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In this article, we study the sharp oracle bounds for Slope and Lasso and generalize the results in Bellec, Lecué, and Tsybakov (2018) to allow the case that the parameter vector is not exactly sparse and obtain the optimal bounds for ℓq estimation errors with 1 ≤ q ≤ ∞ by using some extended Restricted Eigenvalue-type conditions. [ABSTRACT FROM AUTHOR]

The difference-based partially linear model is an appropriate regression model when both linear and nonlinear predictors are present in the data. However, when we want to optimize the weights using the difference-based method, the problem of variable selection can be difficult since low-variance predictors present a challenge. Therefore, this study aims to establish a novel methodology based on marginal theory to tackle such mixed relationships successfully, emphasizing variable selection in low dimensions. We suggest using a marginalized LASSO estimator with a penalty term that is not as severe and related to the difference order. As part of our numerical analysis of small sample performance, we undertake comprehensive simulation experiments to numerically demonstrate the strength of our proposed technique in estimation and prediction compared to the LASSO under a low-dimensional setup. This is done so that we can numerically demonstrate the strength of our proposed method in estimation and prediction. The bootstrapped method is utilized to evaluate how well our proposed prediction method performs when examining the King House dataset. [ABSTRACT FROM AUTHOR]

Smart precision farming leverages IoT, cloud computing, and big data to optimize agricultural productivity, lower costs, and promote sustainability through digitalization and intelligent methodologies. However, it faces challenges such as managing complex variables, addressing multicollinearity, handling outliers, ensuring model robustness, and enhancing accuracy, particularly with small to medium-sized datasets. To overcome these obstacles, reducing retraining time and resolving the complexity issue is essential for improving the machine learning algorithm's performance, scalability, and efficiency, especially when dealing with large or high-dimensional datasets. In a recent study involving 435 drying parameters and 1,914 observations, two machine learning algorithms - Ridge and Lasso - were employed to analyze and compare the impact of two variable selection techniques, specifically the regularization methods Ridge and Lasso, before and after addressing heterogeneity in highly ranked variables (50, 100, 150, 200, 250, 300). Additionally, robust regression methods such as S, M, MM, M-Hampel, M-Huber, M-Tukey, MM-bisquare, MM-Hampel, and MM-Huber were applied. The results demonstrated that the robust methods, when applied to Ridge and Lasso, achieved the highest efficiency, with the smallest values for MAPE, MSE, SSE, and the highest R2 values, both before and after accounting for heterogeneity. As a result of the study, the best models are the Ridge model with the MM bisquares before heterogeneity, the Ridge model with the MM method after heterogeneity, and the Lasso model with the MM method before heterogeneity and the Lasso model with MM Hampel after heterogeneity. [ABSTRACT FROM AUTHOR]

Objective: To develop and validate prediction models for estimating the activity index (AI) of kidney histopathology in lupus nephritis (LN) using clinical and laboratory data. Methods: This study used single-center data from patients with kidney biopsy-confirmed LN between January 2012 and March 2022. The development and validation datasets were temporally cut. We discriminated AI > 10 and ≤ 10 as high and mild/moderate activity status, respectively. We constructed four models for AI: Model 1 included demographic information; Model 2 additionally incorporated data of systemic conditions; Model 3 further included kidney-specific conditions; and Model 4 included all the aforementioned predictors. Logistic regression was employed in Models 1 to 3, while Model 4 utilized least absolute shrinkage and selection operator for predictor selection and model building. Internal validation was performed using 1000 bootstrap resampling, while external validation was performed in the temporal validation dataset. Both calibration and discrimination metrics were evaluated. Results: There were 160 patients in the development dataset and 70 patients in the validation dataset. In the temporal validation, all the models achieved acceptable calibration and excellent discrimination. Model 2 which contained relatively fewer predictors achieved the highest area under the receiver operator characteristic curve of 0.86 (95% confidence interval 0.76 to 0.94). Conclusion: Our Model 2 incorporating demographic and systemic indicators exhibited good performance in estimating the AI of LN. We thus provide a simple yet effective algorithm to predict AI in patients with LN, potentially aiding clinicians in non-invasively assessing disease activity and guiding treatment decisions. Key Points • We developed a prediction model (Model 2) incorporating demographic and systemic indicators to predict AI in patients with LN. • The prediction model can aid clinicians in noninvasively assessing disease activity and guiding treatment decisions. [ABSTRACT FROM AUTHOR]

