Scaling-up Split-Merge MCMC with Locality Sensitive Sampling (LSS)

Split-Merge MCMC (Monte Carlo Markov Chain) is one of the essential and popular variants of MCMC for problems when an MCMC state consists of an unknown number of components. It is well known that state-of-the-art methods for split-merge MCMC do not scale well. Strategies for rapid mixing requires smart and informative proposals to reduce the rejection rate. However, all known smart proposals involve expensive operations to suggest informative transitions. As a result, the cost of each iteration is prohibitive for massive scale datasets. It is further known that uninformative but computationally efficient proposals, such as random split-merge, leads to extremely slow convergence. This tradeoff between mixing time and per update cost seems hard to get around. In this paper, we show a sweet spot. We leverage some unique properties of weighted MinHash, which is a popular LSH, to design a novel class of split-merge proposals which are significantly more informative than random sampling but at the same time efficient to compute. Overall, we obtain a superior tradeoff between convergence and per update cost. As a direct consequence, our proposals are around 6X faster than the state-of-the-art sampling methods on two large real datasets KDDCUP and PubMed with several millions of entities and thousands of clusters

Cosmology with the Laser Interferometer Space Antenna

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe

Higher Order Couplings in the Clustering of Biased Tracers of Large-Scale Structure

The Large-Scale Structure (LSS) of the Universe, i.e. the distribution of matter and luminous tracers (such as galaxies), contains a wealth of information about the origin, composition, and evolution of the Universe. In order to extract this information, the non-linearities present in late-time observables provided by LSS surveys must be understood well. In general, there are three main sources of non-linearities: (1) non-linear matter clustering due to gravity; (2) non-linear biasing, i.e. the relation between the distribution of tracers and dark matter; and (3) primordial non-Gaussianity, which induces non-linearities in the initial conditions. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a powerful framework to model the non-linear clustering due to gravity. In this thesis, we focus on understanding the non-linearities due to galaxy biasing using the EFTofLSS and numerical N-body simulations. This thesis is comprised of the following three projects: In the first part, we present a novel method to constrain quadratic and cubic galaxy bias parameters in dark matter simulations. The natural statistics to constrain quadratic and cubic bias parameters are tree-level bispectrum and trispectrum, respectively. Since these statistics are computationally quite expensive, we use efficient squared and cubic field estimators that contain integrated bispectrum and trispectrum information. We use the constraints to model the one-loop halo-matter power spectrum and show that the results agree with simulations up to kmax = 0.1h Mpc 1 once an additional derivative bias is implemented (Published in: Abidi & Baldauf, JCAP07(2018)029). In the second part, we develop a formalism to reconstruct the linear density field based on quadratic couplings in galaxy clustering. We employ a quadratic estimator inspired by Cosmic Microwave Background (CMB) lensing reconstruction. We incorporate non-linearities due to gravity, galaxy biasing and primordial non-Gaussianity, and verify our predictions with N-body simulations. We perform a Fisher matrix analysis on how the reconstructed field in combination with the biased tracer field can improve constraints on local type primordial non-Gaussianity. We find significant improvement on constraints due to cosmic variance cancellation resulting from the additional correlated modes of the reconstructed field, similar to multi-tracer analyses. In the third part, we develop a method to constrain non-linear galaxy bias parameters using the two- and three-point functions of projected galaxy clustering in correlation with CMB lensing convergence. The project thus aims to bring the methodology developed in project 1 above closer to data. We develop the quadratic field method for projected fields to avoid complications from non-linear redshift space distortions. We perform a Fisher forecast to show that this method can indeed be used to put constraints on bias parameters and the amplitude of matter fluctuations. Finally, using N-body simulations we ascertain that the projected statistics do indeed reduce the impact of finger-of-god corrections.My PhD was generously funded by the Cambridge Commonwealth, European and International Trust and the Higher Education Commission Pakistan. I have additionally received invaluable financial assistance from St. Edmunds College, Cambridge, the Cambridge Philosophical Society, the Centre for Theoretical Cosmology, Dr Blake Sherwin's EPRC grant, the Postgraduate Lundgren Award, and the Santander Award

