Pathwise least angle regression and a significance test for the elastic net

@article{Tabassum2017PathwiseLA,
  title={Pathwise least angle regression and a significance test for the elastic net},
  author={Muhammad Naveed Tabassum and Esa Ollila},
  journal={2017 25th European Signal Processing Conference (EUSIPCO)},
  year={2017},
  pages={1309-1313}
}
Least angle regression (LARS) by Efron et al. (2004) is a novel method for constructing the piece-wise linear path of Lasso solutions. For several years, it remained also as the de facto method for computing the Lasso solution before more sophisticated optimization algorithms preceded it. LARS method has recently again increased its popularity due to its ability to find the values of the penalty parameters, called knots, at which a new parameter enters the active set of non-zero coefficients… 

Figures and Tables from this paper

Model Selection for Vector Autoregressive processes using the Multi-Step Elastic Net

Overall maenet performs well in high-dimensional small samples in terms of selecting the right variables and forecast performance, and empirical results show a sparser model compared to the single-step adaptive elastic net methods.

Simultaneous Signal Subspace Rank and Model Selection with an Application to Single-snapshot Source Localization

The proposed c-LARS-GIC method detects the number of sources with high probability while at the same time it provides accurate estimates of source locations using only a single-snapshot measurement.

Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model

A robust multivariate Fay–Herriot model is proposed that combines compositional data analysis with robust optimization theory and is presented as a linear problem through isometric logratio transformations.

Review of statistical methods for survival analysis using genomic data

Traditional survival methods and regularization methods are reviewed, with various penalty functions, for the analysis of high-dimensional genomics, and machine learning approaches have been adapted for survival analysis to fit nonlinear and complex interaction effects between predictors, and achieve more accurate prediction of individual survival probability.

Comparing Between the Imported and Local Bottled Drinking Water by LASSO Regression

Predict the significant variables of the quality measurement results of 10 and 5 kinds of imported and local bottled drinking water, respectively, tested in the Samawah city, Iraq, using regression

Hyperspectral Remote Sensing Images Unmixing Based on Sparse Concept Coding

Experimental results show that SCC improves unmixing accuracy compared with original NMF, L1/2- NMF and L1-NMF and the presented algorithm is applied on synthetic and real data sets.

Signal Enhancement in Defect Detection of CFRP Material Using a Combination of Difference of Gaussian Convolutions and Sparse Principal Component Thermography

Owing to its advantages of low-cost and fast detection, pulsed thermography has become a promising technique to detect subsurface defects in materials of carbon fiber reinforced polymer (CFRP). Since

Sequential adaptive elastic net approach for single-snapshot source localization

A sequential adaptive EN (SAEN) method is proposed that is based on c-PW-WEN algorithm with adaptive weights that depend on previous solution, and extensive simulation studies illustrate that SAEN improves the probability of exact recovery of true support compared to conventional sparse signal recovery approaches.

References

SHOWING 1-9 OF 9 REFERENCES

Least angle regression

A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.

Regularization and variable selection via the elastic net

It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.

A SIGNIFICANCE TEST FOR THE LASSO.

A simple test statistic based on lasso fitted values is proposed, called the covariance test statistic, and it is shown that when the true model is linear, this statistic has an Exp(1) asymptotic distribution under the null hypothesis (the null being that all truly active variables are contained in the current lasso model).

Regression Shrinkage and Selection via the Lasso

A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.

Statistical Learning with Sparsity: The Lasso and Generalizations

Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data and extract useful and reproducible patterns from big datasets.

Single-snapshot DoA estimation using adaptive elastic net in the complex domain

  • Muhammad Naveed TabassumE. Ollila
  • Computer Science
    2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa)
  • 2016
An efficient algorithm to solve the weighted EN criterion for complex-valued measurements applying the cyclic coordinate descent approach is developed and accurate DoA's estimation performance and error plummet by the proposed algorithm validates its application and advocates its potential usage in other signal processing problems.

The Elements of Statistical Learning

Chapter 11 includes more case studies in other areas, ranging from manufacturing to marketing research, and a detailed comparison with other diagnostic tools, such as logistic regression and tree-based methods.

[Least Angle Regression]: Discussion