Significance: Best-subset selection is a benchmark optimization problem in statistics and machine learning. Although many optimization strategies and algorithms have been proposed to solve this problem, our splicing algorithm, under reasonable conditions, enjoys the following properties simultaneously with high probability: 1) its computational complexity is polynomial; 2) it can recover the true subset; and 3) its solution is globally optimal.

Treating patients with COVID-19 is expensive, thus it is essential to identify factors on admission associated with hospital length of stay (LOS) and provide a risk assessment for clinical treatment. To address this, we conduct a retrospective study, which involved patients with laboratory-confirmed COVID-19 infection in Hefei, China and being discharged between January 20 2020 and March 16 2020. Demographic information, clinical treatment, and laboratory data for the participants were extracted from medical records. A prolonged LOS was defined as equal to or greater than the median length of hospitable stay. The median LOS for the 75 patients was 17 days (IQR 13–22). We used univariable and multivariable logistic regressions to explore the risk factors associated with a prolonged hospital LOS. Adjusted odds ratios (aORs) and 95% confidence intervals (CIs) were estimated. The median age of the 75 patients was 47 years. Approximately 75% of the patients had mild or general disease. The univariate logistic regression model showed that female sex and having a fever on admission were significantly associated with longer duration of hospitalization. The multivariate logistic regression model enhances these associations. Odds of a prolonged LOS were associated with male sex (aOR 0.19, 95% CI 0.05–0.63, p = 0.01), having fever on admission (aOR 8.27, 95% CI 1.47–72.16, p = 0.028) and pre-existing chronic kidney or liver disease (aOR 13.73 95% CI 1.95–145.4, p = 0.015) as well as each 1-unit increase in creatinine level (aOR 0.94, 95% CI 0.9–0.98, p = 0.007). We also found that a prolonged LOS was associated with increased creatinine levels in patients with chronic kidney or liver disease (p < 0.001). In conclusion, female sex, fever, chronic kidney or liver disease before admission and increasing creatinine levels were associated with prolonged LOS in patients with COVID-19.

Non-negative matrix factorization, which decomposes the input non-negative matrix into product of two non-negative matrices, has been widely used in the neuroimaging field due to its flexible interpretability with non-negativity property. Nowadays, especially in the neuroimaging field, it is common to have at least thousands of voxels while the sample size is only hundreds. The non-negative matrix factorization encounters both computational and theoretical challenge with such high-dimensional data, i.e., there is no guarantee for a sparse and part-based representation of data. To this end, we introduce a co-sparse non-negative matrix factorization method to high-dimensional data by simultaneously imposing sparsity in both two decomposed matrices. Instead of adding some sparsity induced penalty such as l₁ norm, the proposed method directly controls the number of non-zero elements, which can avoid the bias issues and thus yield more accurate results. We developed an alternative primal-dual active set algorithm to derive the co-sparse estimator in a computationally efficient way. The simulation studies showed that our method achieved better performance than the state-of-art methods in detecting the basis matrix and recovering signals, especially under the high-dimensional scenario. In empirical experiments with two neuroimaging data, the proposed method successfully detected difference between Alzheimer's patients and normal person in several brain regions, which suggests that our method may be a valuable toolbox for neuroimaging studies.

Multinomial logistic regression is a useful model for predicting the probabilities of multiclass outcomes. Because of the complexity and high dimensionality of some data, it is challenging to fit a valid model with high accuracy and interpretability. We propose a novel sparse reduced-rank multinomial logistic regression model to jointly select variables and reduce the dimension via a nonconvex row constraint. We develop a block-wise iterative algorithm with a majorizing surrogate function to efficiently solve the optimization problem. From an algorithmic aspect, we show that the output estimator enjoys consistency in estimation and sparsity recovery even in a high-dimensional setting. The finite sample performance of the proposed method is investigated via simulation studies and two real image data sets. The results show that our proposal has competitive performance in both estimation accuracy and computation time. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71991474, 12171449, 11801540, and 12071494] and the Natural Science Foundation of Anhui Province [Grant BJ2040170017]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0132 .

Background: Although an increasing number of common variants contributing to Alzheimer’s disease (AD) are uncovered by genome-wide association studies, they can only explain less than half of the heritability of AD. Rare variant association studies (RVAS) has become an increasingly important area to explain the risk or trait variability of AD. Method: To investigate the potential rare variants that cause AD, we screened 70,209 rare variants from two cohorts of a 175 AD cohort and a 214 cognitively normal cohort from the Alzheimer’s Disease Neuroimaging Initiative database. MIRARE, a novel RVAS method, was performed on 232 non-synonymous variants selected by ANNOVAR annotation. Molecular docking and molecular dynamics (MD) simulation were adopted to verify the interaction between the chosen functional variants and BACE1. Results: MIRAGE analysis revealed significant associations between AD and six potential pathogenic genes, including PREX2, FLG, DHX16, NID2, ZnF585B and ZnF875. Only interactions between FLG (including wild type and rs3120654(SER742TYR)) and BACE1 were verified by molecular docking and MD simulation. The interaction of FLG(SER742TYR) with BACE1 was greater than that of wildtype FLG with BACE1. Conclusions: According to the literature search, bio-informatics analysis, and molecular docking and MD simulation, we find non-synonymous rare variants in six genes, especially FLG(rs3120654), that may play key roles in AD.