# Lasso

In cross-condition single-cell data, an existing gene-level batch-effect score can mistake condition-driven genes for highly batch-sensitive ones. Condition-aware GTE first uses scDisInFact to separate condition effects from batch effects, assigns each gene a condition-driven score, and multiplicatively penalizes the original score by that value. On an interferon-beta-stimulated PBMC dataset of 29,065 cells from eight donors, a penalty exponent of 3 moved 18 known interferon-stimulated genes by an average of 870.2 rank positions while ribosomal control genes stayed within baseline fluctuation.

In cross-condition single-cell data, an existing gene-level batch-effect score can mistake condition-driven genes for highly batch-sensitive ones. Condition-aware GTE first uses scDisInFact to separate condition effects from batch effects, assigns each gene a condition-driven score, and multiplicatively penalizes the original score by that value. On an interferon-beta-stimulated PBMC dataset of 29,065 cells from eight donors, a penalty exponent of 3 moved 18 known interferon-stimulated genes by an average of 870.2 rank positions while ribosomal control genes stayed within baseline fluctuation.

The work proposes a Nonmonotone Coderivative-based Newton (NCN) method that builds generalized Hessians from Mordukhovich coderivatives of the gradient mapping and combines a Hybrid Adaptive Nonmonotone (HAN) line search with two adaptive regularization schemes; under standard assumptions it proves global convergence and local superlinear convergence for exact and inexact second-order information, and experiments on Lasso, SVM, and logistic Lasso show competitive iteration counts and CPU times.

The work proposes a Nonmonotone Coderivative-based Newton (NCN) method that builds generalized Hessians from Mordukhovich coderivatives of the gradient mapping and combines a Hybrid Adaptive Nonmonotone (HAN) line search with two adaptive regularization schemes; under standard assumptions it proves global convergence and local superlinear convergence for exact and inexact second-order information, and experiments on Lasso, SVM, and logistic Lasso show competitive iteration counts and CPU times.