State equations (SEs) were first introduced in the approximate message passing process to describe the mean square error in compressed sensing. Since then a set of state equations has appeared in studies of logistic regression, robust estimator, and other high-dimensional statistics problems. Recently, a convex Gaussian min-max theorem approach was proposed to study high-dimensional statistic problems accompanying with another set of different state equations. This article provides a uniform viewpoint on these methods and shows the equivalence of their reduction forms, which causes that the resulting SEs are essentially equivalent and can be converted into the same expression through parameter transformations. Combining these results, we show that these different state equations are derived from several equivalent reduction forms. We believe that this equivalence will shed light on discovering a deeper structure in high-dimensional statistics. [ABSTRACT FROM AUTHOR]

One of the central components of cognitive diagnostic assessment is the Q-matrix, which is an essential loading indicator matrix and is typically constructed by subject matter experts. Nonetheless, to a large extent, the construction of Q-matrix remains a subjective process and might lead to misspecifications. Many researchers have recognized the importance of estimating or validating the Q-matrix, but most of them focus on the conditions of relatively large sample sizes. This article aims to explore Q-matrix validation possibilities under small sample conditions and uses regularized methods to validate the Q-matrix based on the compensatory reparametrized unified model and generalized deterministic inputs, noisy "and" gate models. Simulation studies were conducted to evaluate the viability of the modified least absolute shrinkage and selection operator (Lasso) and modified smoothly clipped absolute deviation (SCAD) methods, comparing them with existing methods. Results show that the modified Lasso and the modified SCAD methods outperform the stepwise, Hull, and MLR-B methods in general, especially under the conditions of small sample sizes. While good recovery in all small sample size conditions is not guaranteed, the modified methods demonstrate advantages across various item quality conditions. Also, a real data set is analyzed to illustrate the application of the modified methods. [ABSTRACT FROM AUTHOR]

In the context of time series modeling, historical data influences the current period, but its impact diminishes rapidly. We propose leveraging the transfer learning technique to harness historical data for forecasting and enhance prediction accuracy. Our method comprises a two-step process. Initially, we cluster the data into auxiliary and target groups, while the target group indicates the current period, and the auxiliary groups contain the past periods. Subsequently, we estimate the current period data by incorporating historical periods using two lasso penalty terms. Our method allows for different periods to influence the current period. Under mild conditions, we demonstrate that the estimator enjoys asymptotic properties, including selection and estimation consistency. We apply the proposed method to index tracking in empirical analysis and conduct a comparative evaluation against three alternative methods. Results indicate that our method outperforms others in prediction accuracy and stability in subset selection. [ABSTRACT FROM AUTHOR]

Abstract.The penalized models have been established to be necessary for classifying the emerging complex, high-dimensional datasets. One of these penalized models is the “modified elastic-net” (M-Enet). The special cases of M-Enet (ridge, bridge, Lasso, and elastic-net) can be produced based on its penalty function. By using the fact that the Fisher-Scoring (FS) and Newton-Raphson (NR) algorithms use different approaches to solve numerical problems but are the same in the canonical link, in order to ease implementation, we developed an FS algorithm for the computation of the parameter estimates of the M-Enet. A simulation study of the microbiome as complex, high-dimensional data shows that each special case of the M-Enet penalty function has superiority in the sense of model accuracy, sensitivity, and feature selection technique. A comparison study is performed between the classification of binary responses using M-Enet as a parametric method and the classification tree via “GUIDE” as a non parametric method. The statistical analysis of the numerical results reveals that the special cases of M-Enet models outperform other M-Enet models and GUIDE in terms of average prediction accuracy and sensitivity, with p-values of 0. 0362 and 0. 0214, respectively. Consequently, these models exhibit superior classification performance compared to other classifier models. [ABSTRACT FROM AUTHOR]

