Learning tensor representations for meta-learning
We introduce a tensor-based model of shared representation for meta-learning from a
diverse set of tasks. Prior works on learning linear representations for meta-learning assume …
diverse set of tasks. Prior works on learning linear representations for meta-learning assume …
Approximability of p → q Matrix Norms: Generalized Krivine Rounding and Hypercontractive Hardness
We study the problem of computing the p→ q operator norm of a matrix A in ℝ m× n, defined
as‖ A‖ p→ q:= sup x∊ ℝ n\{0}‖ Ax‖ q/‖ x‖ p. This problem generalizes the spectral …
as‖ A‖ p→ q:= sup x∊ ℝ n\{0}‖ Ax‖ q/‖ x‖ p. This problem generalizes the spectral …
Inapproximability of Matrix Norms
We study the problem of computing the $ p\rightarrow q $ norm of a matrix $ A\in R^{m\times
n} $, defined as\[\| A\| _ {p\rightarrow q}~:=~\max_ {x\,\in\, R^ n\setminus\{0\}}\frac {\| Ax\| _q} …
n} $, defined as\[\| A\| _ {p\rightarrow q}~:=~\max_ {x\,\in\, R^ n\setminus\{0\}}\frac {\| Ax\| _q} …
The -Levy-Grothendieck problem and norms of Levy matrices
K Ramanan, X Xie - arXiv preprint arXiv:2404.18299, 2024 - arxiv.org
Given an $ n\times n $ matrix $ A_n $ and $1\leq r, p\leq\infty $, consider the following
quadratic optimization problem referred to as the $\ell_r $-Grothendieck problem:\begin …
quadratic optimization problem referred to as the $\ell_r $-Grothendieck problem:\begin …
Streaming Algorithms with Large Approximation Factors
We initiate a broad study of classical problems in the streaming model with insertions and
deletions in the setting where we allow the approximation factor $\alpha $ to be much larger …
deletions in the setting where we allow the approximation factor $\alpha $ to be much larger …
Inapproximability of Matrix Norms
We study the problem of computing the norm of a matrix, defined as. This problem
generalizes the spectral norm of a matrix () and the Grothendieck problem (,) and has been …
generalizes the spectral norm of a matrix () and the Grothendieck problem (,) and has been …
[PDF][PDF] The r-to-p norm of non-negative random matrices: asymptotic normality and entry-wise bounds
arXiv:2005.14056v1 [math.PR] 28 May 2020 Page 1 arXiv:2005.14056v1 [math.PR] 28 May
2020 The r-to-p norm of non-negative random matrices: Asymptotic normality and entry-wise …
2020 The r-to-p norm of non-negative random matrices: Asymptotic normality and entry-wise …
An empirical evaluation of sketched svd and its application to leverage score ordering
The power of randomized algorithms in numerical methods have led to fast solutions which
use the Singular Value Decomposition (SVD) as a core routine. However, given the large …
use the Singular Value Decomposition (SVD) as a core routine. However, given the large …
On r-to-p norms of random matrices with nonnegative entries: Asymptotic normality and -bounds for the maximizer
For an n× n matrix A n, the r→ p operator norm is defined as‖ A n‖ r→ p:= sup x∈ R n:‖
x‖ r≤ 1‖ A nx‖ p for r, p≥ 1. For different choices of r and p, this norm corresponds to key …
x‖ r≤ 1‖ A nx‖ p for r, p≥ 1. For different choices of r and p, this norm corresponds to key …