By S. Ejaz Ahmed
This quantity conveys a number of the surprises, puzzles and good fortune tales in high-dimensional and intricate information research and comparable fields. Its peer-reviewed contributions show off fresh advances in variable choice, estimation and prediction ideas for a bunch of helpful types, in addition to crucial new advancements within the field.
The persevered and fast development of contemporary know-how now permits scientists to assemble facts of more and more extraordinary measurement and complexity. Examples comprise epigenomic information, genomic information, proteomic information, high-resolution photograph information, high-frequency monetary information, useful and longitudinal info, and community info. Simultaneous variable choice and estimation is without doubt one of the key statistical difficulties keen on reading such enormous and complicated data.
the aim of this publication is to stimulate learn and foster interplay among researchers within the quarter of high-dimensional info research. extra concretely, its objectives are to: 1) spotlight and extend the breadth of latest tools in enormous facts and high-dimensional facts research and their strength for the development of either the mathematical and statistical sciences; 2) determine very important instructions for destiny examine within the concept of regularization equipment, in algorithmic improvement, and in methodologies for various program parts; and three) facilitate collaboration among theoretical and subject-specific researchers.
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Additional info for Big and Complex Data Analysis. Methodologies and Applications
0. 22 Y. Feng and M. A/ ! 0, the inequalities (26)–(29) imply (25) under the scaling in Theorem 1. Thus kK1 C K2 k1 < 1 achieves with high probability, which also means ˇLUO nUO1 D 0 achieves asymptotically. From our analysis in the first part, the following goal is the uniqueness of (20). If there is another solution, let’s call it ˇL 0 . t/ L Qc D 0, the convexity. t/ hence it is a solution to (13). From the uniqueness of (13), we conclude that ˇL D ˇL 0 . The last part of this step is to prove ˇNU1 ¤ 0 with high probability.
As for Example 2, we define ˙ 0 D D . a1 ; : : : ; am /. 1Cm/j /: jD1 Á Pd Q8 Denote ıj1 ;:::;j8 D E kD1 F1jk . The other cases of vD1 lv Ä 8 can be proved in the same way. X1> X1Cm /8 D s 8 X Y j1 ;:::;j8 D1 j01 ;:::;j08 D1 kD1 0 ı ı0 0: jk ;j0k j1 ;:::;j8 j1 ;:::;j8 P ıj1 ;:::;j8 ¤ 0 only when fj1 ; : : : ; j8 g form pairs of integers. Denote as the summation of the situations that ıj1 ;:::;j8 ıj01 ;:::;j08 ¤ 0. X1> X1Cm /8 DO 8 XY ! X1 C X1Cm //8 Ä 28 E @ s X 18 aj F1;j A jD1 0 1 0 1 0 1 0 1 X X X X D O@ a8j A C O @ a6j a2j0 A C O @ a4j a4j0 A C O @ a4j a2j0 a2j00 A j;j0 j 0 CO @ X j;j0 1 j;j0 ;j00 a2j a2j0 a2j00 a2j000 A j;j0 ;j00 ;j000 00 14 1 B X 2A C aj A D O D O @@ ˛T T ˛ 4 Á : j t u Then according to Theorem 1, we can prove Theorem 2.
J. R. Stat. Soc. Ser. B Stat. Methodol. 70, 849–911 (2008) 7. : Sure independence screening in generalized linear models with npdimensionality. Ann. Stat. 38, 3567–3604 (2010) 8. : Nonparametric independence screening in sparse ultra-high dimensional additive models. J. Am. Stat. Assoc. 106, 544–557 (2011) 9. : A road to classification in high dimensional space: the regularized optimal affine discriminant. J. R. Stat. Soc. Ser. B. 74, 745–771 (2012) 10. : Feature augmentation via nonparametrics and selection (fans) in high dimensional classification.
Big and Complex Data Analysis. Methodologies and Applications by S. Ejaz Ahmed