Statistics and Computing最新文献_第8页

Screen then select: a strategy for correlated predictors in high-dimensional quantile regression 先筛选后选择：高维量子回归中相关预测因子的策略

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-04-08 DOI: 10.1007/s11222-024-10424-6

Xuejun Jiang, Yakun Liang, Haofeng Wang

{"title":"Screen then select: a strategy for correlated predictors in high-dimensional quantile regression","authors":"Xuejun Jiang, Yakun Liang, Haofeng Wang","doi":"10.1007/s11222-024-10424-6","DOIUrl":"https://doi.org/10.1007/s11222-024-10424-6","url":null,"abstract":"<p>Strong correlation among predictors and heavy-tailed noises pose a great challenge in the analysis of ultra-high dimensional data. Such challenge leads to an increase in the computation time for discovering active variables and a decrease in selection accuracy. To address this issue, we propose an innovative two-stage screen-then-select approach and its derivative procedure based on a robust quantile regression with sparsity assumption. This approach initially screens important features by ranking quantile ridge estimation and subsequently employs a likelihood-based post-screening selection strategy to refine variable selection. Additionally, we conduct an internal competition mechanism along the greedy search path to enhance the robustness of algorithm against the design dependence. Our methods are simple to implement and possess numerous desirable properties from theoretical and computational standpoints. Theoretically, we establish the strong consistency of feature selection for the proposed methods under some regularity conditions. In empirical studies, we assess the finite sample performance of our methods by comparing them with utility screening approaches and existing penalized quantile regression methods. Furthermore, we apply our methods to identify genes associated with anticancer drug sensitivities for practical guidance.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

R-VGAL: a sequential variational Bayes algorithm for generalised linear mixed models R-VGAL：广义线性混合模型的顺序变异贝叶斯算法

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-04-06 DOI: 10.1007/s11222-024-10422-8

Bao Anh Vu, David Gunawan, Andrew Zammit-Mangion

{"title":"R-VGAL: a sequential variational Bayes algorithm for generalised linear mixed models","authors":"Bao Anh Vu, David Gunawan, Andrew Zammit-Mangion","doi":"10.1007/s11222-024-10422-8","DOIUrl":"https://doi.org/10.1007/s11222-024-10422-8","url":null,"abstract":"<p>Models with random effects, such as generalised linear mixed models (GLMMs), are often used for analysing clustered data. Parameter inference with these models is difficult because of the presence of cluster-specific random effects, which must be integrated out when evaluating the likelihood function. Here, we propose a sequential variational Bayes algorithm, called Recursive Variational Gaussian Approximation for Latent variable models (R-VGAL), for estimating parameters in GLMMs. The R-VGAL algorithm operates on the data sequentially, requires only a single pass through the data, and can provide parameter updates as new data are collected without the need of re-processing the previous data. At each update, the R-VGAL algorithm requires the gradient and Hessian of a “partial” log-likelihood function evaluated at the new observation, which are generally not available in closed form for GLMMs. To circumvent this issue, we propose using an importance-sampling-based approach for estimating the gradient and Hessian via Fisher’s and Louis’ identities. We find that R-VGAL can be unstable when traversing the first few data points, but that this issue can be mitigated by introducing a damping factor in the initial steps of the algorithm. Through illustrations on both simulated and real datasets, we show that R-VGAL provides good approximations to posterior distributions, that it can be made robust through damping, and that it is computationally efficient.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Automated generation of initial points for adaptive rejection sampling of log-concave distributions 自动生成对数凹分布自适应剔除采样的初始点

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-04-05 DOI: 10.1007/s11222-024-10425-5

Jonathan James

引用次数: 0

Parsimonious ultrametric Gaussian mixture models 解析超参量高斯混合物模型

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-04-01 DOI: 10.1007/s11222-024-10405-9

Carlo Cavicchia, Maurizio Vichi, Giorgia Zaccaria

引用次数: 0

Stochastic three-term conjugate gradient method with variance technique for non-convex learning 用于非凸学习的随机三项共轭梯度法与方差技术

