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 "unbiased estimates for linear regression via volume sampling"):
  Abstract: For a full rank $n\times d$ matrix $X$ with $n\ge d$, consider the task of solving the linear least squares problem, where we try to predict a response value for each of the $n$ rows of $X$. Assume that obtaining the responses is expensive and we can only afford to attain the responses for a small subset of rows. We show that a good approximate solution to this least squares problem can be obtained from just dimension $d$ many responses. Concretely, if the rows are in general position and if a subset of $d$ rows is chosen proportional to the squared volume spanned by those rows, then the expected total square loss (on all $n$ rows) of the least squares solution found for the subset is exactly $d+1$ times the minimum achievable total loss. We provide lower bounds showing that the factor of $d+1$ is optimal, and any iid row sampling procedure requires $\Omega(d\log d)$ responses to achieve a finite factor guarantee. Moreover, the least squares solution obtained for the volume sampled subproblem is an unbiased estimator of optimal solution based on all $n$ responses. #R##N#Our methods lead to general matrix expectation formulas for volume sampling which go beyond linear regression. In particular, we propose a matrix estimator for the pseudoinverse $X^+$, computed from a small subset of rows of the matrix $X$. The estimator is unbiased and surprisingly its covariance also has a closed form: It equals a specific factor times $X^{+}X^{+\top}$. We believe that these new formulas establish a fundamental connection between linear least squares and volume sampling. Our analysis for computing matrix expectations is based on reverse iterative volume sampling, a technique which also leads to a new algorithm for volume sampling that is by a factor of $n^2$ faster than the state-of-the-art.

Includes members:
  Member "subsampling for ridge regression via regularized volume sampling":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "exact expressions for double descent and implicit regularization via surrogate random design")
  Member "low rank approximation and regression in input sparsity time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "fast approximation of matrix coherence and statistical leverage":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "optimal column based low rank matrix reconstruction":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "improved guarantees and a multiple descent curve for the column subset selection problem and the nystr om method")
  Member "randomized algorithms for matrices and data":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "solving tall dense linear programs in nearly linear time")
  Member "relative error cur matrix decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "good feature matching towards accurate robust vo vslam with low latency")

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.LG(Machine Learning)