144,269 research outputs found
Computational barriers in minimax submatrix detection
This paper studies the minimax detection of a small submatrix of elevated
mean in a large matrix contaminated by additive Gaussian noise. To investigate
the tradeoff between statistical performance and computational cost from a
complexity-theoretic perspective, we consider a sequence of discretized models
which are asymptotically equivalent to the Gaussian model. Under the hypothesis
that the planted clique detection problem cannot be solved in randomized
polynomial time when the clique size is of smaller order than the square root
of the graph size, the following phase transition phenomenon is established:
when the size of the large matrix , if the submatrix size
for any , computational complexity
constraints can incur a severe penalty on the statistical performance in the
sense that any randomized polynomial-time test is minimax suboptimal by a
polynomial factor in ; if for any
, minimax optimal detection can be attained within
constant factors in linear time. Using Schatten norm loss as a representative
example, we show that the hardness of attaining the minimax estimation rate can
crucially depend on the loss function. Implications on the hardness of support
recovery are also obtained.Comment: Published at http://dx.doi.org/10.1214/14-AOS1300 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Parity of Anti-Decuplet Baryons Revisited from Chiral Soliton Models
We recalculate masses and widths of anti-decuplet baryons in the case of
positive parity from chiral soliton models, provided that the member
of the anti-decuplet has a mass 1.86 GeV as reported recently.
Calculations show that there are no convincing candidates for the nonexotic
members of the anti-decuplet available in the baryon listings. Up to the
leading order of and 1/, the width formula for the decay of the
anti-decuplet baryons to the octet depends only on SU(3) symmetry
model-independently, except the coupling constant. Similarly we give a width
formula for the decay of negative parity baryons belong to certain SU(3) baryon
multiplet by pure symmetry consideration. By this formula, we find that if we
have an anti-decuplet with negative parity and that the masses are the same as
those given by chiral soltion models, the identification of N(1650) as
are inconsistent with experiments for while
the widths agree with other two decay channels involving strangeness. And
seems to be a reasonable candidate for .Comment: 4 pages in revtex format, version for journal publication. Arguments
revised, with conclusion unchange
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