Extreme learning machine (ELM) is one of the most notable machine learning algorithms with many advantages, especially its training speed. However, ELM has some drawbacks such as instability, poor generalizability and overfitting in the case of multicollinearity in the linear model. This paper introduces square-root lasso ELM (SQRTL-ELM) as a novel regularized ELM algorithm to deal with these drawbacks of ELM. A modified version of the alternating minimization algorithm is used to obtain the estimates of the proposed method. Various techniques are presented to determine the tuning parameter of SQRTL-ELM. The method is compared with the basic ELM, RIDGE-ELM, LASSO-ELM and ENET-ELM on six benchmark data sets. Performance evaluation results show that the SQRTL-ELM exhibits satisfactory performance in terms of testing root mean squared error in benchmark data sets for the sake of slightly extra computation time. The superiority level of the method depends on the tuning parameter selection technique. As a result, the proposed method can be considered a powerful alternative to avoid performance loss in regression problems .

We propose a new shrinkage and variable selection method in linear regression, which is based on triple shrinkage on the regression coefficients. The new estimation method contains the ridge, lasso and elastic net as special cases. The term based on the shrunken estimator in the new method can provide estimates with a smaller length depending on the size of a new tuning parameter compared to the elastic net, maintaining the variable selection feature in the case of multicollinearity. The new estimator has the property of the grouping effect similar to that of the elastic net. The well-known coordinate descent algorithm is used to compute the coefficient path of the new estimator, efficiently. We conduct real data analysis and simulation studies to compare the new estimator with several methods including the lasso and elastic net.

Variable selection approaches are often employed in high-dimensionality and multicollinearity problems. Since lasso selects variables by shrinking the coefficients, it has extensive use in many fields. On the other, we may sometime have extra information on the model. In this case, the extra information should be considered in the estimation procedure. In this paper, we propose a stochastic restricted lasso estimator in linear regression model which uses the extra information as stochastic linear restrictions. The estimator is a generalization of mixed estimator with L₁ type penalization. We give the coordinate descent algorithm to estimate the coefficient vector of the proposed method and strong rules for the coordinate descent algorithm to discard variables from the model. Also, we propose a method to estimate the tuning parameter. We conduct two real data analyses and simulation studies to compare the new estimator with several estimators including the ridge, lasso and stochastic restricted ridge. The real data analyses and simulation studies show that the new estimator enjoys the automatic variable selection property of the lasso while outperforms standard methods, achieving lower test mean squared error.

Cancer classification and gene selection are important applications in DNA microarray gene expression data analysis. Since DNA microarray data suffers from the high-dimensionality problem, automatic gene selection methods are used to enhance the classification performance of expert classifier systems. In this paper, a new penalized logistic regression method that performs simultaneous gene coefficient estimation and variable selection in DNA microarray data is discussed. The method employs prior information about the gene coefficients to improve the classification accuracy of the underlying model. The coordinate descent algorithm with screening rules is given to obtain the gene coefficient estimates of the proposed method efficiently. The performance of the method is examined on five high-dimensional cancer classification datasets using the area under the curve, the number of selected genes, misclassification rate and F-score measures. The real data analysis results indicate that the proposed method achieves a good cancer classification performance with a small misclassification rate, large area under the curve and F-score by trading off some sparsity level of the underlying model. Hence, the proposed method can be seen as a reliable penalized logistic regression method in the scope of high-dimensional cancer classification.

The Unit Inverse Maxwell–Boltzmann (UIMB) distribution is introduced as a novel single-parameter model for data constrained within the unit interval ($0,1$), derived through an exponential transformation of the Inverse Maxwell–Boltzmann distribution. Designed to address the limitations of traditional unit-interval distributions, the UIMB model exhibits flexible density shapes and hazard rate behaviors, including right-skewed, left-skewed, unimodal, and bathtub-shaped patterns, making it suitable for applications in reliability engineering, environmental science, and health studies. This study derives the statistical properties of the UIMB distribution, including moments, quantiles, survival, and hazard functions, as well as stochastic ordering, entropy measures, and the moment-generating function, and evaluates its performance through simulation studies and real-data applications. Various estimation methods, including maximum likelihood, Anderson–Darling, maximum product spacing, least-squares, and Cramér–von Mises, are assessed, with maximum likelihood demonstrating superior accuracy. Simulation studies confirm the model’s robustness under normal and outlier-contaminated scenarios, with MLE showing resilience across varying skewness levels. Applications to manufacturing and environmental datasets reveal the UIMB distribution’s exceptional fit compared to competing models, as evidenced by lower information criteria and goodness-of-fit statistics. The UIMB distribution’s computational efficiency and adaptability position it as a robust tool for modeling complex unit-interval data, with potential for further extensions in diverse domains.