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Tracking Truth with Liquid Democracy

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arXiv 2021年

作者： Berinsky, Adam J. Halpern, Daniel Halpern, Joseph Y. Jadbabaie, Ali Mossel, Elchanan Procaccia, Ariel Revel, Manon Department of Political Science MIT United States School of Engineering and Applied Sciences Harvard University United States Department of Computer Science Cornell University United States Institute for Data Systems and Society MIT United States Department of Mathematics MIT United States

The dynamics of random transitive delegations on a graph are of particular interest when viewed through the lens of an emerging voting paradigm, liquid democracy. This paradigm allows voters to choose between directly voting and transitively delegating their votes to other voters, so that those selected cast a vote weighted by the number of delegations they received. In the epistemic setting, where voters decide on a binary issue for which there is a ground truth, previous work showed that a few voters may amass such a large amount of influence that liquid democracy is less likely to identify the ground truth than direct voting. We quantify the amount of permissible concentration of power and examine more realistic delegation models, showing they behave well by ensuring that (with high probability) there is a permissible limit on the maximum number of delegations received. Our theoretical results demonstrate that the delegation process is similar to well-known processes on random graphs that are sufficiently bounded for our purposes. Along the way, we prove new bounds on the size of the largest component in an infinite Pólya urn process, which may be of independent interest. In addition, we empirically validate the theoretical results, running six experiments (for a total of N = 168 participants, 62 delegation graphs and over 11k votes collected). We find that empirical delegation behaviors meet the conditions for our positive theoretical guarantees. Overall, our work alleviates concerns raised about liquid democracy and bolsters the case for the applicability of this emerging paradigm. Copyright © 2021, The Authors. All rights reserved.

关键词： Decision theory

A Multiagent Path Search Algorithm for Large-Scale Coalition Structure Generation 39

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A Multiagent Path Search Algorithm for Large-Scale Coalition...

39th Annual AAAI Conference on Artificial Intelligence, AAAI 2025

作者： Taguelmimt, Redha Aknine, Samir Boukredera, Djamila Changder, Narayan Sandholm, Tuomas Clermont Auvergne University Clermont Auvergne INP CNRS LIMOS Clermont-FerrandF-63000 France Univ Lyon UCBL CNRS INSA Lyon Centrale Lyon Univ Lyon 2 LIRIS UMR5205 Lyon France Laboratory of Applied Mathematics Faculty of Exact Sciences University of Bejaia Bejaia Algeria TCG Centres for Research and Education in Science and Technology Kolkata India Carnegie Mellon University Computer Science Department Pittsburgh United States Strategy Robot Inc. United States Strategic Machine Inc. United States Optimized Markets Inc. United States

ISBN: (纸本)157735897X

Coalition structure generation (CSG), i.e. the problem of optimally partitioning a set of agents into coalitions to maximize social welfare, is a fundamental computational problem in multiagent systems. This problem is important for many applications where small run times are necessary, including transportation and disaster response. In this paper, we develop SALDAE, a multiagent path finding algorithm for CSG that operates on a graph of coalition structures. Our algorithm utilizes a variety of heuristics and strategies to perform the search and guide it. It is an anytime algorithm that can handle large problems with hundreds and thousands of agents. We show empirically on nine standard value distributions, including disaster response and electric vehicle allocation benchmarks, that our algorithm enables a rapid finding of high-quality solutions and compares favorably with other state-of-the-art methods. Copyright © 2025, Association for the Advancement of Artificial Intelligence (***). All rights reserved.

关键词： Learning algorithms

CONSTRUCTIVE CONTROLLABILITY FOR INCOMPRESSIBLE VECTOR FIELDS

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arXiv 2022年

作者： Kryzhevich, Sergey G. Stepanov, Eugene Institute of Applied Mathematics Faculty of Applied Physics and Mathematics Gdańsk University of Technology Gdańsk80-233 Poland BioTechMed Center Gdańsk University of Technology Faculty of Mathematics and Computer Science St. Petersburg State University 13B Universitetskaya Emb. St. Petersburg199034 Russia St.Petersburg Branch of the Steklov Mathematical Institute of the Russian Academy of Sciences Fontanka 27 St. Petersburg191023 Russia Higher School of Economics Faculty of Mathematics Usacheva str. 6 Moscow119048 Russia Department of Mathematical Physics Faculty of Mathematics and Mechanics St. Petersburg State University Universitetskij pr. 28 Old Peterhof St. Petersburg198504 Russia

