Margin-based Loss Function Research Articles

Large Margin Feature Selection for Support Vector Machine

Feature selection is an preprocessing step in pattern analysis and machine learning. In this paper, we design a algorithm for feature subset. We present L1-norm regularization technique for sparse feature weight. Margin loss are introduced to evaluate features, and we employs gradient descent to search the optimal solution to maximize margin. The proposed technique is tested on UCI data sets. Compared with four margin based loss functions for SVM, the proposed technique is effective and efficient.

Support vector regression for porosity prediction in a heterogeneous reservoir: A comparative study

In wells with limited log and core data, porosity, a fundamental and essential property to characterize reservoirs, is challenging to estimate by conventional statistical methods from offset well log and core data in heterogeneous formations. Beyond simple regression, neural networks have been used to develop more accurate porosity correlations. Unfortunately, neural network-based correlations have limited generalization ability and global correlations for a field are usually less accurate compared to local correlations for a sub-region of the reservoir. In this paper, support vector machines are explored as an intelligent technique to correlate porosity to well log data. Recently, support vector regression (SVR), based on the statistical learning theory, have been proposed as a new intelligence technique for both prediction and classification tasks. The underlying formulation of support vector machines embodies the structural risk minimization (SRM) principle which has been shown to be superior to the traditional empirical risk minimization (ERM) principle employed by conventional neural networks and classical statistical methods. This new formulation uses margin-based loss functions to control model complexity independently of the dimensionality of the input space, and kernel functions to project the estimation problem to a higher dimensional space, which enables the solution of more complex nonlinear problem optimization methods to exist for a globally optimal solution. SRM minimizes an upper bound on the expected risk using a margin-based loss function ( ε-insensitivity loss function for regression) in contrast to ERM which minimizes the error on the training data. Unlike classical learning methods, SRM, indexed by margin-based loss function, can also control model complexity independent of dimensionality. The SRM inductive principle is designed for statistical estimation with finite data where the ERM inductive principle provides the optimal solution (the empirical risk approaches the expected risk) only for asymptotic (large sample data). The SRM principle matches model complexity to the available data through controlling the tradeoff between complexity of the model and quality of fitting the data. It is this difference which equips support vector machines (SVM) with a greater ability to generalize beyond the training data. Here, a SVR-based porosity prediction model is developed for a heterogeneous sandstone reservoir. The SVR method has been compared to multilayer perceptron, General Regression Neural Networks, and Radial Basis Function Neural Networks. The results reveal that the SVR method exhibits superior accuracy and robustness with respect to these neural network methods especially with respect to accuracy when generalizing to previously unseen porosity data.

A note on margin-based loss functions in classification

In many classification procedures, the classification function is obtained by minimizing a certain empirical risk on the training sample. The classification is then based on the sign of the classification function. In recent years, there have been a host of classification methods proposed that use different margin-based loss functions. The margin-based loss functions are often motivated as upper bounds of the misclassification loss, but this cannot explain the statistical properties of the classification procedures. We show that a large family of margin-based loss functions are Fisher consistent for classification. That is, the population minimizer of the loss function leads to the Bayes optimal rule of classification. Our result covers almost all margin-based loss functions that have been proposed in the literature. We give an inequality that links the Fisher consistency of margin-based loss functions with the consistency of methods based on these loss functions. We use this inequality to obtain the rate of convergence for the method of sieves based on a class of margin-based loss functions.