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This paper introduces a robust procedure for controlling the false discovery rate utilizing empirical likelihood. Traditional approaches assume a normal or parametric distribution as the null distribution. However, it may be challenging to constrain the null distribution within specific parametric models. We focus on the cases where the null distribution may not precisely follow a normal distribution. Multiple testing procedures based on exact normality can lead to misleading outcomes. To address this issue, we adopt the empirical likelihood to estimate the null distribution. Additionally, we introduce the concept of a pilot distribution to establish constraints on the null distribution, which aids in estimating the empirical null distribution. We present a fast algorithm and provide theoretical justification for its efficiency. Furthermore, simulation studies demonstrate that our method outperforms existing approaches in controlling the false discovery rate. We also include examples involving gene expression data and compare the performance of different methods. [ABSTRACT FROM AUTHOR]

Lasso-type models are a popular approach for analysing high-dimensional data. The size of modern data sets can be quite large, so developing efficient algorithms is important. Feature screening techniques have proven to be effective at increasing efficiency, as they allow for considerable dimension reduction during the optimization process. In this paper, we develop an adaptive hybrid screening framework where screening is carried out adaptively along the path of tuning parameter values, reusing previous solutions to reduce heavy screening computations if they fail to significantly reduce dimensionality. We focus on the standard lasso model and sparse logistic model, but the proposed framework is flexible and can be easily extended to different types of lasso models. Through experiments involving a wide variety of simulated and real data sets, we show that the adaptive hybrid methods significantly outperform other state-of-the-art methods, with the greatest speedup occurring in the most challenging scenarios. [ABSTRACT FROM AUTHOR]

This paper devotes to propose a nuclear-norm-based deep survival algorithm (NN-DeepSurv), to study the regression problem of survival data with right censoring. The nuclear norm method is used to impute missing covariates, and it's combined with DeepSurv algorithm to train the regression model. We compare our algorithm with other state-of-the-art methods: Cox proportional hazards regression model (Coxph), Cox proportional hazards model with lasso regression (Cox-lasso), random survival forests (RSF), DeepSurv, and Xgboost algorithm, on 2 simulated datasets and 6 clinical datasets, to show the superiority of the performance of our algorithm. [ABSTRACT FROM AUTHOR]

In the era of big data, structural variation and heterogeneity of high-dimensional data bring a great challenge to statistical modelling and computation. In this paper, wepropose a high-dimensional continuous threshold model for such data and develop a regularized expectile framework with the non-convex SCAD penalty. Due to theexistence of threshold, we have to tackle a non-linear and non-differentiable optimization problem. Inspired by the linear reparameterization technique and LLA strategy,we propose an efficient algorithm to solve this problem. Theoretical analysis and simulation results show that compared with the classical grid-search method, ouralgorithm has considerable computational advantages. Besides, our proposed method also performs well in variable selection, parameter estimation, thresholdidentification and data heterogeneity detection. These results indicate that our proposed method is effective in analysing high-dimensional heterogeneous data. [ABSTRACT FROM AUTHOR]

In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal criteria, D- and A-optimal criteria. For D-optimality, we provide an alternative proof for the monotonic convergence for D-optimal criterion and propose an efficient computational algorithm to obtain the approximate D-optimal design. We further show that the proposed algorithm converges to the D-optimal design and then proves that the approximate D-optimal design converges to the continuous D-optimal design under certain conditions. For A-optimality, we provide an efficient algorithm to obtain approximate A-optimal design and conjecture the monotonicity of the proposed algorithm. Numerical comparisons suggest that the proposed algorithms perform well and they are comparable or superior to some existing algorithms. [ABSTRACT FROM AUTHOR]

In a support vector regression (SVR) model, using the squared ϵ-insensitive loss function makes the optimization problem strictly convex and yields a more concise solution. However, the formulation of L 2 -SVR leads to a quadratic programming which is expensive to solve. This paper reformulates the optimization problem of L 2 -SVR by absorbing the constraints in the objective function, which can be solved efficiently by a majorization-minimization approach, in which an upper bound for the objective function is derived in each iteration which is easier to be minimized. The proposed approach is easy to implement, without requiring any additional computing package other than basic linear algebra operations. Numerical studies on real-world datasets show that, compared to the alternatives, the proposed approach can achieve similar prediction accuracy with substantially higher time efficiency in training. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalized logistic regression model. We propose a Pólya–Gamma sampler algorithm that allows us to sample from the exact posterior distribution, rather than relying on approximations. A simulation study illustrates the flexibility and accuracy of the proposed approach to capture heavy and light tails in binary response data of different dimensions. The algorithm performance is tested on simulated data. Furthermore, the methodology is applied to two different real datasets, where we demonstrate that the Pólya–Gamma sampler provides more precise estimates than the empirical likelihood method, outperforming approximate approaches. [ABSTRACT FROM AUTHOR]

One of the major challenges in modern day statistics is to formulate models and develop inferential procedures to understand the complex multivariate relationships present in high-dimensional datasets. In this paper, we address the issue of model determination for DAGs, with respect to a given ordering of the variables, together with the corresponding parameter estimation. For this, we use a hierarchical mixture prior and develop a Gibbs sampling algorithm to carry out the posterior computations. We first focus on the Gaussian DAG models and calculate the posterior probability of being the edge between two nodes. We then extend our idea to construct a DAG for discrete data under the assumption that the data generated by discretization of the marginal distributions of a latent multivariate Gaussian distribution via a set of predetermined threshold values. Results show that the proposed method has high accuracy. The source code is available at [ABSTRACT FROM AUTHOR]