We give a constructive proof of a global controllability result for an autonomous system of ODEs guided by bounded locally Lipschitz and divergence free (i.e. incompressible) vector field, when the phase space is the whole Euclidean space and the vector field satisfies so-called vanishing mean drift condition. For the case when the ODE is defined over some smooth compact connected Riemannian manifold, we significantly strengthen the assertion of the known controllability theorem in absence of nonholonomic constraints by proving that one can find a control steering the state vector from one given point to another by using the observations of only the state vector, i.e., in other words, by changing slightly the vector field, and such a change can be made small not only in uniform, but also in Lipschitz (i.e. C1) *** Codes 37C10, 37C40, 34H05 © 2022, CC BY.

关键词： Ordinary differential equations

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Preface

Studies in Big Data

Studies in Big Data 2023年 138卷 v-vi页

作者： Lotfi, Farhad Hosseinzadeh Allahviranloo, Tofigh Pedrycz, Witold Mozaffari, Mohammad Reza Gerami, Javad Department of Mathematics Science and Research Branch Islamic Azad University Tehran Iran Department of Applied Mathematics Istinye University Istanbul Turkey Department of Electrical and Computer Engineering University of Alberta EdmontonAB Canada Department of Mathematics Shiraz Branch Islamic Azad University Shiraz Iran

Unified approach for solving exit problems for additive-increase and multiplicative-decrease processes

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arXiv 2021年

作者： van der Hofstad, Remco Kapodistria, Stella Palmowski, Zbigniew Shneer, Seva Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 Eindhoven5600 MB Netherlands Heriot-Watt University Edinburgh United Kingdom Faculty of Pure and Applied Mathematics Wroclaw University of Science and Technology Wyb. Wyspiá nskiego 27 Wroclaw50-370 Poland

We analyse an additive-increase and multiplicative-decrease (aka growth-collapse) process that grows linearly in time and that experiences downward jumps at Poisson epochs that are (deterministically) proportional to its present position. This process is used for example in modelling of Transmission Control Protocol (TCP) and can be viewed as a particular example of the so-called shot noise model, a basic tool in modeling earthquakes, avalanches and neuron firings. For this process, and also for its reflected versions, we consider one- and two-sided exit problems that concern the identification of the laws of exit times from fixed intervals and half-lines. All proofs are based on a unified first-step analysis approach at the first jump epoch, which allows us to give explicit, yet involved, formulas for their Laplace transforms. All the eight Laplace transforms can be described in terms of two so-called scale functions Z↑ and L↑. Here Z↑ is described in terms of multiple explicit sums, and L↑ in terms of an explicit recursion formula. All other Laplace transforms can be obtained from Z↑ and L↑ by taking limits, derivatives, integrals and combinations of these. Copyright © 2021, The Authors. All rights reserved.

关键词： Laplace transforms

On Doubly Robust Inference for Double Machine Learning in Semiparametric Regression

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arXiv 2021年

作者： Dukes, Oliver Vansteelandt, Stijn Whitney, David Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent9000 Belgium GSK Gunnels Wood Road StevenageSG1 2NY United Kingdom

Due to concerns about parametric model misspecification, there is interest in using machine learning to adjust for confounding when evaluating the causal effect of an exposure on an outcome. Unfortunately, exposure effect estimators that rely on machine learning predictions are generally subject to so-called plug-in bias, which can render naive p-values and confidence intervals invalid. Progress has been made via proposals like targeted minimum loss estimation and more recently double machine learning, which rely on learning the conditional mean of both the outcome and exposure. Valid inference can then be obtained so long as both predictions converge (sufficiently fast) to the truth. Focusing on partially linear regression models, we show that a specific implementation of the machine learning techniques can yield exposure effect estimators that have small bias even when one of the first-stage predictions does not converge to the truth. The resulting tests and confidence intervals are doubly robust. We also show that the proposed estimators may fail to be regular when only one nuisance parameter is consistently estimated;nevertheless, we observe in simulation studies that our proposal can lead to reduced bias and improved confidence interval coverage in moderate-to-large samples. © 2021, CC BY.

