On kissing numbers and spherical codes in high dimensions
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2018.07.001
Abstract: We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on the kissing number in dimension $d$. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in the dimension.… read more here.
Keywords: codes high; spherical codes; high dimensions; numbers spherical ... See more keywords
Early warning signals for bifurcations embedded in high dimensions
Sign Up to like & getrecommendations! Published in 2024 at "Scientific Reports"
DOI: 10.1038/s41598-024-68177-1
Abstract: Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can play out on… read more here.
Keywords: embedded high; bifurcations embedded; signals bifurcations; early warning ... See more keywords
An ADMM with continuation algorithm for non-convex SICA-penalized regression in high dimensions
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Statistical Computation and Simulation"
DOI: 10.1080/00949655.2018.1448397
Abstract: Abstract The smooth integration of counting and absolute deviation (SICA) penalty has been demonstrated theoretically and practically to be effective in non-convex penalization for variable selection. However, solving the non-convex optimization problem associated with the… read more here.
Keywords: sica penalized; convex; high dimensions; continuation algorithm ... See more keywords
Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review. E"
DOI: 10.1103/physreve.99.031301
Abstract: The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse glass forming mixtures bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions d=2 and 3. Here, we… read more here.
Keywords: bypassing sluggishness; swap; swap algorithm; high dimensions ... See more keywords
Canonical correlation analysis in high dimensions with structured regularization
Sign Up to like & getrecommendations! Published in 2021 at "Statistical Modelling"
DOI: 10.1177/1471082x211041033
Abstract: Canonical correlation analysis (CCA) is a technique for measuring the association between two multivariate data matrices. A regularized modification of canonical correlation analysis (RCCA) which imposes an [Formula: see text] penalty on the CCA coefficients… read more here.
Keywords: high dimensions; correlation analysis; canonical correlation; regularization ... See more keywords
Group inference in high dimensions with applications to hierarchical testing
Sign Up to like & getrecommendations! Published in 2021 at "Electronic Journal of Statistics"
DOI: 10.1214/21-ejs1955
Abstract: Group inference has been a long-standing question in statistics and the development of high-dimensional group inference is an essential part of statistical methods for analyzing complex data sets, including hierarchical testing, tests of interaction, detection… read more here.
Keywords: group; inference high; group inference; high dimensions ... See more keywords
The Gaussian core model in high dimensions
Sign Up to like & getrecommendations! Published in 2018 at "Duke Mathematical Journal"
DOI: 10.1215/00127094-2018-0018
Abstract: We prove lower bounds for energy in the Gaussian core model, in which point particles interact via a Gaussian potential. Under the potential function $t \mapsto e^{-\alpha t^2}$ with $0 \pi e$. As a consequence… read more here.
Keywords: high dimensions; core model; gaussian core; model high ... See more keywords
A robust and nonparametric two-sample test in high dimensions
Sign Up to like & getrecommendations! Published in 2021 at "Statistica Sinica"
DOI: 10.5705/ss.202019.0170
Abstract: Many tests are proposed in the literature to test homogeneity of two random samples, that is, the exact equivalence of their statistical distributions. When the two random samples are high-dimensional or not normally distributed, the… read more here.
Keywords: nonparametric two; high dimensions; two sample; test ... See more keywords