27,311 research outputs found
Two monotonic functions involving gamma function and volume of unit ball
In present paper, we prove the monotonicity of two functions involving the
gamma function and relating to the -dimensional volume of the
unit ball in .Comment: 7 page
A Feature Selection Method for Multivariate Performance Measures
Feature selection with specific multivariate performance measures is the key
to the success of many applications, such as image retrieval and text
classification. The existing feature selection methods are usually designed for
classification error. In this paper, we propose a generalized sparse
regularizer. Based on the proposed regularizer, we present a unified feature
selection framework for general loss functions. In particular, we study the
novel feature selection paradigm by optimizing multivariate performance
measures. The resultant formulation is a challenging problem for
high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed
to solve this problem, and the convergence is presented. In addition, we adapt
the proposed method to optimize multivariate measures for multiple instance
learning problems. The analyses by comparing with the state-of-the-art feature
selection methods show that the proposed method is superior to others.
Extensive experiments on large-scale and high-dimensional real world datasets
show that the proposed method outperforms -SVM and SVM-RFE when choosing a
small subset of features, and achieves significantly improved performances over
SVM in terms of -score
Efficient Multi-Template Learning for Structured Prediction
Conditional random field (CRF) and Structural Support Vector Machine
(Structural SVM) are two state-of-the-art methods for structured prediction
which captures the interdependencies among output variables. The success of
these methods is attributed to the fact that their discriminative models are
able to account for overlapping features on the whole input observations. These
features are usually generated by applying a given set of templates on labeled
data, but improper templates may lead to degraded performance. To alleviate
this issue, in this paper, we propose a novel multiple template learning
paradigm to learn structured prediction and the importance of each template
simultaneously, so that hundreds of arbitrary templates could be added into the
learning model without caution. This paradigm can be formulated as a special
multiple kernel learning problem with exponential number of constraints. Then
we introduce an efficient cutting plane algorithm to solve this problem in the
primal, and its convergence is presented. We also evaluate the proposed
learning paradigm on two widely-studied structured prediction tasks,
\emph{i.e.} sequence labeling and dependency parsing. Extensive experimental
results show that the proposed method outperforms CRFs and Structural SVMs due
to exploiting the importance of each template. Our complexity analysis and
empirical results also show that our proposed method is more efficient than
OnlineMKL on very sparse and high-dimensional data. We further extend this
paradigm for structured prediction using generalized -block norm
regularization with , and experiments show competitive performances when
On the Application of Gluon to Heavy Quarkonium Fragmentation Functions
We analyze the uncertainties induced by different definitions of the momentum
fraction in the application of gluon to heavy quarkonium fragmentation
function. We numerically calculate the initial fragmentation
functions by using the non-covariant definitions of with finite gluon
momentum and find that these fragmentation functions have strong dependence on
the gluon momentum . As , these fragmentation
functions approach to the fragmentation function in the light-cone definition.
Our numerical results show that large uncertainties remains while the
non-covariant definitions of are employed in the application of the
fragmentation functions. We present for the first time the polarized gluon to
fragmentation functions, which are fitted by the scheme exploited in
this work.Comment: 11 pages, 7 figures;added reference for sec.
Monotonicity results and bounds for the inverse hyperbolic sine
In this note, we present monotonicity results of a function involving to the
inverse hyperbolic sine. From these, we derive some inequalities for bounding
the inverse hyperbolic sine.Comment: 3 page
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