关键词： Adversarial machine learning

Joint Variable Selection of both Fixed and Random Effects for Gaussian Process-based Spatially Varying Coefficient Models

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arXiv 2021年

作者： Dambon, Jakob A. Sigrist, Fabio Furrer, Reinhard Department of Computational Science University of Zurich Switzerland Department of Mathematics University of Zurich Winterthurerstrasse 190 Zurich8057 Switzerland Institute of Financial Services Zug Lucerne University of Applied Sciences and Arts Campus Zug-Rotkreuz Suurstoffi 1 Rotkreuz6343 Switzerland Department of Mathematics University of Zurich Winterthurerstrasse 190 Zurich8057 Switzerland

Spatially varying coefficient (SVC) models are a type of regression model for spatial data where covariate effects vary over space. If there are several covariates, a natural question is which covariates have a spatially varying effect and which not. We present a new variable selection approach for Gaussian process-based SVC models. It relies on a penalized maximum likelihood estimation (PMLE) and allows variable selection both with respect to fixed effects and Gaussian process random effects. We validate our approach both in a simulation study as well as a real world data set. Our novel approach shows good selection performance in the simulation study. In the real data application, our proposed PMLE yields sparser SVC models and achieves a smaller information criterion than classical MLE. In a cross-validation applied on the real data, we show that sparser PML estimated SVC models are on par with ML estimated SVC models with respect to predictive performance. © 2021, CC BY-NC-SA.

关键词： Maximum likelihood estimation

Probing nucleon strange and charm distributions with lattice QCD

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Physical Review D 2021年第9期104卷 094511-094511页

作者： Rui Zhang Huey-Wen Lin Boram Yoon Department of Physics and Astronomy Michigan State University East Lansing Michigan 48824 USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing Michigan 48824 USA Computer Computational and Statistical Sciences CCS-7 Los Alamos National Laboratory Los Alamos New Mexico 87545 USA

We present the first lattice-QCD calculation of the unpolarized strange and charm parton distribution functions using large-momentum effective theory. We use a lattice ensemble with (2+1+1) flavors of highly improved staggered quarks generated by the MILC Collaboration, with lattice spacing a≈0.12 fm and Mπ≈310 MeV, and clover valence fermions with two valence pion masses: 310 and 690 MeV. We use momentum-smeared sources to improve the signal up to nucleon boost momentum Pz=2.15 GeV, and determine nonperturbative renormalization factors in regularization independent momentum subtraction scheme. We compare our lattice results with the matrix elements obtained from matching the parton distribution functions (PDFs) from CT18NNLO and NNPDF3.1NNLO global fits. Our data support the assumptions of strange-antistrange and charm-anticharm symmetry that are commonly used in global PDF fits.

关键词： Lattice QCD Protons

Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions

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arXiv 2023年

作者： Maher, Charles Emmett Jiao, Yang Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The maximally random jammed (MRJ) state is the most random (i.e., disordered) configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors S(k) tend to zero as the wave number |k| tends to zero. Here, we show that generating high-quality strictly jammed states for Euclidean space dimensions d = 3, 4, and 5 is of paramount importance in ensuring hyperuniformity and extracting precise values of the hyperuniformity exponent α > 0 for MRJ states, defined by the power-law behavior of S(k) ∼ |k|α in the limit |k| → 0. Moreover, we show that for fixed d it is more difficult to ensure jamming as the particle number N increases, which results in packings that are nonhyperuniform. Free-volume theory arguments suggest that the ideal MRJ state does not contain rattlers, which act as defects in numerically generated packings. As d increases, we find that the fraction of rattlers decreases substantially. Our analysis of the largest truly jammed packings suggests that the ideal MRJ packings for all dimensions d ≥ 3 are hyperuniform with α = d − 2, implying the packings become more hyperuniform as d increases. The differences in α between MRJ packings and recently proposed Manna-class random close packed (RCP) states, which were reported to have α = 0.25 in d = 3 and be nonhyperuniform (α = 0) for d = 4 and d = 5, demonstrate the vivid distinctions between the large-scale structure of RCP and MRJ states in these dimensions. Our paper clarifies the importance of the link between true jamming and hyperuniformity and motivates the development of an algorithm to produce rattler-free three-dimensional MRJ packings. © 2023, CC BY.

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