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-27 DOI: 10.1007/s11222-024-10409-5

Chen Ouyang, Chenkaixiang Lu, Xiong Zhao, Ruping Huang, Gonglin Yuan, Yiyan Jiang

{"title":"Stochastic three-term conjugate gradient method with variance technique for non-convex learning","authors":"Chen Ouyang, Chenkaixiang Lu, Xiong Zhao, Ruping Huang, Gonglin Yuan, Yiyan Jiang","doi":"10.1007/s11222-024-10409-5","DOIUrl":"https://doi.org/10.1007/s11222-024-10409-5","url":null,"abstract":"<p>In the training process of machine learning, the minimization of the empirical risk loss function is often used to measure the difference between the model’s predicted value and the real value. Stochastic gradient descent is very popular for this type of optimization problem, but converges slowly in theoretical analysis. To solve this problem, there are already many algorithms with variance reduction techniques, such as SVRG, SAG, SAGA, etc. Some scholars apply the conjugate gradient method in traditional optimization to these algorithms, such as CGVR, SCGA, SCGN, etc., which can basically achieve linear convergence speed, but these conclusions often need to be established under some relatively strong assumptions. In traditional optimization, the conjugate gradient method often requires the use of line search techniques to achieve good experimental results. In a sense, line search embodies some properties of the conjugate methods. Taking inspiration from this, we apply the modified three-term conjugate gradient method and line search technique to machine learning. In our theoretical analysis, we obtain the same convergence rate as SCGA under weaker conditional assumptions. We also test the convergence of our algorithm using two non-convex machine learning models.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Novel sampling method for the von Mises–Fisher distribution von Mises-Fisher 分布的新型抽样方法

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-26 DOI: 10.1007/s11222-024-10419-3

引用次数: 0

Generalized spherical principal component analysis 广义球形主成分分析

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-23 DOI: 10.1007/s11222-024-10413-9

Sarah Leyder, Jakob Raymaekers, Tim Verdonck

引用次数: 0

Variable selection using axis-aligned random projections for partial least-squares regression 利用轴对齐随机投影为部分最小二乘回归选择变量

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-23 DOI: 10.1007/s11222-024-10417-5

{"title":"Variable selection using axis-aligned random projections for partial least-squares regression","authors":"","doi":"10.1007/s11222-024-10417-5","DOIUrl":"https://doi.org/10.1007/s11222-024-10417-5","url":null,"abstract":"<h3>Abstract</h3> <p>In high-dimensional data modeling, variable selection plays a crucial role in improving predictive accuracy and enhancing model interpretability through sparse representation. Unfortunately, certain variable selection methods encounter challenges such as insufficient model sparsity, high computational overhead, and difficulties in handling large-scale data. Recently, axis-aligned random projection techniques have been applied to address these issues by selecting variables. However, these techniques have seen limited application in handling complex data within the regression framework. In this study, we propose a novel method, sparse partial least squares via axis-aligned random projection, designed for the analysis of high-dimensional data. Initially, axis-aligned random projection is utilized to obtain a sparse loading vector, significantly reducing computational complexity. Subsequently, partial least squares regression is conducted within the subspace of the top-ranked significant variables. The submatrices are iteratively updated until an optimal sparse partial least squares model is achieved. Comparative analysis with some state-of-the-art high-dimensional regression methods demonstrates that the proposed method exhibits superior predictive performance. To illustrate its effectiveness, we apply the method to four cases, including one simulated dataset and three real-world datasets. The results show the proposed method’s ability to identify important variables in all four cases.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An expectile computation cookbook 预期计算食谱

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-23 DOI: 10.1007/s11222-024-10403-x

引用次数: 0

Simultaneous estimation and variable selection for a non-crossing multiple quantile regression using deep neural networks 利用深度神经网络实现非交叉多元量级回归的同步估计和变量选择

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-22 DOI: 10.1007/s11222-024-10418-4

Jungmin Shin, Seunghyun Gwak, Seung Jun Shin, Sungwan Bang

引用次数: 0