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Support vector machines regression (SVMR) is an important tool in many machine learning applications. In this paper, we focus on the theoretical understanding of SVMR based on the ??insensitive loss. For fixed ??≥?0 and general data generating distributions, we show that the minimizer of the expected risk for ??insensitive loss used in SVMR is a set-valued function called conditional ??median. We then establish a calibration inequality of ??insensitive loss under a noise condition on the conditional distributions. This inequality also ensures us to present a nontrivial variance-expectation bound for ??insensitive loss, and which is known to be important in statistical analysis of the regularized learning algorithms. With the help of the calibration inequality and variance-expectation bound, we finally derive an explicit learning rate for SVMR in some Lr?space.  相似文献   

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This paper formulates the pose (attitude and position) estimation problem as nonlinear stochastic filter kinematics evolved directly on the Special Euclidean Group 3 (SE(3)). This work proposes an alternate way of potential function selection and handles the problem as a stochastic filtering problem. The problem is mapped from SE(3) to vector form, using the Rodriguez vector and the position vector, and then followed by the definition of the pose problem in the sense of Stratonovich. The proposed filter guarantees that the errors present in position and Rodriguez vector estimates are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and that they converge to small neighborhood of the origin in probability. Simulation results show the robustness and effectiveness of the proposed filter in presence of high levels of noise and bias associated with the velocity vector as well as body-frame measurements.  相似文献   

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This article is concerned with the non-fragile sampled-data control for T-S fuzzy system with parameter uncertainties. Firstly, a novel augmented Lyapunov-Krasovskii functional with sufficient sampled-data information is constructed. And a novel h(t)-depended exponential stability criterion with H performance is gotten by reciprocally convex matrix inequality. Beyond that, compared with the existing methods, the gain matrices for non-fragile sampled-data controller expected are less conservative by linear matrix inequality technique. And numerical examples are provided to support the viability and validity of the results.  相似文献   

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This paper studies the stability of linear continuous-time systems with time-varying delay by employing new Lyapunov–Krasovskii functionals. Based on the new Lyapunov–Krasovskii functionals, more relaxed stability criteria are obtained. Firstly, in order to coordinate with the use of the third-order Bessel-Legendre inequality, a proper quadratic functional is constructed. Secondly, two couples of integral terms {t?htsx(s)ds,stx(s)ds} and {t?hMsx(s)ds,st?htx(s)ds} are involved in the integral functionals t?htt(·)ds and t?hMt?ht(·)ds, respectively, so that the coupling information between them can be fully utilized. Finally, two commonly-used numerical examples are given to demonstrate the effectiveness of the proposed method.  相似文献   

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