Introduction: Melanoma (MM), the deadliest form of skin cancer, originates from melanocytes. Despite advances in immunotherapy that have somewhat improved the prognosis for MM patients, high levels of resistance to treatment continue to result in poor clinical outcomes. Identifying novel biomarkers and therapeutic targets is critical for improving the prognosis and treatment of MM. Methods: In this study, we analyzed the expression patterns of WNT signaling pathway genes in MM and explored their potential mechanisms. Using Cox regression analysis, we identified 19 prognostic-related genes. Consistency clustering was performed to evaluate the potential of these genes as classifiers for prognosis. The Least Absolute Shrinkage and Selection Operator (LASSO) algorithm was then applied to refine the gene set and construct a 13-gene prognostic model. We validated the model at multiple time points to assess its predictive performance. Additionally, correlation analyses were performed to investigate the relationships between key genes and processes, including epithelial-to-mesenchymal transition (EMT) and immune responses. Results: We identified that CSNK1E and RAC3 were significantly positively correlated with the EMT process, with CSNK1E showing a similar expression trend to EMT-related genes. Both genes were also negatively correlated with multiple immune cell types and immune checkpoint genes. The 13-gene prognostic model demonstrated excellent predictive performance in MM prognosis. Pan-cancer analysis further revealed heterogeneous expression patterns and prognostic potential of CSNK1E across various cancers. Wet experiments confirmed that CSNK1E promotes MM cell proliferation, invasion, and migration, and enhances malignant progression through the TGF-β signaling pathway. Discussion: Our findings suggest that CSNK1E plays a crucial role in MM progression and could serve as a potential therapeutic target. The WNT and TGF-β pathways may work synergistically in regulating the EMT process in MM, highlighting their potential as novel therapeutic targets. These insights may contribute to the development of more effective treatments for MM, particularly for overcoming resistance to current therapies. [ABSTRACT FROM AUTHOR]

Background: Sarcopenia is a prevalent condition associated with aging. Inflammation and pyroptosis significantly contribute to sarcopenia. Methods: Two sarcopenia-related datasets (GSE111016 and GSE167186) were obtained from the Gene Expression Omnibus (GEO), followed by batch effect removal post-merger. The "limma" R package was utilized to identify differentially expressed genes (DEGs). Subsequently, LASSO analysis was conducted on inflammation and pyroptosis-related genes (IPRGs), resulting in the identification of six hub IPRGs. A novel skeletal muscle aging model was developed and validated using an independent dataset. Additionally, Gene Ontology (GO) enrichment analysis was performed on DEGs, along with Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis and gene set enrichment analysis (GSEA). ssGSEA was employed to assess differences in immune cell proportions between healthy muscle groups in older versus younger adults. The expression levels of the six core IPRGs were quantified via qRT-PCR. Results: A total of 44 elderly samples and 68 young healthy samples were analyzed for DEGs. Compared to young healthy muscle tissue, T cell infiltration levels in aged muscle tissue were significantly reduced, while mast cell and monocyte infiltration levels were relatively elevated. A new diagnostic screening model for sarcopenia based on the six IPRGs demonstrated high predictive efficiency (AUC = 0.871). qRT-PCR results indicated that the expression trends of these six IPRGs aligned with those observed in the database. Conclusion: Six biomarkers—BTG2, FOXO3, AQP9, GPC3, CYCS, and SCN1B—were identified alongside a diagnostic model that offers a novel approach for early diagnosis of sarcopenia. [ABSTRACT FROM AUTHOR]

In tree-based algorithms like random forest and deep forest, due to the presence of numerous inefficient trees and forests in the model, the computational load increases and the efficiency decreases. To address this issue, in the present paper, a model called Automatic Deep Forest Shrinkage (ADeFS) is proposed based on shrinkage techniques. The purpose of this model is to reduce the number of trees, enhance the efficiency of the gcforest, and reduce computational load. The proposed model comprises four steps. The first step is multi-grained scanning, which carries out a sliding window strategy to scan the input data and extract the relations between features. The second step is cascade forest, which is structured layer-by-layer with a number of forests consisting of random forest (RF) and completely random forest (CRF) within each layer. In the third step, which is the innovation of this paper, shrinkage techniques such as LASSO and elastic net (EN) are employed to decrease the number of trees in the last layer of the previous step, thereby decreasing the computational load, and improving the gcforest performance. Among several shrinkage techniques, elastic net (EN) provides better performance. Finally, in the last step, the simple average ensemble method is employed to combine the remaining trees. The proposed model is evaluated by Monte Carlo simulation and three real datasets. Findings demonstrate the superior performance of the proposed ADeFS-EN model over both gcforest and RF, as well as the combination of RF with shrinkage techniques. [ABSTRACT FROM AUTHOR]

This article gives large sample theory for the one component partial least squares estimator, including some hypothesis tests for high dimensional data, under much weaker conditions than those in the literature. Simple theory is also given for some data splitting estimators and the marginal maximum likelihood estimators. It is shown that lasso, one component partial least squares, and ordinary least squares often estimate different population multiple linear regression models. The article also proves that there are often many valid population models for regression methods such as binary regression. [ABSTRACT FROM AUTHOR]