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 "does ell_p minimization outperform ell_1 minimization"):
  Abstract: In many application areas we are faced with the following question: Can we recover a sparse vector $x_o \in \mathbb{R}^N$ from its undersampled set of noisy observations $y \in \mathbb{R}^n$, $y=A x_o+w$. The last decade has witnessed a surge of algorithms and theoretical results addressing this question. One of the most popular algorithms is the $\ell_p$-regularized least squares (LPLS) given by the following formulation: \[ \hat{x}(\gamma,p )\in \arg\min_x \frac{1}{2}\|y - Ax\|_2^2+\gamma\|x\|_p^p, \] where $p \in [0,1]$. Despite the non-convexity of these problems for $p<1$, they are still appealing because of the following folklores in compressed sensing: (i) $\hat{x}(\gamma,p )$ is closer to $x_o$ than $\hat{x}(\gamma,1)$. (ii) If we employ iterative methods that aim to converge to a local minima of LPLS, then under good initialization these algorithms converge to a solution that is closer to $x_o$ than $\hat{x}(\gamma,1)$. In spite of the existence of plenty of empirical results that support these folklore theorems, the theoretical progress to establish them has been very limited. #R##N#This paper aims to study the above folklore theorems and establish their scope of validity. Starting with approximate message passing algorithm as a heuristic method for solving LPLS, we study the impact of initialization on the performance of AMP. Then, we employ the replica analysis to show the connection between the solution of AMP and $\hat{x}(\gamma, p)$ in the asymptotic settings. This enables us to compare the accuracy of $\hat{x}(\gamma,p)$ for $p \in [0,1]$. In particular, we will characterize the phase transition and noise sensitivity of LPLS for every $0\leq p\leq 1$ accurately. Our results in the noiseless setting confirm that LPLS exhibits the same phase transition for every $0\leq p <1$ and this phase transition is much higher than that of LASSO.

Includes members:
  Member "from denoising to compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a novel learnable gradient descent type algorithm for non convex non smooth inverse problems")
  Member "lifting l q optimization thresholds":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "compressed sensing of block sparse positive vectors")
  Member "accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "living near the edge a lower bound on the phase transition of total variation minimization")
  Member "asymptotic analysis of complex lasso via complex approximate message passing camp":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "optimal errors and phase transitions in high dimensional generalized linear models")
  Member "the dynamics of message passing on dense graphs with applications to compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "generalized approximate message passing for estimation with random linear mixing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "optimally tuned iterative reconstruction algorithms for compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "random access for massive machine type communications")
  Member "a typical reconstruction limit of compressed sensing based on lp norm minimization":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "understanding overfitting peaks in generalization error analytical risk curves for l 2 and l 1 penalized interpolation")

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)