New bounds for soft margin estimator via concavity of Gaussian weighting function

被引:15
作者
Ullah, Hidayat [1 ]
Adil Khan, Muhammad [1 ]
Pecaric, Josip [2 ]
机构
[1] Univ Peshawar, Dept Math, Peshawar 25000, Pakistan
[2] 2 RUDN Univ, Miklukho Maklaya Str 6, Moscow 117198, Russia
关键词
Concave function; Soft margin estimator; Gaussian weighting function; Jensen’ s inequality; Jaccard similarity function;
D O I
10.1186/s13662-020-03103-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the present article, we elaborate on the notion to obtain bounds for the soft margin estimator of "Identification of Patient Zero in Static and Temporal Network-Robustness and Limitations". To achieve these bounds for the soft margin estimator, we utilize the concavity of the Gaussian weighting function and well-known Jensen's inequality. To acquire some more general bounds for the soft margin estimator, we consider some general functions defined on rectangles. We also use the behavior of the Jaccard similarity function to extract some handsome bounds for the soft margin estimator.
引用
收藏
页数:10
相关论文
共 28 条
[11]   GENERALIZATION OF JENSEN'S AND JENSEN-STEFFENSEN'S INEQUALITIES BY GENERALIZED MAJORIZATION THEOREM [J].
Khan, M. Adil ;
Khan, Jamroz ;
Pecaric, Josip .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2017, 11 (04) :1049-1074
[12]   GENERALIZATION OF MAJORIZATION THEOREM [J].
Khan, M. Adil ;
Latif, N. ;
Pecaric, J. .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2015, 9 (03) :847-872
[13]   New refinement of the Jensen inequality associated to certain functions with applications [J].
Khan, Muhammad ;
Pecaric, Dilda ;
Pecaric, Josip .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020, 2020 (01)
[14]   A New Bound for the Jensen Gap With Applications in Information Theory [J].
Khan, Muhammad Adil ;
Khan, Shahid ;
Chu, Yuming .
IEEE ACCESS, 2020, 8 :98001-98008
[15]   Discrete majorization type inequalities for convex functions on rectangles [J].
Khan, Muhammad Adil ;
Wu, Shan-He ;
Ullah, Hidayat ;
Chu, Yu-Ming .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (1)
[16]  
Khan MA, 2015, RAD HRVAT AKAD ZNAN, V19, P91
[17]   A new bound for the Jensen gap pertaining twice differentiable functions with applications [J].
Khan, Shahid ;
Khan, Muhammad Adil ;
Butt, Saad Ihsan ;
Chu, Yu-Ming .
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[18]   New converses of Jensen inequality via Green functions with applications [J].
Khan, Shahid ;
Khan, Muhammad Adil ;
Chu, Yu-Ming .
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2020, 114 (03)
[19]   Understanding the dynamics of Ebola epidemics [J].
Legrand, J. ;
Grais, R. F. ;
Boelle, P. Y. ;
Valleron, A. J. ;
Flahault, A. .
EPIDEMIOLOGY AND INFECTION, 2007, 135 (04) :610-621
[20]   Inferring the origin of an epidemic with a dynamic message-passing algorithm [J].
Lokhov, Andrey Y. ;
Mezard, Marc ;
Ohta, Hiroki ;
Zdeborova, Lenka .
PHYSICAL REVIEW E, 2014, 90 (01)