human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "an elementary proof of convex phase retrieval in the natural parameter space via the linear program phasemax"
  Abstract: The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to lifting, many approaches to phase retrieval have been developed, including non-convex optimization algorithms which operate in the natural parameter space, such as Wirtinger Flow. Very recently, a convex formulation called PhaseMax has been discovered, and it has been proven to achieve phase retrieval via linear programming in the natural parameter space under optimal sample complexity. The current proofs of PhaseMax rely on statistical learning theory or geometric probability theory. Here, we present a short and elementary proof that PhaseMax exactly recovers real-valued vectors from random measurements under optimal sample complexity. Our proof only relies on standard probabilistic concentration and covering arguments, yielding a simpler and more direct proof than those that require statistical learning theory, geometric probability or the highly technical arguments for Wirtinger Flow-like approaches.

Connected through hyperedge HE-1 (induced by source paper "a deterministic convergence framework for exact non convex phase retrieval"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "optimal spectral initialization for signal recovery with applications to phase retrieval"
    - "linear spectral estimators and an application to phase retrieval"
    - "phase transitions of spectral initialization for high dimensional nonconvex estimation"
    - "structured signal recovery from quadratic measurements breaking sample complexity barriers via nonconvex optimization"
    - "non convex phase retrieval from stft measurements"
    - "phasemax convex phase retrieval via basis pursuit"
    - "rapid robust and reliable blind deconvolution via nonconvex optimization"

Connected through hyperedge HE-2 (induced by source paper "a precise analysis of phasemax in phase retrieval"):
  with members:
    - "phase retrieval via linear programming fundamental limits and algorithmic improvements"
    - "fundamental limits of phasemax for phase retrieval a replica analysis"
    - "multiple illumination phaseless super resolution mips with applications to phaseless doa estimation and diffraction imaging"
    - "blind deconvolution with additional autocorrelations via convex programs"
    - "phasemax convex phase retrieval via basis pursuit"
    - "precise error analysis of regularized m estimators in high dimensions"
    - "phase retrieval meets statistical learning theory a flexible convex relaxation"
    - "ber analysis of the box relaxation for bpsk signal recovery"

Connected through hyperedge HE-3 (induced by source paper "towards the optimal construction of a loss function without spurious local minima for solving quadratic equations"):
  with members:
    - "the non convex geometry of low rank matrix optimization"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "on the optimization landscape of tensor decompositions"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "phasemax convex phase retrieval via basis pursuit"
    - "matrix completion has no spurious local minimum"
    - "a geometric analysis of phase retrieval"
    - "phase retrieval meets statistical learning theory a flexible convex relaxation"

Connected through hyperedge HE-4 (induced by source paper "phase retrieval via polytope optimization geometry phase transitions and new algorithms"):
  with members:
    - "a precise analysis of phasemax in phase retrieval"
    - "phase retrieval via linear programming fundamental limits and algorithmic improvements"
    - "fundamental limits of phasemax for phase retrieval a replica analysis"
    - "phase transitions of spectral initialization for high dimensional nonconvex estimation"
    - "precise error analysis of regularized m estimators in high dimensions"
    - "phase retrieval meets statistical learning theory a flexible convex relaxation"
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"
    - "phase retrieval an overview of recent developments"

Connected through hyperedge HE-5 (induced by source paper "implicit regularization in nonconvex statistical estimation gradient descent converges linearly for phase retrieval matrix completion and blind deconvolution"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "on the global geometry of sphere constrained sparse blind deconvolution"
    - "fast robust and non convex subspace recovery"
    - "nonconvex matrix factorization from rank one measurements"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "phase retrieval via linear programming fundamental limits and algorithmic improvements"
    - "regularized gradient descent a nonconvex recipe for fast joint blind deconvolution and demixing"
    - "recovery guarantees for one hidden layer neural networks"

Connected through hyperedge HE-6 (induced by source paper "structured signal recovery from quadratic measurements breaking sample complexity barriers via nonconvex optimization"):
  with members:
    - "multiple illumination phaseless super resolution mips with applications to phaseless doa estimation and diffraction imaging"
    - "improved recovery guarantees for phase retrieval from coded diffraction patterns"
    - "sparse phase retrieval via truncated amplitude flow"
    - "non convex phase retrieval from stft measurements"
    - "reconstruction of signals from their autocorrelation and cross correlation vectors with applications to phase retrieval and blind channel estimation"
    - "stft phase retrieval uniqueness guarantees and recovery algorithms"
    - "compressed sensing from phaseless gaussian measurements via linear programming in the natural parameter space"
    - "phasemax convex phase retrieval via basis pursuit"

Connected through hyperedge HE-7 (induced by source paper "almost optimal phaseless compressed sensing with sublinear decoding time"):
  with members:
    - "phasemax convex phase retrieval via basis pursuit"
    - "fast and robust compressive phase retrieval with sparse graph codes"
    - "heavy hitters via cluster preserving clustering"
    - "phase retrieval meets statistical learning theory a flexible convex relaxation"
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"
    - "phase retrieval via wirtinger flow theory and algorithms"
    - "super sparse signals with unknown phases efficiently recovered"
    - "sample optimal average case sparse fourier transform in two dimensions"

Connected through hyperedge HE-8 (induced by source paper "solving equations of random convex functions via anchored regression"):
  with members:
    - "learning relus via gradient descent"
    - "corruption robust phase retrieval via linear programming"
    - "compressed sensing from phaseless gaussian measurements via linear programming in the natural parameter space"
    - "phase retrieval meets statistical learning theory a flexible convex relaxation"
    - "self calibration and biconvex compressive sensing"
    - "convex recovery of a structured signal from independent random linear measurements"
    - "the generalized lasso with non linear observations"
    - "phase retrieval via wirtinger flow theory and algorithms"

Question: Please tell me which class the center node 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)