In late 2014, it was proven that the elastic net can be reduced to the linear support vector machine.A similar reduction was previously proven for the LASSO in 2014. The authors showed that for every instance of the elastic net, an artificial binary classification problem can be constructed such that the hyper-plane solution of a linear support vector machine (SVM) is identical to the solution {\displaystyle \beta }\beta  (after re-scaling). The reduction immediately enables the use of highly optimized SVM solvers for elastic net problems. It also enables the use of GPU acceleration, which is often already used for large-scale SVM solvers. The reduction is a simple transformation of the original data and regularization constants into new artificial data instances and a regularization constant that specify a binary classification problem and the SVM regularization constant. 
Here,  y 2 consists of binary labels -1,1 . When 2p>n it is typically faster to solve the linear SVM in the primal, whereas otherwise the dual formulation is faster. The authors referred to the transformation as Support Vector Elastic Net (SVEN),

Reduction to support vector machine

Milanez-Almeida, Pedro; Martins, Andrew J.; Germain, Ronald N.; Tsang, John S. (2020-02-10). "Cancer prognosis with shallow tumor RNA sequencing". Nature Medicine. 26 (2): 188–192. doi:10.1038/s41591-019-0729-3. ISSN 1546-170X. PMID 32042193. S2CID 211074147.(https://www.nature.com/articles/s41591-019-0729-3)

Cancer prognosis reference paper

Shen, Weiwei; Wang, Jun; Ma, Shiqian (2014). "Doubly Regularized Portfolio with Risk Minimization". Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence: 1286–1292. S2CID 11017740 (https://www.semanticscholar.org/paper/Doubly-Regularized-Portfolio-with-Risk-Minimization-Shen-Wang/60814c0450d453169045500d9299b458998a3540)

Portfolio optimization

Liu, Meizhu; Vemuri, Baba (2012). "A robust and efficient doubly regularized metric learning approach". Proceedings of the 12th European Conference on Computer Vision. Lecture Notes in Computer Science. Part IV: 646–659. doi:10.1007/978-3-642-33765-9_46. ISBN 978-3-642-33764-2. PMC 3761969. PMID 24013160.(https://dl.acm.org/doi/10.1007/978-3-642-33765-9_46)

Metric learning reference paper

Deep learning uses the neural networks to increase the computational work and provide accurate results. Assisting medical professionals and researchers to discover the hidden opportunities in data is one of the best things we can accomplish with Deep Learning. The possible applications of deep learning in the field of healthcare are: 

1. Drug discovery
2. Medical imaging
3. Insurance fraud
4. Alzheimer's disease
5. Genome

Reference: https://www.allerin.com/blog/top-5-applications-of-deep-learning-in-healthcare

Application of Deep Learning in HealthCare

1. Support vector machine
2. Metric learning
3. Portfolio optimization
4. Cancer prognosis

University of Michigan - Ann Arbor

In statistics, particularly in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the $$L_1$$ and $$L_2$$ penalties of the lasso and ridge regression methods.

Elastic Net Regression

1. A Generalization of Ridge, Lasso and Elastic Net Regression to Interval Data(https://www.researchgate.net/publication/265905932_A_Generalization_of_Ridge_Lasso_and_Elastic_Net_Regression_to_Interval_Data)
2. Regularization and variable selection via the elastic net(https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.445.4562&rep=rep1&type=pdf)

ElasticNet Regression First Paper

Application Areas

LASSO uses an $$L_1$$ penalty and can encounter two important limitations: when the number of predictors exceeds the number of examples, it selects at most as many predictors as there are examples before saturating; and among highly correlated predictors, it tends to select one while excluding the others. Elastic net combines the LASSO penalty with a quadratic $$L_2$$ penalty, helping address these limitations. When its $$L_2$$ component is positive, the objective is strongly convex and has a unique minimum. LASSO and ridge regression are special cases of elastic net. A naive elastic-net procedure first estimates ridge coefficients for a fixed $$\lambda_2$$ and then applies LASSO-type shrinkage, causing double shrinkage that can increase bias and impair prediction. Rescaling the resulting coefficients by $$1+\lambda_2$$ corrects this additional shrinkage.

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