Cosmology with the Laser Interferometer Space Antenna

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe

Cosmology with the Laser Interferometer Space Antenna

This work is partly supported by: A.G. Leventis Foundation; Academy of Finland Grants 328958 and 345070; Alexander S. Onassis Foundation, Scholarship ID: FZO 059-1/2018-2019; Amaldi Research Center funded by the MIUR program “Dipartimento di Eccellenza” (CUP: B81I18001170001); ASI Grants No. 2016-24-H.0 and No. 2016-24-H.1-2018; Atracción de Talento Grant 2019-T1/TIC-15784; Atracción de Talento contract no. 2019-T1/TIC-13177 granted by the Comunidad de Madrid; Ayuda ‘Beatriz Galindo Senior’ by the Spanish ‘Ministerio de Universidades’, Grant BG20/00228; Basque Government Grant (IT-979-16); Belgian Francqui Foundation; Centre national d’Etudes spatiales; Ben Gurion University Kreitman Fellowship, and the Israel Academy of Sciences and Humanities (IASH) & Council for Higher Education (CHE) Excellence Fellowship Program for International Postdoctoral Researchers; Centro de Excelencia Severo Ochoa Program SEV-2016-0597; CERCA program of the Generalitat de Catalunya; Cluster of Excellence “Precision Physics, Fundamental Interactions, and Structure of Matter” (PRISMA+ EXC 2118/1); Comunidad de Madrid, Contrato de Atracción de Talento 2017-T1/TIC-5520; Czech Science Foundation GAČR, Grant No. 21-16583M; Delta ITP consortium; Department of Energy under Grant No. DE-SC0008541, DE-SC0009919 and DE-SC0019195; Deutsche Forschungsgemeinschaft (DFG), Project ID 438947057; Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy - EXC 2121 Quantum Universe - 390833306; European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (Project CoGraDS - CZ.02.1.01/0.0/0.0/15 003/0000437); European Union’s H2020 ERC Consolidator Grant “GRavity from Astrophysical to Microscopic Scales” (Grant No. GRAMS-815673); European Union’s H2020 ERC, Starting Grant Agreement No. DarkGRA-757480; European Union’s Horizon 2020 programme under the Marie Sklodowska-Curie Grant Agreement 860881 (ITN HIDDeN); European Union’s Horizon 2020 Research and Innovation Programme Grant No. 796961, “AxiBAU” (K.S.); European Union’s Horizon 2020 Research Council grant 724659 MassiveCosmo ERC-2016-COG; FCT through national funds (PTDC/FIS-PAR/31938/2017) and through project “BEYLA – BEYond LAmbda” with Ref. Number PTDC/FIS-AST/0054/2021; FEDER-Fundo Europeu de Desenvolvimento Regional through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI-01-0145-FEDER-031938) and research Grants UIDB/04434/2020 and UIDP/04434/2020; Fondation CFM pour la Recherche in France; Foundation for Education and European Culture in Greece; French ANR project MMUniverse (ANR-19-CE31-0020); FRIA Grant No.1.E.070.19F of the Belgian Fund for Research, F.R.S.-FNRS Fundação para a Ciência e a Tecnologia (FCT) through Contract No. DL 57/2016/CP1364/CT0001; Fundação para a Ciência e a Tecnologia (FCT) through Grants UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-OUT/29048/2017, CERN/FIS-PAR/0037/2019 and “CosmoTests – Cosmological tests of gravity theories beyond General Relativity” CEECIND/00017/2018; Generalitat Valenciana Grant PROMETEO/2021/083; Grant No. 758792, project GEODESI; Government of Canada through the Department of Innovation, Science and Economic Development and Province of Ontario through the Ministry of Colleges and Universities; Grants-in-Aid for JSPS Overseas Research Fellow (No. 