient Tester-Learner for Halfspaces

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

  • 4 authors
·
Feb 28, 2023

Euclid Quick Data Release (Q1). Active galactic nuclei identification using diffusion-based inpainting of Euclid VIS images

Light emission from galaxies exhibit diverse brightness profiles, influenced by factors such as galaxy type, structural features and interactions with other galaxies. Elliptical galaxies feature more uniform light distributions, while spiral and irregular galaxies have complex, varied light profiles due to their structural heterogeneity and star-forming activity. In addition, galaxies with an active galactic nucleus (AGN) feature intense, concentrated emission from gas accretion around supermassive black holes, superimposed on regular galactic light, while quasi-stellar objects (QSO) are the extreme case of the AGN emission dominating the galaxy. The challenge of identifying AGN and QSO has been discussed many times in the literature, often requiring multi-wavelength observations. This paper introduces a novel approach to identify AGN and QSO from a single image. Diffusion models have been recently developed in the machine-learning literature to generate realistic-looking images of everyday objects. Utilising the spatial resolving power of the Euclid VIS images, we created a diffusion model trained on one million sources, without using any source pre-selection or labels. The model learns to reconstruct light distributions of normal galaxies, since the population is dominated by them. We condition the prediction of the central light distribution by masking the central few pixels of each source and reconstruct the light according to the diffusion model. We further use this prediction to identify sources that deviate from this profile by examining the reconstruction error of the few central pixels regenerated in each source's core. Our approach, solely using VIS imaging, features high completeness compared to traditional methods of AGN and QSO selection, including optical, near-infrared, mid-infrared, and X-rays.

  • 274 authors
·
Mar 19

Euclid Quick Data Release (Q1): From images to multiwavelength catalogues: the Euclid MERge Processing Function

The Euclid satellite is an ESA mission that was launched in July 2023. \Euclid is working in its regular observing mode with the target of observing an area of 14,000~deg^2 with two instruments, the Visible Camera (VIS) and the Near IR Spectrometer and Photometer (NISP) down to I_{rm E} = 24.5~mag (10, sigma) in the Euclid Wide Survey. Ground-based imaging data in the ugriz bands complement the \Euclid data to enable photo-z determination and VIS PSF modeling for week lensing analysis. Euclid investigates the distance-redshift relation and the evolution of cosmic structures by measuring shapes and redshifts of galaxies and clusters of galaxies out to zsim 2. Generating the multi-wavelength catalogues from \Euclid and ground-based data is an essential part of the \Euclid data processing system. In the framework of the \Euclid Science Ground Segment (SGS), the aim of the MER Processing Function (PF) pipeline is to detect objects in the \Euclid imaging data, measure their properties, and MERge them into a single multi-wavelength catalogue. The MER PF pipeline performs source detection on both visible (VIS) and near-infrared (NIR) images and offers four different photometric measurements: Kron total flux, aperture photometry on PSF-matched images, template fitting photometry, and S\'ersic fitting photometry. Furthermore, the MER PF pipeline measures a set of ancillary quantities, spanning from morphology to quality flags, to better characterise all detected sources. In this paper, we show how the MER PF pipeline is designed, detailing its main steps, and we show that the pipeline products meet the tight requirements that Euclid aims to achieve on photometric accuracy. We also present the other measurements (e.g. morphology) that are included in the OU-MER output catalogues and we list all output products coming out of the MER PF pipeline.

  • 348 authors
·
Mar 19

Euclid. II. The VIS Instrument

This paper presents the specification, design, and development of the Visible Camera (VIS) on the ESA Euclid mission. VIS is a large optical-band imager with a field of view of 0.54 deg^2 sampled at 0.1" with an array of 609 Megapixels and spatial resolution of 0.18". It will be used to survey approximately 14,000 deg^2 of extragalactic sky to measure the distortion of galaxies in the redshift range z=0.1-1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes of Euclid. With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and, from how this has changed with look-back time, the nature of dark energy and theories of gravity can be constrained. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, reaching m_AB>24.5 with S/N >10 in a single broad I_E~(r+i+z) band over a six year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the VIS concept and describes the instrument design and development before reporting the pre-launch performance derived from ground calibrations and brief results from the in-orbit commissioning. VIS should reach fainter than m_AB=25 with S/N>10 for galaxies of full-width half-maximum of 0.3" in a 1.3" diameter aperture over the Wide Survey, and m_AB>26.4 for a Deep Survey that will cover more than 50 deg^2. The paper also describes how VIS works with the other Euclid components of survey, telescope, and science data processing to extract the cosmological information.

  • 435 authors
·
May 22, 2024