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pro vyhledávání: '"Abdalla, Pedro P"'
We study the optimization landscape of a smooth nonconvex program arising from synchronization over the two-element group $\mathbf{Z}_2$, that is, recovering $z_1, \dots, z_n \in \{\pm 1\}$ from (noisy) relative measurements $R_{ij} \approx z_i z_j$.
Externí odkaz:
http://arxiv.org/abs/2407.13407
Autor:
Abdalla, Pedro, Kur, Gil
Quantifying uncertainty in high-dimensional sparse linear regression is a fundamental task in statistics that arises in various applications. One of the most successful methods for quantifying uncertainty is the debiased LASSO, which has a solid theo
Externí odkaz:
http://arxiv.org/abs/2402.16764
Autor:
Abdalla, Pedro, Mendelson, Shahar
We construct an estimator $\widehat{\Sigma}$ for covariance matrices of unknown, centred random vectors X, with the given data consisting of N independent measurements $X_1,...,X_N$ of X and the wanted confidence level. We show under minimal assumpti
Externí odkaz:
http://arxiv.org/abs/2402.08288
Autor:
Abdalla, Pedro
We consider the problem of estimating the covariance matrix of a random vector by observing i.i.d samples and each entry of the sampled vector is missed with probability $p$. Under the standard $L_4-L_2$ moment equivalence assumption, we construct th
Externí odkaz:
http://arxiv.org/abs/2305.12981
Autor:
Abdalla, Pedro, Bandeira, Afonso S., Kassabov, Martin, Souza, Victor, Strogatz, Steven H., Townsend, Alex
The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show that a graph
Externí odkaz:
http://arxiv.org/abs/2210.12788
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's topology and
Externí odkaz:
http://arxiv.org/abs/2208.12246
Autor:
Abdalla, Pedro, Zhivotovskiy, Nikita
We provide an estimator of the covariance matrix that achieves the optimal rate of convergence (up to constant factors) in the operator norm under two standard notions of data contamination: We allow the adversary to corrupt an $\eta$-fraction of the
Externí odkaz:
http://arxiv.org/abs/2205.08494
Autor:
Abdalla, Pedro
Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with lower sto
Externí odkaz:
http://arxiv.org/abs/2112.14148
Autor:
Abdalla, Pedro, Bandeira, Afonso S.
Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques such as sk
Externí odkaz:
http://arxiv.org/abs/2102.01419
Autor:
Abdalla, Pedro, Kümmerle, Christian
The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard compressed se
Externí odkaz:
http://arxiv.org/abs/2101.08298