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: "sharp mse bounds for proximal denoising"
  Abstract: Denoising has to do with estimating a signal $x_0$ from its noisy observations $y=x_0+z$. In this paper, we focus on the "structured denoising problem", where the signal $x_0$ possesses a certain structure and $z$ has independent normally distributed entries with mean zero and variance $\sigma^2$. We employ a structure-inducing convex function $f(\cdot)$ and solve $\min_x\{\frac{1}{2}\|y-x\|_2^2+\sigma\lambda f(x)\}$ to estimate $x_0$, for some $\lambda>0$. Common choices for $f(\cdot)$ include the $\ell_1$ norm for sparse vectors, the $\ell_1-\ell_2$ norm for block-sparse signals and the nuclear norm for low-rank matrices. The metric we use to evaluate the performance of an estimate $x^*$ is the normalized mean-squared-error $\text{NMSE}(\sigma)=\frac{\mathbb{E}\|x^*-x_0\|_2^2}{\sigma^2}$. We show that NMSE is maximized as $\sigma\rightarrow 0$ and we find the \emph{exact} worst case NMSE, which has a simple geometric interpretation: the mean-squared-distance of a standard normal vector to the $\lambda$-scaled subdifferential $\lambda\partial f(x_0)$. When $\lambda$ is optimally tuned to minimize the worst-case NMSE, our results can be related to the constrained denoising problem $\min_{f(x)\leq f(x_0)}\{\|y-x\|_2\}$. The paper also connects these results to the generalized LASSO problem, in which, one solves $\min_{f(x)\leq f(x_0)}\{\|y-Ax\|_2\}$ to estimate $x_0$ from noisy linear observations $y=Ax_0+z$. We show that certain properties of the LASSO problem are closely related to the denoising problem. In particular, we characterize the normalized LASSO cost and show that it exhibits a "phase transition" as a function of number of observations. Our results are significant in two ways. First, we find a simple formula for the performance of a general convex estimator. Secondly, we establish a connection between the denoising and linear inverse problems.

Connected through hyperedge HE-1 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery"):
  with members:
    - "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"
    - "the generalized lasso with non linear observations"
    - "robust analysis l1 recovery from gaussian measurements and total variation minimization"
    - "stable image reconstruction using total variation minimization"
    - "stable and robust sampling strategies for compressive imaging"

Connected through hyperedge HE-2 (induced by source paper "near optimal matrix recovery from random linear measurements"):
  with members:
    - "phase diagram of matrix compressed sensing"
    - "parametric bilinear generalized approximate message passing"
    - "an overview of low rank matrix recovery from incomplete observations"
    - "sharp time data tradeoffs for linear inverse problems"
    - "bilinear generalized approximate message passing part i derivation"
    - "low rank modeling and its applications in image analysis"
    - "from denoising to compressed sensing"
    - "living on the edge phase transitions in convex programs with random data"

Connected through hyperedge HE-3 (induced by source paper "joint activity detection and channel estimation for iot networks phase transition and computation estimation tradeoff"):
  with members:
    - "energy sustainable iot with individual qos constraints through miso swipt multicasting"
    - "sparse representation for wireless communications"
    - "sparse activity detection for massive connectivity"
    - "massive connectivity with massive mimo part ii achievable rate characterization"
    - "sparse signal processing for grant free massive connectivity a future paradigm for random access protocols in the internet of things"
    - "massive connectivity with massive mimo part i device activity detection and channel estimation"
    - "compressive channel estimation and multi user detection in c ran"
    - "a random access protocol for pilot allocation in crowded massive mimo systems"

Connected through hyperedge HE-4 (induced by source paper "atomic norm minimization for modal analysis from random and compressed samples"):
  with members:
    - "sparse methods for direction of arrival estimation"
    - "on the sample complexity of multichannel frequency estimation via convex optimization"
    - "generalized line spectral estimation via convex optimization"
    - "super resolution of complex exponentials from modulations with unknown waveforms"
    - "distributed compressed sensing off the grid"
    - "off the grid line spectrum denoising and estimation with multiple measurement vectors"
    - "exact joint sparse frequency recovery via optimization methods"
    - "continuous compressed sensing with a single or multiple measurement vectors"

Connected through hyperedge HE-5 (induced by source paper "on the error in phase transition computations for compressed sensing"):
  with members:
    - "exploiting prior information in block sparse signals"
    - "ell 1 analysis minimization and generalized co sparsity when does recovery succeed"
    - "precise phase transition of total variation minimization"
    - "corrupted sensing novel guarantees for separating structured signals"
    - "living on the edge phase transitions in convex programs with random data"
    - "simple bounds for recovering low complexity models"
    - "accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising"
    - "various thresholds for ell_1 optimization in compressed sensing"

Connected through hyperedge HE-6 (induced by source paper "sensitivity of ell_ 1 minimization to parameter choice"):
  with members:
    - "the generalized lasso with non linear observations"
    - "living on the edge phase transitions in convex programs with random data"
    - "the squared error of generalized lasso a precise analysis"
    - "robust 1 bit compressed sensing and sparse logistic regression a convex programming approach"
    - "the dynamics of message passing on dense graphs with applications to compressed sensing"
    - "how well can we estimate a sparse vector"

Connected through hyperedge HE-7 (induced by source paper "parameter instability regimes for sparse proximal denoising programs"):
  with members:
    - "the generalized lasso with non linear observations"
    - "living on the edge phase transitions in convex programs with random data"
    - "robust 1 bit compressed sensing and sparse logistic regression a convex programming approach"
    - "the dynamics of message passing on dense graphs with applications to compressed sensing"

Connected through hyperedge HE-8 (induced by source paper "sharp time data tradeoffs for linear inverse problems"):
  with members:
    - "isometric sketching of any set via the restricted isometry property"
    - "the generalized lasso with non linear observations"
    - "does ell_p minimization outperform ell_1 minimization"
    - "phase retrieval via wirtinger flow theory and algorithms"
    - "learning without concentration"
    - "dimensionality reduction with subgaussian matrices a unified theory"
    - "from denoising to compressed sensing"
    - "simple bounds for noisy linear inverse problems with exact side information"

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)