20,705 research outputs found
Diffuse PeV neutrinos from gamma-ray bursts
The IceCube collaboration recently reported the potential detection of two
cascade neutrino events in the energy range 1-10 PeV. We study the possibility
that these PeV neutrinos are produced by gamma-ray bursts (GRBs), paying
special attention to the contribution by untriggered GRBs that elude detection
due to their low photon flux. Based on the luminosity function, rate
distribution with redshift and spectral properties of GRBs, we generate, using
Monte-Carlo simulation, a GRB sample that reproduce the observed fluence
distribution of Fermi/GBM GRBs and an accompanying sample of untriggered GRBs
simultaneously. The neutrino flux of every individual GRBs is calculated in the
standard internal shock scenario, so that the accumulative flux of the whole
samples can be obtained. We find that the neutrino flux in PeV energies
produced by untriggered GRBs is about 2 times higher than that produced by the
triggered ones. Considering the existing IceCube limit on the neutrino flux of
triggered GRBs, we find that the total flux of triggered and untriggered GRBs
can reach at most a level of ~10^-9 GeV cm^-2 s^-1 sr^-1, which is insufficient
to account for the reported two PeV neutrinos. Possible contributions to
diffuse neutrinos by low-luminosity GRBs and the earliest population of GRBs
are also discussed.Comment: Accepted by ApJ, one more figure added to show the contribution to
the diffuse neutrino flux by untriggered GRBs with different luminosity,
results and conclusions unchange
Stability of matrix factorization for collaborative filtering
We study the stability vis a vis adversarial noise of matrix factorization
algorithm for matrix completion. In particular, our results include: (I) we
bound the gap between the solution matrix of the factorization method and the
ground truth in terms of root mean square error; (II) we treat the matrix
factorization as a subspace fitting problem and analyze the difference between
the solution subspace and the ground truth; (III) we analyze the prediction
error of individual users based on the subspace stability. We apply these
results to the problem of collaborative filtering under manipulator attack,
which leads to useful insights and guidelines for collaborative filtering
system design.Comment: ICML201
Graph Connectivity in Noisy Sparse Subspace Clustering
Subspace clustering is the problem of clustering data points into a union of
low-dimensional linear/affine subspaces. It is the mathematical abstraction of
many important problems in computer vision, image processing and machine
learning. A line of recent work (4, 19, 24, 20) provided strong theoretical
guarantee for sparse subspace clustering (4), the state-of-the-art algorithm
for subspace clustering, on both noiseless and noisy data sets. It was shown
that under mild conditions, with high probability no two points from different
subspaces are clustered together. Such guarantee, however, is not sufficient
for the clustering to be correct, due to the notorious "graph connectivity
problem" (15). In this paper, we investigate the graph connectivity problem for
noisy sparse subspace clustering and show that a simple post-processing
procedure is capable of delivering consistent clustering under certain "general
position" or "restricted eigenvalue" assumptions. We also show that our
condition is almost tight with adversarial noise perturbation by constructing a
counter-example. These results provide the first exact clustering guarantee of
noisy SSC for subspaces of dimension greater then 3.Comment: 14 pages. To appear in The 19th International Conference on
Artificial Intelligence and Statistics, held at Cadiz, Spain in 201
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