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: "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.

Connected through hyperedge HE-1 (induced by source paper "on the convex geometry of blind deconvolution and matrix completion"):
  with members:
    - "phase retrieval without small ball probability assumptions"
    - "blind deconvolution by a steepest descent algorithm on a quotient manifold"
    - "blind demixing and deconvolution at near optimal rate"
    - "implicit regularization in nonconvex statistical estimation gradient descent converges linearly for phase retrieval matrix completion and blind deconvolution"
    - "low rank matrix recovery from clifford orbits"
    - "rapid robust and reliable blind deconvolution via nonconvex optimization"
    - "matrix completion has no spurious local minimum"
    - "guaranteed matrix completion via non convex factorization"

Connected through hyperedge HE-2 (induced by source paper "information theoretic lower bounds for compressive sensing with generative models"):
  with members:
    - "an introductory guide to fano s inequality with applications in statistical estimation"
    - "lower bounds for compressed sensing with generative models"
    - "solving inverse problems via auto encoders"
    - "deep decoder concise image representations from untrained non convolutional networks"
    - "the universal approximation power of finite width deep relu networks"
    - "global guarantees for enforcing deep generative priors by empirical risk"
    - "benefits of depth in neural networks"
    - "understanding deep neural networks with rectified linear units"

Connected through hyperedge HE-3 (induced by source paper "simultaneous structures in convex signal recovery revisiting the convex combination of norms"):
  with members:
    - "sparse power factorization balancing peakiness and sample complexity"
    - "near optimal sample complexity for convex tensor completion"
    - "branchhull convex bilinear inversion from the entrywise product of signals with known signs"
    - "reliable recovery of hierarchically sparse signals and application in machine type communications"
    - "low rank tensor recovery via iterative hard thresholding"
    - "tensor theta norms and low rank recovery"
    - "self calibration and biconvex compressive sensing"
    - "convex recovery of a structured signal from independent random linear measurements"

Connected through hyperedge HE-4 (induced by source paper "quickly finding the best linear model in high dimensions"):
  with members:
    - "quantized compressive sensing with rip matrices the benefit of dithering"
    - "stochastic gradient descent learns state equations with nonlinear activations"
    - "learning compact neural networks with regularization"
    - "robust one bit compressed sensing with non gaussian measurements"
    - "non gaussian hyperplane tessellations and robust one bit compressed sensing"
    - "robust one bit compressed sensing with partial circulant matrices"
    - "the generalized lasso for sub gaussian measurements with dithered quantization"
    - "one bit compressed sensing with partial gaussian circulant matrices"

Connected through hyperedge HE-5 (induced by source paper "living near the edge a lower bound on the phase transition of total variation minimization"):
  with members:
    - "on the error in phase transition computations for compressed sensing"
    - "sample complexity of total variation minimization"
    - "total variation minimization in compressed sensing"
    - "ell 1 analysis minimization and generalized co sparsity when does recovery succeed"
    - "precise phase transition of total variation minimization"
    - "convex recovery of a structured signal from independent random linear measurements"
    - "robust analysis l1 recovery from gaussian measurements and total variation minimization"
    - "corrupted sensing novel guarantees for separating structured signals"

Connected through hyperedge HE-6 (induced by source paper "exploiting prior information in block sparse signals"):
  with members:
    - "maximum a posteriori signal recovery with prior information applications to compressive sensing"
    - "performance limits for noisy multimeasurement vector problems"
    - "convex recovery of a structured signal from independent random linear measurements"
    - "spectral super resolution with prior knowledge"
    - "accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising"
    - "accelerating multi echo t2 weighted mr imaging analysis prior group sparse optimization"
    - "recovering compressively sampled signals using partial support information"
    - "from theory to practice sub nyquist sampling of sparse wideband analog signals"

Connected through hyperedge HE-7 (induced by source paper "derandomized compressed sensing with nonuniform guarantees for 120001 1 recovery"):
  with members:
    - "kesten mckay law for random subensembles of paley equiangular tight frames"
    - "random subsets of structured deterministic frames have manova spectra"
    - "average case hardness of rip certification"
    - "the restricted isometry property of subsampled fourier matrices"
    - "compressed sensing with sparse binary matrices instance optimal error guarantees in near optimal time"
    - "kirkman equiangular tight frames and codes"
    - "sharp rip bound for sparse signal and low rank matrix recovery"
    - "restricted isometry of fourier matrices and list decodability of random linear codes"

Connected through hyperedge HE-8 (induced by source paper "recovery of structured signals from corrupted non linear measurements"):
  with members:
    - "corrupted sensing with sub gaussian measurements"
    - "stable recovery of structured signals from corrupted sub gaussian measurements"
    - "on the phase transition of corrupted sensing"
    - "convex recovery of a structured signal from independent random linear measurements"
    - "the generalized lasso with non linear observations"
    - "corrupted sensing novel guarantees for separating structured signals"
    - "sharp recovery bounds for convex demixing with applications"

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)