201960698); I+D Grant PID2020-118159GB-C41 of the Spanish Ministry of Science and Innovation; INFN iniziativa specifica TEONGRAV; Israel Science Foundation (Grant No. 2562/20); Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Nos. 20H01899 and 20H05853; IFT Centro de Excelencia Severo Ochoa Grant SEV-2; Kavli Foundation and its founder Fred Kavli; Minerva Foundation; Ministerio de Ciencia e Innovacion Grant PID2020-113644GB-I00; NASA Grant 80NSSC19K0318; NASA Hubble Fellowship grants No. HST-HF2-51452.001-A awarded by the Space Telescope Science Institute with NASA contract NAS5-26555; Netherlands Organisation for Science and Research (NWO) Grant Number 680-91-119; new faculty seed start-up grant of the Indian Institute of Science, Bangalore, the Core Research Grant CRG/2018/002200 of the Science and Engineering; NSF Grants PHY-1820675, PHY-2006645 and PHY-2011997; Polish National Science Center Grant 2018/31/D/ST2/02048; Polish National Agency for Academic Exchange within the Polish Returns Programme under Agreement PPN/PPO/2020/1/00013/U/00001; Pró-Reitoria de Pesquisa of Universidade Federal de Minas Gerais (UFMG) under Grant No. 28359; Ramón y Cajal Fellowship contract RYC-2017-23493; Research Project PGC2018-094773-B-C32 [MINECO-FEDER]; Research Project PGC2018-094773-B-C32 [MINECO-FEDER]; ROMFORSK Grant Project. No. 302640; Royal Society Grant URF/R1/180009 and ERC StG 949572: SHADE; Shota Rustaveli National Science Foundation (SRNSF) of Georgia (Grant FR/18-1462); Simons Foundation/SFARI 560536; SNSF Ambizione grant; SNSF professorship Grant (No. 170547); Spanish MINECO’s “Centro de Excelencia Severo Ochoa” Programme Grants SEV-2016-0597 and PID2019-110058GB-C22; Spanish Ministry MCIU/AEI/FEDER Grant (PGC2018-094626-B-C21); Spanish Ministry of Science and Innovation (PID2020-115845GB-I00/AEI/10.13039/501100011033); Spanish Proyectos de I+D via Grant PGC2018-096646-A-I00; STFC Consolidated Grant ST/T000732/1; STFC Consolidated Grants ST/P000762/1 and ST/T000791/1; STFC Grant ST/S000550/1; STFC Grant ST/T000813/1; STFC Grants ST/P000762/1 and ST/T000791/1; STFC under the research Grant ST/P000258/1; Swiss National Science Foundation (SNSF), project The Non-Gaussian Universe and Cosmological Symmetries, Project Number: 200020-178787; Swiss National Science Foundation Professorship Grants No. 170547 and No. 191957; SwissMap National Center for Competence in Research; “The Dark Universe: A Synergic Multi-messenger Approach” Number 2017X7X85K under the MIUR program PRIN 2017; UK Space Agency; UKSA Flagship Project, Euclid.The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe.Atracción de Talento 2019-T1/TIC-13177Centro de Excelencia Severo Ochoa Program EXC 2118/1, SEV-2016-0597Contrato de Atracción de Talento 2017-T1/TIC-5520European Union’s H2020 ERC GRAMS-815673European Union’s Horizon 2020 Research Council 724659 MassiveCosmo ERC-2016-COGEuropean Union’s Horizon 2020 programme 860881, ITN HIDDeNIFT Centro de Excelencia Severo OchoaSpanish Ministry MCIU PGC2018-094626-B-C21, PGC2018-096646-A-I00, PID2020-115845GB-I00/AEI/10.13039/501100011033Horizon 2020 Framework Programme 796961 H2020Comunidad de MadridEusko Jaurlaritza IT-979-16Ministerio de Economía y Competitividad 302640 MINECOGeneralitat Valenciana 758792, PROMETEO/2021/083 GVAMinisterio de Ciencia e Innovación PID2020-113644GB-I00 MICINNMinisterio de Universidades BG20/00228 MIUEuropean Union’s H2020 ERC, DarkGRA-75748

