Machine learning methods for delay estimation in gravitationally lensed signals

Strongly lensed variable quasars can serve as precise cosmological probes, provided that time delays between the image fluxes can be accurately measured. This thesis, explores in detail a new approach based on kernel regression estimates, which is able to estimate a single time delay given several data sets for the same quasar. We develop realistic artificial data sets in order to carry out controlled experiments to test the performance of this new approach. We also test our method on real data from strongly lensed quasar Q0957+561 and compare our estimates against existing results. Furthermore, we attempt to resolve the problem for smaller delays in gravitationally lensed photon streams. We test whether a more principled treatment of delay estimation in lensed photon streams, compared with the standard kernel estimation method, can have benefits of more accurate (less biased) and/or more stable (less variance) estimation. To that end, we propose a delay estimation method in which a single latent nonhomogeneous Poisson process underlying the lensed photon streams is imposed. The rate function model is formulated as a linear combination of nonlinear basis functions. Such a unifying rate function is then used in delay estimation based on the corresponding Innovation Process

Uncovering delayed patterns in noisy and irregularly sampled time series: an astronomy application

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.Comment: 36 pages, 10 figures, 16 tables, accepted for publication in Pattern Recognition. This is a shortened version of the article: interested readers are urged to refer to the published versio

Estimating time delays between irregularly sampled time series

The time delay estimation between time series is a real-world problem in gravitational lensing, an area of astrophysics. Lensing is the most direct method of measuring the distribution of matter, which is often dark, and the accurate measurement of time delays set the scale to measure distances over cosmological scales. For our purposes, this means that we have to estimate a time delay between two or more noisy and irregularly sampled time series. Estimations have been made using statistical methods in the astrophysics literature, such as interpolation, dispersion analysis, discrete correlation function, Gaussian processes and Bayesian method, among others. Instead, this thesis proposes a kernel-based approach to estimating the time delay, which is inspired by kernel methods in the context of statistical and machine learning. Moreover, our methodology is evolved to perform model selection, regularisation and time delay estimation globally and simultaneously. Experimental results show that this approach is one of the most accurate methods for gaps (missing data) and distinct noise levels. Results on artificial and real data are shown

How accurate are the time delay estimates in gravitational lensing?

We present a novel approach to estimate the time delay between light curves of multiple images in a gravitationally lensed system, based on Kernel methods in the context of machine learning. We perform various experiments with artificially generated irregularly-sampled data sets to study the effect of the various levels of noise and the presence of gaps of various size in the monitoring data. We compare the performance of our method with various other popular methods of estimating the time delay and conclude, from experiments with artificial data, that our method is least vulnerable to missing data and irregular sampling, within reasonable bounds of Gaussian noise. Thereafter, we use our method to determine the time delays between the two images of quasar Q0957+561 from radio monitoring data at 4 cm and 6 cm, and conclude that if only the observations at epochs common to both wavelengths are used, the time delay gives consistent estimates, which can be combined to yield 408\pm 12 days. The full 6 cm dataset, which covers a longer monitoring period, yields a value which is 10% larger, but this can be attributed to differences in sampling and missing data.Comment: 14 pages, 12 figures; accepted for publication in Astronomy & Astrophysic

Deep learning in high angular-resolution radio interferometry

This thesis has addressed several challenges of the big data era in the field of high angular-resolution radio astronomy using machine learning algorithms. The methodologies presented in this thesis were designed with the aim of minimizing the need for human interactions, while still providing robust results. This thesis has an interdisciplinary approach and uses knowledge in computer science to advance our understanding of the radio sky. The main objectives of this thesis can be categorized into four subjects. First, it provides an analysis to the properties of the detected radio sources with Very Long Baseline Array (VLBA). Then we have provided the details of our developed source detection and characterization pipeline that can localize the source in any observed image from the VLBA. Beside source detection, the implemented pipeline can remove the observational noise, restore the structure of the celestial sources and predict their properties, such as size and brightness. In the fourth chapter, we have designed an algorithm that can find rare types of galaxies, called strong gravitationally lensed systems, among the many observed radio emitting objects observed with the International LOFAR Telescope. We also have provided preliminary results on using machine learning algorithms to predict the lensing parameters such as the Einstein radius, axis ratio and position angle

Probing the Higher Redshift Universe by Studying Strong Lensing of Gravitational Waves and Enhancing Search Sensitivity of the GstLAL Search Pipeline

The LIGO-Virgo-KAGRA (LVK) collaboration first observed gravitational waves in 2015, and more than $90$ gravitational-wave events have been observed, all coming from mergers of compact objects (black holes and neutron stars), known as compact binary coalescences (CBC). Studying and observing gravitational waves opens a new window for us to understand the nature of spacetime and the universe. Strain data from LVK's detectors are analyzed by search pipelines to identify weak gravitational-wave signals in noisy data. To maximize the potential of gravitational waves, it is essential to continue to improve search pipelines' sensitivity to probe GW sources with the broadest range of parameters and from the furthest distances. I will give a detailed overview of the GstLAL pipeline and present related development (ongoing) work for GstLAL to enhance its search effectiveness and efficiency. In the second part of my thesis, I will focus on gravitational lensing of gravitational waves. As masses can produce curvature in spacetime, gravitational waves, like electromagnetic (EM) waves, are deflected when passing by massive intervening objects before reaching gravitational-wave detectors on Earth, an effect known as gravitational lensing. Observing lensed gravitational waves confirms another prediction in Einstein's general relativity and enables us to conduct cosmography studies, test general relativity, search for dark matter and other exotic phenomena, and deepen our understanding of the universe. I will give a detailed introduction to gravitational lensing of gravitational waves. We then introduce a Targeted subthreshold search for strongly-lensed gravitational wave pipeline called "TESLA". The TESLA pipeline is the flagship to look for sub-threshold lensed gravitational waves. Next, we present the results of the LVK collaboration-wide effort to search for lensing signatures in gravitational-wave data from the third observing run O3. Next, we introduce a significant update to the TESLA pipeline, now known as the TESLA-X pipeline, with enhanced search sensitivity towards lensed gravitational waves. We also introduce an alternative ranking statistic implemented into the TESLA-X pipeline that considers the signal's consistency with the assumed lens model. Finally, we end the thesis with a summary and an outline of possible future work.</p

Searching for strong gravitational lenses

Strong gravitational lenses provide unique laboratories for cosmological and astrophysical investigations, but they must first be discovered - a task that can be met with significant contamination by other astrophysical objects and asterisms. Here we review strong lens searches, covering various sources (quasars, galaxies, supernovae, FRBs, GRBs, and GWs), lenses (early- and late-type galaxies, groups, and clusters), datasets (imaging, spectra, and lightcurves), and wavelengths. We first present the physical characteristics of the lens and source populations, highlighting relevant details for constructing targeted searches. Search techniques are described based on the main lensing feature that is required for the technique to work, namely one of: (i) an associated magnification, (ii) multiple spatially-resolved images, (iii) multiple redshifts, or (iv) a non-zero time delay between images. To use the current lens samples for science, and for the design of future searches, we list several selection biases that exist due to these discovery techniques. We conclude by discussing the future of lens searches in upcoming surveys and the new population of lenses that will be discovered.Comment: 54 pages, 15 figures, submitted to Space Science Reviews, Topical Collection "Strong Gravitational Lensing", eds. J. Wambsganss et a