103,845 research outputs found
Support Vector Machines for Credit Scoring and discovery of significant features
The assessment of risk of default on credit is important for financial institutions. Logistic regression and discriminant analysis are techniques traditionally used in credit scoring for determining likelihood to default based on consumer application and credit reference agency data. We test support vector machines against these traditional methods on a large credit card database. We find that they are competitive and can be used as the basis of a feature selection method to discover those features that are most significant in determining risk of default. 1
Training Support Vector Machines Using Frank-Wolfe Optimization Methods
Training a Support Vector Machine (SVM) requires the solution of a quadratic
programming problem (QP) whose computational complexity becomes prohibitively
expensive for large scale datasets. Traditional optimization methods cannot be
directly applied in these cases, mainly due to memory restrictions.
By adopting a slightly different objective function and under mild conditions
on the kernel used within the model, efficient algorithms to train SVMs have
been devised under the name of Core Vector Machines (CVMs). This framework
exploits the equivalence of the resulting learning problem with the task of
building a Minimal Enclosing Ball (MEB) problem in a feature space, where data
is implicitly embedded by a kernel function.
In this paper, we improve on the CVM approach by proposing two novel methods
to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast
method to approximate the solution of a MEB problem. In contrast to CVMs, our
algorithms do not require to compute the solutions of a sequence of
increasingly complex QPs and are defined by using only analytic optimization
steps. Experiments on a large collection of datasets show that our methods
scale better than CVMs in most cases, sometimes at the price of a slightly
lower accuracy. As CVMs, the proposed methods can be easily extended to machine
learning problems other than binary classification. However, effective
classifiers are also obtained using kernels which do not satisfy the condition
required by CVMs and can thus be used for a wider set of problems
Modified Frank-Wolfe Algorithm for Enhanced Sparsity in Support Vector Machine Classifiers
This work proposes a new algorithm for training a re-weighted L2 Support
Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Cand\`es
et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In
particular, the margin required for each training vector is set independently,
defining a new weighted SVM model. These weights are selected to be binary, and
they are automatically adapted during the training of the model, resulting in a
variation of the Frank-Wolfe optimization algorithm with essentially the same
computational complexity as the original algorithm. As shown experimentally,
this algorithm is computationally cheaper to apply since it requires less
iterations to converge, and it produces models with a sparser representation in
terms of support vectors and which are more stable with respect to the
selection of the regularization hyper-parameter
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