9,491 research outputs found
A congruence involving products of -binomial coefficients
In this paper we establish a -analogue of a congruence of Sun concerning
the products of binomial coefficients modulo the square of a prime.Comment: 9 page
On the adaptive elastic-net with a diverging number of parameters
We consider the problem of model selection and estimation in situations where
the number of parameters diverges with the sample size. When the dimension is
high, an ideal method should have the oracle property [J. Amer. Statist. Assoc.
96 (2001) 1348--1360] and [Ann. Statist. 32 (2004) 928--961] which ensures the
optimal large sample performance. Furthermore, the high-dimensionality often
induces the collinearity problem, which should be properly handled by the ideal
method. Many existing variable selection methods fail to achieve both goals
simultaneously. In this paper, we propose the adaptive elastic-net that
combines the strengths of the quadratic regularization and the adaptively
weighted lasso shrinkage. Under weak regularity conditions, we establish the
oracle property of the adaptive elastic-net. We show by simulations that the
adaptive elastic-net deals with the collinearity problem better than the other
oracle-like methods, thus enjoying much improved finite sample performance.Comment: Published in at http://dx.doi.org/10.1214/08-AOS625 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Note on a Rapid Grid Search Method for Solving Dynamic Programming Problems in Economics
We introduce a rapid grid search method in solving the dynamic programming problems in economics. Compared to mainstream grid search methods, by using local information of the Bellman equation, this method can significantly increase the efficiency in solving dynamic programming problems by reducing the grid points searched in the control space.Dynamic Programming, Grid Search, Control Space
Measuring robustness of community structure in complex networks
The theory of community structure is a powerful tool for real networks, which
can simplify their topological and functional analysis considerably. However,
since community detection methods have random factors and real social networks
obtained from complex systems always contain error edges, evaluating the
robustness of community structure is an urgent and important task. In this
letter, we employ the critical threshold of resolution parameter in Hamiltonian
function, , to measure the robustness of a network. According to
spectral theory, a rigorous proof shows that the index we proposed is inversely
proportional to robustness of community structure. Furthermore, by utilizing
the co-evolution model, we provides a new efficient method for computing the
value of . The research can be applied to broad clustering problems
in network analysis and data mining due to its solid mathematical basis and
experimental effects.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1303.7434 by other author
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