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 "critical behavior and universality classes for an algorithmic phase transition in sparse reconstruction"):
  Abstract: Optimization problems with sparsity-inducing penalties exhibit sharp algorithmic phase transitions when the numbers of variables tend to infinity, between regimes of `good' and `bad' performance. The nature of these phase transitions and associated universality classes remain incompletely understood. We analyze the mean field equations from the cavity method for two sparse reconstruction algorithms, Basis Pursuit and Elastic Net. These algorithms are associated with penalized regression problems $(\mathbf{y}-\mathbf{H} \mathbf{x})^2+\lambda V(\mathbf{x})$, where $V(\mathbf{x})$ is an algorithm-dependent penalty function. Here $\lambda$ is the penalty parameter, $\mathbf{x}$ is the $N$-dimensional, $K$-sparse solution to be recovered, $\mathbf{y}$ is the $M$ dimensional vector of measurements, and $\mathbf{H}$ is a known `random' matrix. In the limit $\lambda \rightarrow 0$ and $N\rightarrow \infty$, keeping $\rho=K/N$ fixed, exact recovery is possible for sufficiently large values of fractional measurement number $\alpha=M/N$, with an algorithmic phase transition occurring at a known critical value $\alpha_c = \alpha(\rho)$. We find that Basis Pursuit $V(\mathbf{x})=||\mathbf{x}||_{1} $and Elastic Net $V(\mathbf{x})=\lambda_1 ||\mathbf{x}||_{1} + \tfrac{\lambda_2}{2} ||\mathbf{x}||_{2}^2$ belong to two different universality classes. The Mean Squared Error goes to zero as $MSE \sim(\alpha_c-\alpha)^2$ as $\alpha$ approaches $\alpha_c$ from below for both algorithms. However, for Basis Pursuit, precisely on the phase transition line $\alpha=\alpha_c$, $MSE \sim \lambda^{4/3}$ for Basis Pursuit, whereas $MSE\sim\lambda$ for Elastic Net. We also find that in presence of additive noise, within the perfect reconstruction phase $\alpha>\alpha_c$ there is a non-zero setting for $\lambda$ that minimizes MSE, whereas at $\alpha=\alpha_c$ a finite $\lambda$ always increases the MSE.

Includes members:
  Member "living on the edge phase transitions in convex programs with random data":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the convex geometry of blind deconvolution and matrix completion")
  Member "a rigorous geometry probability equivalence in characterization of ell_1 optimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the squared error of generalized lasso a precise analysis")
  Member "statistical mechanics approach to 1 bit compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "bayesian online compressed sensing")
  Member "the dynamics of message passing on dense graphs with applications to compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "a typical reconstruction limit of compressed sensing based on lp norm minimization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "understanding overfitting peaks in generalization error analytical risk curves for l 2 and l 1 penalized interpolation")
  Member "message passing algorithms for compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")

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)