Restricted strong convexity and weighted matrix completion: Optimal bounds with noise. The Journal of Machine Learning Research, 13(1):1665-1697, 2012.Negahban, S., Wainwright, M.J.: Restricted strong convexity and weighted matrix completion: optimal bounds with noise. J. Mach. Learn. Res. 13...
We analyze the associated random observation operator, and provethat with high probability, it satisfies a form of restricted strong convexitywith respect to weighted Frobenius norm. Using this property, we obtain ascorollaries a number of error bounds on matrix completion in the weightedFrobenius ...
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this connection allows us to obtain strong multiplicative performance bounds...
() Citation Context ...restricted-orientation convexity, called strong convexity and O-convexity [7], to higher-dimensional spaces and presented an extensive study of restricted-orientation convex sets in higher dimensions =-=[2, 3]-=... E Fink,D Wood - International Society for Optics and ...
For the final inequality we used the convexity of \exp (-x^2). We substitute this bound into our expression (10.2) for F_Y, which gives for Y=10^k \begin{aligned} F_{Y}(t)&=\prod _{i=0}^{k-1}\frac{1}{9}\left|\sum _{n_i\in \{0,\ldots ,9\}\backslash \{a_0\...
12 We previously reported that even in the normally sized or mildly dilated BAV aorta, the convexity can display initial signs of extracellular matrix degradation.22 According to the described mechanisms of flow-induced vascular remodeling,23 the flow jet impacting on the convexity area since birth ...
Re- stricted strong convexity implies weak submodularity. Annals of Statistics, 2018. To appear.Elenberg, E. R., Khanna, R., Dimakis, A. G., Negahban, S., et al. Restricted strong convexity implies weak submodularity. The Annals of Statistics, 46(6B):3539-3568, 2018....
H. Zhang. The restricted strong convexity revisited: analysis of equivalence to error bound and quadratic growth. Optimization Letter, 11:817-833, 2017.H. Zhang. The restricted strong convexity revisited: analysis of equivalence to error bound and quadratic growth. Optimization Letters, pages 1-17...
Cheng, Restricted strong convexity and its applications to convergence analysis of gradient type methods in convex optimization, Optimization Letters, 9: 961- 979, 2015.H. Zhang and L. Cheng, Restricted strong convexity and its applications to convergence analysis of gradient-type methods in convex ...
H. Zhang. The restricted strong convexity revisited: analysis of equivalence to error bound and quadratic growth. Optimization Letter, 11:817-833, 2017.H. Zhang. The restricted strong convexity revisited: analysis of equivalence to error bound and quadratic growth. Optimization Letters, pages 1-17...