HiQR: An efficient algorithm for high dimensional quadratic regression with penalties

This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. We propose a novel and efficient algorithm for ridge-penalized quadratic regression that leverages the matrix structures of the regression with interactions. Building on this formulation, we develop an alternating direction method of multipliers (ADMM) framework for penalized quadratic regression with general penalties, including both single and hybrid penalty functions. Our approach greatly simplifies the calculations to basic matrix-based operations, making it appealing in terms of both memory storage and computational complexity.Comment: 18 page

A direct approach for sparse quadratic discriminant analysis

Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however, when the dimensionality is relatively large. To address this, we propose a novel procedure named DA-QDA for QDA in analyzing high-dimensional data. Formulated in a simple and coherent framework, DA-QDA aims to directly estimate the key quantities in the Bayes discriminant function including quadratic interactions and a linear index of the variables for classification. Under appropriate sparsity assumptions, we establish consistency results for estimating the interactions and the linear index, and further demonstrate that the misclassification rate of our procedure converges to the optimal Bayes risk, even when the dimensionality is exponentially high with respect to the sample size. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed for finding interactions, which is much faster than its competitor in the literature. The promising performance of DA-QDA is illustrated via extensive simulation studies and the analysis of four real datasets

Three-Phase Transformer Inrush Current Reduction Strategy Based on Prefluxing and Controlled Switching

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Prognostic and clinicopathological significance of fatty acid synthase in breast cancer: A systematic review and meta-analysis

BackgroundAberrant expression of fatty acid synthase (FASN) was demonstrated in various tumors including breast cancer. A meta-analysis was conducted to investigate the role of FASN in breast cancer development and its potential prognostic significance.MethodsThe Web of Science, PubMed, Embase, and Cochrane Library databases were searched to identify studies that evaluated the relationship between FASN expression and overall survival (OS), relapse-free survival (RFS), and disease-free survival (DFS) of breast cancer patients. To analyze the clinicopathological and prognostic values of FASN expression in breast cancer, pooled hazard ratios (HRs), odds ratios (ORs), and 95% confidence intervals (CIs) were clustered based on random-effects models. To confirm whether the findings were stable and impartial, a sensitivity analysis was performed, and publication bias was estimated. Data were analyzed using Engauge Digitizer version 5.4 and Stata version 15.0.ResultsFive studies involving 855 participants were included. Patients with higher FASN expression did not have a shorter survival period compared to those with lower FASN expression (summary HR: OS, 0.73 [95% CI, 0.41-1.32; P=0.300]; DFS/RFS, 1.65 [95% CI, 0.61-4.43; P=0.323]). However, increased FASN expression was correlated with large tumor size (OR, 2.04; 95% CI, 1.04-4.00; P=0.038), higher human epidermal growth factor receptor 2 (HER2) positivity (OR, 1.53; 95% CI, 1.05-2.23; P=0.028). No significant associations were observed between FASN expression and histological grade (OR, 0.92; 95% CI, 0.41-2.04; P=0.832), Tumor Node Metastasis (TNM) stage (OR, 1.11; 95% CI, 0.49-2.53; P=0.795), nodal metastasis (OR, 1.42; 95% CI, 0.84-2.38; P=0.183), Ki-67 labelling index (OR, 0.64; 95% CI, 0.15-2.63; P=0.533), estrogen receptor (ER) status (OR, 0.90; 95% CI, 0.61-1.32; P=0.586), or progesterone receptor (PR) status (OR, 0.67; 95% CI, 0.29-1.56; P=0.354).ConclusionFASN is associated with HER2 expression and may contribute to tumor growth, but it has no significant impact on the overall prognosis of breast cancer

Interaction of serum vitamin B12 and folate with MTHFR genotypes on risk of ischemic stroke

ObjectiveWe evaluated the interaction of serum folate and vitamin B12 with methylenetetrahydrofolate reductase (MTHFR) C677T genotypes on the risk of first ischemic stroke and on the efficacy of folic acid treatment in prevention of first ischemic stroke.MethodsA total of 20,702 hypertensive adults were randomized to a double-blind treatment of daily enalapril 10 mg and folic acid 0.8 mg or enalapril 10 mg alone. Participants were followed up every 3 months.ResultsMedian values of folate and B12 concentrations at baseline were 8.1 ng/mL and 280.2 pmol/L, respectively. Over a median of 4.5 years, among those not receiving folic acid, participants with baseline serum B12 or serum folate above the median had a significantly lower risk of first ischemic stroke (hazard ratio [HR], 0.74; 95% confidence interval [CI], 0.57-0.96), especially in those with MTHFR 677 CC genotype (wild-type) (HR, 0.49; 95% CI, 0.31-0.78). Folic acid treatment significantly reduced the risk of first ischemic stroke in participants with both folate and B12 below the median (2.3% in enalapril-folic acid group vs 3.6% in enalapril-only group; HR, 0.62; 95% CI, 0.46-0.86), particularly in MTHFR 677 CC carriers (1.6% vs 4.9%; HR, 0.24; 95% CI, 0.11-0.55). However, TT homozygotes responded better with both folate and B12 levels above the median (HR, 0.28; 95% CI, 0.10-0.75).ConclusionsThe risk of first ischemic stroke was significantly higher in hypertensive patients with low levels of both folate and B12. Effect of folic acid treatment was greatest in patients with low folate and B12 with the CC genotype, and with high folate and B12 with the TT genotype