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 "living on the edge phase transitions in convex programs with random data"):
  Abstract: Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the $\ell_1$ minimization method for identifying a sparse vector from random linear measurements. Indeed, the $\ell_1$ approach succeeds with high probability when the number of measurements exceeds a threshold that depends on the sparsity level; otherwise, it fails with high probability. #R##N#This paper provides the first rigorous analysis that explains why phase transitions are ubiquitous in random convex optimization problems. It also describes tools for making reliable predictions about the quantitative aspects of the transition, including the location and the width of the transition region. These techniques apply to regularized linear inverse problems with random measurements, to demixing problems under a random incoherence model, and also to cone programs with random affine constraints. #R##N#The applied results depend on foundational research in conic geometry. This paper introduces a summary parameter, called the statistical dimension, that canonically extends the dimension of a linear subspace to the class of convex cones. The main technical result demonstrates that the sequence of intrinsic volumes of a convex cone concentrates sharply around the statistical dimension. This fact leads to accurate bounds on the probability that a randomly rotated cone shares a ray with a fixed cone.

Includes members:
  Member "corrupted sensing novel guarantees for separating structured signals":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "gradient descent with early stopping is provably robust to label noise for overparameterized neural networks")
  Member "the achievable performance of convex demixing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "exact matrix completion based on low rank hankel structure in the fourier domain")
  Member "regularly random duality":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the squared error of generalized lasso a precise analysis")
  Member "the phase transition of matrix recovery from gaussian measurements matches the minimax mse of matrix denoising":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "implicit regularization of normalization methods")
  Member "sharp mse bounds for proximal denoising":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "sharp recovery bounds for convex demixing with applications":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the convex geometry of blind deconvolution and matrix completion")
  Member "anti sparse coding for approximate nearest neighbor search":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "unsupervised rank preserving hashing for large scale image retrieval")
  Member "accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "living near the edge a lower bound on the phase transition of total variation minimization")

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)