human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "low rank matrix recovery from rank one measurements"):
  Abstract: We study the recovery of Hermitian low rank matrices $X \in \mathbb{C}^{n \times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j a_j^*$ for some measurement vectors $a_1,...,a_m$, i.e., the measurements are given by $y_j = \mathrm{tr}(X a_j a_j^*)$. The case where the matrix $X=x x^*$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements, $y_j = |\langle x,a_j\rangle|^2$ via the PhaseLift approach, which has been introduced recently. We derive bounds for the number $m$ of measurements that guarantee successful uniform recovery of Hermitian rank $r$ matrices, either for the vectors $a_j$, $j=1,...,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective $t$-design with $t=4$. In the Gaussian case, we require $m \geq C r n$ measurements, while in the case of $4$-designs we need $m \geq Cr n \log(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank $r$-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate $4$-designs generalizes and improves a recent bound on phase retrieval due to Gross, Kueng and Krahmer. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.

Includes members:
  Member "improved recovery guarantees for phase retrieval from coded diffraction patterns":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "complex phase retrieval from subgaussian measurements")
  Member "incoherence optimal matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "matrix completion with prior subspace information via maximizing correlation")
  Member "a partial derandomization of phaselift using spherical designs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "complex phase retrieval from subgaussian measurements")
  Member "convex recovery of a structured signal from independent random linear measurements":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "phase retrieval via wirtinger flow theory and algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "learning without concentration":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "learning with correntropy induced losses for regression with mixture of symmetric stable noise")
  Member "phase retrieval with application to optical imaging":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "phase retrieval without small ball probability assumptions")
  Member "exact and stable covariance estimation from quadratic sampling via convex programming":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "phase retrieval of low rank matrices by anchored regression")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.IT(Information Theory)