805 research outputs found
Multilevel Weighted Support Vector Machine for Classification on Healthcare Data with Missing Values
This work is motivated by the needs of predictive analytics on healthcare
data as represented by Electronic Medical Records. Such data is invariably
problematic: noisy, with missing entries, with imbalance in classes of
interests, leading to serious bias in predictive modeling. Since standard data
mining methods often produce poor performance measures, we argue for
development of specialized techniques of data-preprocessing and classification.
In this paper, we propose a new method to simultaneously classify large
datasets and reduce the effects of missing values. It is based on a multilevel
framework of the cost-sensitive SVM and the expected maximization imputation
method for missing values, which relies on iterated regression analyses. We
compare classification results of multilevel SVM-based algorithms on public
benchmark datasets with imbalanced classes and missing values as well as real
data in health applications, and show that our multilevel SVM-based method
produces fast, and more accurate and robust classification results.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0625
M-Power Regularized Least Squares Regression
Regularization is used to find a solution that both fits the data and is
sufficiently smooth, and thereby is very effective for designing and refining
learning algorithms. But the influence of its exponent remains poorly
understood. In particular, it is unclear how the exponent of the reproducing
kernel Hilbert space~(RKHS) regularization term affects the accuracy and the
efficiency of kernel-based learning algorithms. Here we consider regularized
least squares regression (RLSR) with an RKHS regularization raised to the power
of m, where m is a variable real exponent. We design an efficient algorithm for
solving the associated minimization problem, we provide a theoretical analysis
of its stability, and we compare its advantage with respect to computational
complexity, speed of convergence and prediction accuracy to the classical
kernel ridge regression algorithm where the regularization exponent m is fixed
at 2. Our results show that the m-power RLSR problem can be solved efficiently,
and support the suggestion that one can use a regularization term that grows
significantly slower than the standard quadratic growth in the RKHS norm
SVM-Maj: a majorization approach to linear support vector machines with different hinge errors
Support vector machines (SVM) are becoming increasingly popular for the prediction of a binary dependent variable. SVMs perform very well with respect to competing techniques. Often, the solution of an SVM is obtained by switching to the dual. In this paper, we stick to the primal support vector machine (SVM) problem, study its effective aspects, and propose varieties of convex loss functions such as the standard for SVM with the absolute hinge error as well as the quadratic hinge and the Huber hinge errors. We present an iterative majorization algorithm that minimizes each of the adaptations. In addition, we show that many of the features of an SVM are also obtained by an optimal scaling approach to regression. We illustrate this with an example from the literature and do a comparison of different methods on several empirical data sets.iterative majorization;I-splines;absolute hinge error;huber hinge error;optimal scaling;quadratic hinge error;support vector machines
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