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To avoid the expensive quadratic programming in the L2-loss support vector regression (SVR) model, smooth approximation and iteratively reweighted least square (IRLS) techniques were introduced in literature, resulting in smoothed SVR (SSVR) and IRLS-SVR. However, for nonlinear models, SSVR and IRLS-SVR both involve operations with matrices and vectors of the same size as the training set. Thus, as the training set becomes large, nonlinear SSVR and IRLS-SVR both need long training time and large memory. To further alleviate the training cost, this paper projects the original data into a low dimensional space via random Fourier feature. The inner product of the random Fourier features of two data points is approximately the same as the kernel function evaluated at these two data points. Hence, it is possible to use a linear model in the new low dimensional space to approximate the original nonlinear model, and consequently the time/memory efficient linear training algorithms could be applied. This paper applies the idea of random Fourier features to nonlinear SSVR and IRLS-SVR, and our testing results on real-world datasets show that, the introduction of random Fourier features makes SSVR and IRLS-SVR achieve similar prediction accuracy as the original nonlinear version with substantially higher time efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a learning based method for automatic extraction of the major cortical sulci from MRI volumes or extracted surfaces. Instead of using a few pre-defined rules such as the mean curvature properties, to detect the major sulci, the algorithm learns a discriminative model by selecting and combining features from a large pool of candidates. We used the Probabilistic Boosting Tree algorithm to learn the model, which implicitly discovers and combines rules based on manually annotated sulci traced by neuroanatomists. The algorithm almost has no parameters to tune and is fast because of the adoption of integral volume and 3D Haar filters. For a given approximately registered MRI volume, the algorithm computes the probability of how likely it is that each voxel lies on a major sulcus curve. Dynamic programming is then applied to extract the curve based on the probability map and a shape prior. Because the algorithm can be applied to MRI volumes directly, there is no need to perform preprocessing such as tissue segmentation or mapping to a canonical space. The learning aspect makes the approach flexible and it also works on extracted cortical surfaces.

In a support vector regression (SVR) model, using the squared ϵ-insensitive loss function makes the optimization problem strictly convex and yields a more concise solution. However, the formulation of L 2 -SVR leads to a quadratic programming which is expensive to solve. This paper reformulates the optimization problem of L 2 -SVR by absorbing the constraints in the objective function, which can be solved efficiently by a majorization-minimization approach, in which an upper bound for the objective function is derived in each iteration which is easier to be minimized. The proposed approach is easy to implement, without requiring any additional computing package other than basic linear algebra operations. Numerical studies on real-world datasets show that, compared to the alternatives, the proposed approach can achieve similar prediction accuracy with substantially higher time efficiency in training. [ABSTRACT FROM AUTHOR]

In support vector regression (SVR) model, using the squared ϵ -insensitive loss function makes the objective function of the optimization problem strictly convex and yields a more concise solution. However, the formulation leads to a quadratic programing which is expensive to solve. This paper reformulates the optimization problem by absorbing the constraints in the objective function, and the new formulation shares similarity with weighted least square regression problem. Based on this formulation, we propose an iteratively reweighted least square approach to train the L2-loss SVR, for both linear and nonlinear models. The proposed approach is easy to implement, without requiring any additional computing package other than basic linear algebra operations. Numerical studies on real-world datasets show that, compared to the alternatives, the proposed approach can achieve similar prediction accuracy with substantially higher time efficiency. [ABSTRACT FROM AUTHOR]

This paper gives an improvement to Bennett's inequality for tail probability of sum of independent random variables, without imposing any additional condition. The improved version has a closed form expression. Using a refined arithmetic-geometric mean inequality, we further improve the obtained inequality. Numerical comparisons show that the proposed inequalities often improve the upper bound significantly in the far tail area, and these improvements get more prominent for larger sample size. [ABSTRACT FROM AUTHOR]