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 "the estimation performance of nonlinear least squares for phase retrieval"):
  Abstract: Suppose that $\mathbf{y}=\lvert A\mathbf{x_0}\rvert+\eta$ where $\mathbf{x_0} \in \mathbb{R}^d$ is the target signal and $\eta\in \mathbb{R}^m$ is a noise vector. The aim of phase retrieval is to estimate $\mathbf{x_0}$ from $\mathbf{y}$. A popular model for estimating $\mathbf{x_0} $ is the nonlinear least square $ \widehat{\mathbf{x}}:={\rm argmin}_{\mathbf{x}} \| \lvert A \mathbf{x}\rvert-\mathbf{y}\|_2$. One already develops many efficient algorithms for solving the model, such as the seminal error reduction algorithm. In this paper, we present the estimation performance of the model with proving that $\|\widehat{\mathbf{x}}-\mathbf{x_0} \|\lesssim {\|\eta\|_2}/{\sqrt{m}}$ under the assumption of $A$ being a Gaussian random matrix. We also prove the reconstruction error ${\|\eta\|_2}/{\sqrt{m}}$ is sharp. For the case where $\mathbf{x_0}$ is sparse, we study the estimation performance of both the nonlinear Lasso of phase retrieval and its unconstrained version. Our results are non-asymptotic, and we do not assume any distribution on the noise $\eta$. To the best of our knowledge, our results represent the first theoretical guarantee for the nonlinear least square and for the nonlinear Lasso of phase retrieval.

Includes members:
  Member "phase retrieval from the norms of affine transformations":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on dc based methods for phase retrieval")
  Member "sparse phase retrieval via truncated amplitude flow":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "provable low rank phase retrieval and compressive pca")
  Member "generalized phase retrieval measurement number matrix recovery and beyond":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "solving complex quadratic systems with full rank random matrices")
  Member "phasemax convex phase retrieval via basis pursuit":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "deep s 3 pr simultaneous source separation and phase retrieval using deep generative models")
  Member "a geometric analysis of phase retrieval":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "solving random quadratic systems of equations is nearly as easy as solving linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "the generalized lasso with non linear observations":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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-8 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")

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)