6,621 research outputs found
A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computing
The past years have witnessed many dedicated open-source projects that built
and maintain implementations of Support Vector Machines (SVM), parallelized for
GPU, multi-core CPUs and distributed systems. Up to this point, no comparable
effort has been made to parallelize the Elastic Net, despite its popularity in
many high impact applications, including genetics, neuroscience and systems
biology. The first contribution in this paper is of theoretical nature. We
establish a tight link between two seemingly different algorithms and prove
that Elastic Net regression can be reduced to SVM with squared hinge loss
classification. Our second contribution is to derive a practical algorithm
based on this reduction. The reduction enables us to utilize prior efforts in
speeding up and parallelizing SVMs to obtain a highly optimized and parallel
solver for the Elastic Net and Lasso. With a simple wrapper, consisting of only
11 lines of MATLAB code, we obtain an Elastic Net implementation that naturally
utilizes GPU and multi-core CPUs. We demonstrate on twelve real world data
sets, that our algorithm yields identical results as the popular (and highly
optimized) glmnet implementation but is one or several orders of magnitude
faster.Comment: 10 page
Robustness and Regularization of Support Vector Machines
We consider regularized support vector machines (SVMs) and show that they are
precisely equivalent to a new robust optimization formulation. We show that
this equivalence of robust optimization and regularization has implications for
both algorithms, and analysis. In terms of algorithms, the equivalence suggests
more general SVM-like algorithms for classification that explicitly build in
protection to noise, and at the same time control overfitting. On the analysis
front, the equivalence of robustness and regularization, provides a robust
optimization interpretation for the success of regularized SVMs. We use the
this new robustness interpretation of SVMs to give a new proof of consistency
of (kernelized) SVMs, thus establishing robustness as the reason regularized
SVMs generalize well
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
Structural Agnostic Modeling: Adversarial Learning of Causal Graphs
A new causal discovery method, Structural Agnostic Modeling (SAM), is
presented in this paper. Leveraging both conditional independencies and
distributional asymmetries in the data, SAM aims at recovering full causal
models from continuous observational data along a multivariate non-parametric
setting. The approach is based on a game between players estimating each
variable distribution conditionally to the others as a neural net, and an
adversary aimed at discriminating the overall joint conditional distribution,
and that of the original data. An original learning criterion combining
distribution estimation, sparsity and acyclicity constraints is used to enforce
the end-to-end optimization of the graph structure and parameters through
stochastic gradient descent. Besides the theoretical analysis of the approach
in the large sample limit, SAM is extensively experimentally validated on
synthetic and real data
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