Convex Risk
Perturbation of convex risk minimization and its application in differential private learning algorithms
... The first one is the perturbation results for general convex risk minimization algorithms. We studied two cases of the general algorithms. The second one is applied in the following analysis, as it leads to ...
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On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition
... the convex risk minimization principle have − besides other good prop- erties − also the advantage of being ...on convex risk minimization are investigated for the problem of pattern ...
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Real-valued conditional convex risk measures in Lp(ℱ, R)
... conditional convex risk measures in the spaces L p (F , R) in terms of the corresponding penalty ...conditional convex risk measures defined in a space L ∞ (F, R) which can be extended to a ...
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Svindland, Gregor (2009): Convex Risk Measures Beyond Bounded Risks. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik
... over all allocations (Y 1 , . . . , Y n ). By cash-invariance an optimal allocation ( Y e 1 , . . . , Y e n ) does not only minimise the group risk (0.1), but by rebalancing the cash we may assume that ρ( Y e i ) ...
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To split or not to split: capital allocation with convex risk measures
... on risk measures than positive homogeneity / subadditivity is convexity, proposed by Deprez and Gerber (1985), who in- troduce convex risk measures and study them in the context of optimal ...
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To split or not to split: Capital allocation with convex risk measures
... (non-homogenous) convex risk mea- sure for capital allocation produces an incentive for infinite fragmentation of ...using convex risk measures in a risk management ...
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Classification Methods with Reject Option Based on Convex Risk Minimization
... We have focused thus far on the case where misclassifying from one class to the other, either g(X ) = 1 while Y = − 1 or g(X) = − 1 while Y = 1, is assigned the same loss. In many applications, however, one type of ...
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Nonlinear and evolutionary phenomena in deterministic growing economies
... Our first proposal deals with an economy populated by representative agents seeking to maximize consumption utility by taking optimal consumption and in- vestment decisions. Agents face convex risk premium ...
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Robustness Regions for Measures of Risk Aggregation
... neither convex risk measures such as ES nor VaR, are robust on L 1 ...functions. Convex risk measures like ES place requirements on the tail of the underlying dis- tribution functions via the ...
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Risk Measures and Nonlinear Expectations
... We show that 1 in the family of convex risk measures, only coherent risk measures satisfy Jensen’s inequality; 2 coherent risk measures are always bounded by the corresponding Choquet ex[r] ...
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Regularized Bundle Methods for Convex and Non-Convex Risks
... where t is the number of cutting planes (it is equal to the iteration number in CRBM) and D is the dimensionality of w. In addition, the computational cost for solving the dual program is usually quadratic or cubic in t. ...
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fis convex if its epigraph is a convex set, andf is closed
... nondifferentiable convex functions. Lemma 1. Let f : S → R ∪ { } + ∞ be a convex function defined on a convex set S ⊆ R n , and x ′ ∈ int S ...
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Convex functions
... First Set of criteria for convexity.. LISTGFHGURES Figure 1... To show that f is convex, we have to verify that the following inequality holds.. i displays a geometric interpTetatio[r] ...
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On convex permutations
... all convex permutations, ...finite convex generic set. For example, the permutation 1243 is convex, as can be seen from Figure ...not convex. There are far fewer permutations whose standard ...
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Some properties of harmonic convex and harmonic quasi-convex functions
... of convex function which is known as harmonically convex ...harmonically convex functions which implies that harmonically quasi-convex ...
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Unsupervised Data Classification for Convex and Non Convex Classes
... In this experiment, two types of simulation are carried out. For both simulations the classes have convex form, we have three classes in each case, and the data have been generated by a Gaussian distribution ...
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Minimum Risk Training of Approximate CRF Based NLP Systems
... Motivated by the recently proposed method of Stoy- anov et al. (2011) for minimum-risk training of CRF-based systems, we revisited three NLP do- mains that can naturally be modeled with approx- imate CRF-based ...
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On Hadamard and Fej\'{e}r-Hadamard inequalities for Caputo $\small{k}$-fractional derivatives
... In this paper, in Section 2 we define Caputo k-fractional derivatives and utilize them to give the Hadamard inequality for functions whose nth derivatives are convex. We also find the bound of a difference of this ...
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On Convexity and Approximating the Perimeter of an Ellipse
... x ∈Ν ⊂ S be a dense subset and assume x 0 to be a point of intS. Denote by C x ( ) 0 the family of all convex, closed subsets of S, containing x 0 in their relative interior with respect to S. Endow the nonempty ...
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Convex Quadratic Optimization Based on Generator Matrix in Credit Risk Transfer Process
... Abstract. In this paper, the generator matrix is calculated based on the grade transfer matrix over a period of time in the quantitative analysis of credit risk, which has become one of the hot issues that many ...
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