78 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Perfect Sampling for Hard Spheres from Strong Spatial Mixing
We provide a perfect sampling algorithm for the hard-sphere model on subsets of R^d with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Asymptotics and Statistical Inference in High-Dimensional Low-Rank Matrix Models
High-dimensional matrix and tensor data is ubiquitous in machine learning and statistics
and often exhibits low-dimensional structure. With the rise of these types of data is the need to develop statistical inference procedures that adequately address the low-dimensional structure in a principled manner. In this dissertation we study asymptotic theory and statistical inference in structured low-rank matrix models in high-dimensional regimes where the column and row dimensions of the matrix are allowed to grow, and we consider a variety of settings for which structured low-rank matrix models manifest.
Chapter 1 establishes the general framework for statistical analysis in high-dimensional low-rank matrix models, including introducing entrywise perturbation bounds, asymptotic theory, distributional theory, and statistical inference, illustrated throughout via the matrix denoising model. In Chapter 2, Chapter 3, and Chapter 4 we study the entrywise estimation of singular vectors and eigenvectors in different structured settings, with Chapter 2 considering heteroskedastic and dependent noise, Chapter 3 sparsity, and Chapter 4 additional tensor structure. In Chapter 5 we apply previous asymptotic theory to study a two-sample
test for equality of distribution in network analysis, and in Chapter 6 we study a model for shared community memberships across multiple networks, and we propose and analyze a joint spectral clustering algorithm that leverages newly developed asymptotic theory for this setting.
Throughout this dissertation we emphasize tools and techniques that are data-driven, nonparametric, and adaptive to signal strength, and, where applicable, noise distribution. The contents of Chapters 2-6 are based on the papers Agterberg et al. (2022b); Agterberg and Sulam (2022); Agterberg and Zhang (2022); Agterberg et al. (2020a) and Agterberg et al. (2022a) respectively, and Chapter 1 contains several novel results
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Fundamentals
Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
Semidefinite programming relaxations for quantum correlations
Semidefinite programs are convex optimisation problems involving a linear
objective function and a domain of positive semidefinite matrices. Over the
last two decades, they have become an indispensable tool in quantum information
science. Many otherwise intractable fundamental and applied problems can be
successfully approached by means of relaxation to a semidefinite program. Here,
we review such methodology in the context of quantum correlations. We discuss
how the core idea of semidefinite relaxations can be adapted for a variety of
research topics in quantum correlations, including nonlocality, quantum
communication, quantum networks, entanglement, and quantum cryptography.Comment: To be submitted to Reviews of Modern Physic
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