Cosmology with the Laser Interferometer Space Antenna

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, los autores pertenecientes a la UAM y el nombre del grupo de colaboración, si lo hubiereThe Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universeThis work is partly supported by: A.G. Leventis Foundation; Academy of Finland Grants 328958 and 345070; Alexander S. Onassis Foundation, Scholarship ID: FZO 059-1/2018-2019; Amaldi Research Center funded by the MIUR program “Dipartimento di Eccellenza” (CUP: B81I18001170001); ASI Grants No. 2016-24-H.0 and No. 2016-24-H.1-2018; Atracción de Talento Grant 2019-T1/TIC-15784; Atracción de Talento contract no. 2019-T1/TIC-13177 granted by the Comunidad de Madrid; Ayuda ‘Beatriz Galindo Senior’ by the Spanish ‘Ministerio de Universidades’, Grant BG20/00228; Basque Government Grant (IT-979-16); Belgian Francqui Foundation; Centre national d’Etudes spatiales; Ben Gurion University Kreitman Fellowship, and the Israel Academy of Sciences and Humanities (IASH) & Council for Higher Education (CHE) Excellence Fellowship Program for International Postdoctoral Researchers; Centro de Excelencia Severo Ochoa Program SEV-2016-0597; CERCA program of the Generalitat de Catalunya; Cluster of Excellence “Precision Physics, Fundamental Interactions, and Structure of Matter” (PRISMA? EXC 2118/1); Comunidad de Madrid, Contrato de Atracción de Talento 2017-T1/TIC-5520; Czech Science Foundation GAČR, Grant No. 21-16583M; Delta ITP consortium; Department of Energy under Grant No. DE-SC0008541, DE-SC0009919 and DESC0019195; Deutsche Forschungsgemeinschaft (DFG), Project ID 438947057; Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy - EXC 2121 Quantum Universe - 390833306; European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (Project CoGraDS - CZ.02.1.01/0.0/0.0/15 003/0000437); European Union’s H2020 ERC Consolidator Grant “GRavity from Astrophysical to Microscopic Scales” (Grant No. GRAMS-815673); European Union’s H2020 ERC, Starting Grant Agreement No. DarkGRA-757480; European Union’s Horizon 2020 programme under the Marie Sklodowska-Curie Grant Agreement 860881 (ITN HIDDeN); European Union’s Horizon 2020 Research and Innovation Programme Grant No. 796961, “AxiBAU” (K.S.); European Union’s Horizon 2020 Research Council grant 724659 MassiveCosmo ERC-2016-COG; FCT through national funds (PTDC/FIS-PAR/31938/2017) and through project “BEYLA – BEYond LAmbda” with Ref. Number PTDC/FIS-AST/0054/2021; FEDER-Fundo Europeu de Desenvolvimento Regional through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI-01-0145- FEDER-031938) and research Grants UIDB/04434/2020 and UIDP/04434/2020; Fondation CFM pour la Recherche in France; Foundation for Education and European Culture in Greece; French ANR project MMUniverse (ANR-19-CE31-0020); FRIA Grant No.1.E.070.19F of the Belgian Fund for Research, F.R. S.-FNRS Fundação para a Ciência e a Tecnologia (FCT) through Contract No. DL 57/2016/CP1364/ CT0001; Fundação para a Ciência e a Tecnologia (FCT) through Grants UIDB/04434/2020, UIDP/04434/ 2020, PTDC/FIS-OUT/29048/2017, CERN/FIS-PAR/0037/2019 and “CosmoTests – Cosmological tests of gravity theories beyond General Relativity” CEECIND/00017/2018; Generalitat Valenciana Grant PROMETEO/2021/083; Grant No. 758792, project GEODESI; Government of Canada through the Department of Innovation, Science and Economic Development and Province of Ontario through the Ministry of Colleges and Universities; Grants-in-Aid for JSPS Overseas Research Fellow (No. 201960698); I?D Grant PID2020-118159GB-C41 of the Spanish Ministry of Science and Innovation; INFN iniziativa specifica TEONGRAV; Israel Science Foundation (Grant No. 2562/20); Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Nos. 20H01899 and 20H05853; IFT Centro de Excelencia Severo Ochoa Grant SEV-2; Kavli Foundation and its founder Fred Kavli; Minerva Foundation; Ministerio de Ciencia e Innovacion Grant PID2020-113644GB-I00; NASA Grant 80NSSC19K0318; NASA Hubble Fellowship grants No. HST-HF2-51452.001-A awarded by the Space Telescope Science Institute with NASA contract NAS5-26555; Netherlands Organisation for Science and Research (NWO) Grant Number 680-91-119; new faculty seed start-up grant of the Indian Institute of Science, Bangalore, the Core Research Grant CRG/2018/002200 of the Science and Engineering; NSF Grants PHY-1820675, PHY-2006645 and PHY-2011997; Polish National Science Center Grant 2018/31/D/ ST2/02048; Polish National Agency for Academic Exchange within the Polish Returns Programme under Agreement PPN/PPO/2020/1/00013/U/00001; Pró-Reitoria de Pesquisa of Universidade Federal de Minas Gerais (UFMG) under Grant No. 28359; Ramón y Cajal Fellowship contract RYC-2017-23493; Research Project PGC2018-094773-B-C32 [MINECO-FEDER]; Research Project PGC2018-094773-B-C32 [MINECO-FEDER]; ROMFORSK Grant Project. No. 302640; Royal Society Grant URF/R1/180009 and ERC StG 949572: SHADE; Shota Rustaveli National Science Foundation (SRNSF) of Georgia (Grant FR/18-1462); Simons Foundation/SFARI 560536; SNSF Ambizione grant; SNSF professorship Grant (No. 170547); Spanish MINECO’s “Centro de Excelencia Severo Ochoa” Programme Grants SEV-2016- 0597 and PID2019-110058GB-C22; Spanish Ministry MCIU/AEI/FEDER Grant (PGC2018-094626-BC21); Spanish Ministry of Science and Innovation (PID2020-115845GB-I00/AEI/10.13039/ 501100011033); Spanish Proyectos de I?D via Grant PGC2018-096646-A-I00; STFC Consolidated Grant ST/T000732/1; STFC Consolidated Grants ST/P000762/1 and ST/T000791/1; STFC Grant ST/ S000550/1; STFC Grant ST/T000813/1; STFC Grants ST/P000762/1 and ST/T000791/1; STFC under the research Grant ST/P000258/1; Swiss National Science Foundation (SNSF), project The Non-Gaussian Universe and Cosmological Symmetries, Project Number: 200020-178787; Swiss National Science Foundation Professorship Grants No. 170547 and No. 191957; SwissMap National Center for Competence in Research; “The Dark Universe: A Synergic Multi-messenger Approach” Number 2017X7X85K under the MIUR program PRIN 2017; UK Space Agency; UKSA Flagship Project, Eucli