Statistics and Computing最新文献_第10页

Total effects with constrained features 有限制特征的总效果

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-05 DOI: 10.1007/s11222-024-10398-5

{"title":"Total effects with constrained features","authors":"","doi":"10.1007/s11222-024-10398-5","DOIUrl":"https://doi.org/10.1007/s11222-024-10398-5","url":null,"abstract":"<h3>Abstract</h3> Recent studies have emphasized the connection between machine learning feature importance measures and total order sensitivity indices (total effects, henceforth). Feature correlations and the need to avoid unrestricted permutations make the estimation of these indices challenging. Additionally, there is no established theory or approach for non-Cartesian domains. We propose four alternative strategies for computing total effects that account for both dependent and constrained features. Our first approach involves a generalized winding stairs design combined with the Knothe-Rosenblatt transformation. This approach, while applicable to a wide family of input dependencies, becomes impractical when inputs are physically constrained. Our second approach is a U-statistic that combines the Jansen estimator with a weighting factor. The U-statistic framework allows the derivation of a central limit theorem for this estimator. However, this design is computationally intensive. Then, our third approach uses derangements to significantly reduce computational burden. We prove consistency and central limit theorems for these estimators as well. Our fourth approach is based on a nearest-neighbour intuition and it further reduces computational burden. We test these estimators through a series of increasingly complex computational experiments with features constrained on compact and connected domains (circle, simplex), non-compact and non-connected domains (Sierpinski gaskets), we provide comparisons with machine learning approaches and conclude with an application to a realistic simulator.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"8 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140035815","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

Estimation of regime-switching diffusions via Fourier transforms 通过傅立叶变换估计制度切换扩散

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-03-05 DOI: 10.1007/s11222-024-10397-6

Thomas Lux

引用次数: 0

High-dimensional sparse single–index regression via Hilbert–Schmidt independence criterion 通过希尔伯特-施密特独立性准则实现高维稀疏单索引回归

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-02-27 DOI: 10.1007/s11222-024-10399-4

Xin Chen, Chang Deng, Shuaida He, Runxiong Wu, Jia Zhang

{"title":"High-dimensional sparse single–index regression via Hilbert–Schmidt independence criterion","authors":"Xin Chen, Chang Deng, Shuaida He, Runxiong Wu, Jia Zhang","doi":"10.1007/s11222-024-10399-4","DOIUrl":"https://doi.org/10.1007/s11222-024-10399-4","url":null,"abstract":"Hilbert-Schmidt Independence Criterion (HSIC) has recently been introduced to the field of single-index models to estimate the directions. Compared with other well-established methods, the HSIC based method requires relatively weak conditions. However, its performance has not yet been studied in the prevalent high-dimensional scenarios, where the number of covariates can be much larger than the sample size. In this article, based on HSIC, we propose to estimate the possibly sparse directions in the high-dimensional single-index models through a parameter reformulation. Our approach estimates the subspace of the direction directly and performs variable selection simultaneously. Due to the non-convexity of the objective function and the complexity of the constraints, a majorize-minimize algorithm together with the linearized alternating direction method of multipliers is developed to solve the optimization problem. Since it does not involve the inverse of the covariance matrix, the algorithm can naturally handle large p small n scenarios. Through extensive simulation studies and a real data analysis, we show that our proposal is efficient and effective in the high-dimensional settings. The (texttt {Matlab}) codes for this method are available online.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140005016","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

Improvements on scalable stochastic Bayesian inference methods for multivariate Hawkes process 改进多变量霍克斯过程的可扩展随机贝叶斯推理方法

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-02-27 DOI: 10.1007/s11222-024-10392-x

Alex Ziyu Jiang, Abel Rodriguez

引用次数: 0

Maximum likelihood estimation of log-concave densities on tree space 树空间对数凹密度的最大似然估计

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-02-23 DOI: 10.1007/s11222-024-10400-0

Yuki Takazawa, Tomonari Sei

{"title":"Maximum likelihood estimation of log-concave densities on tree space","authors":"Yuki Takazawa, Tomonari Sei","doi":"10.1007/s11222-024-10400-0","DOIUrl":"https://doi.org/10.1007/s11222-024-10400-0","url":null,"abstract":"Phylogenetic trees are key data objects in biology, and the method of phylogenetic reconstruction has been highly developed. The space of phylogenetic trees is a nonpositively curved metric space. Recently, statistical methods to analyze samples of trees on this space are being developed utilizing this property. Meanwhile, in Euclidean space, the log-concave maximum likelihood method has emerged as a new nonparametric method for probability density estimation. In this paper, we derive a sufficient condition for the existence and uniqueness of the log-concave maximum likelihood estimator on tree space. We also propose an estimation algorithm for one and two dimensions. Since various factors affect the inferred trees, it is difficult to specify the distribution of a sample of trees. The class of log-concave densities is nonparametric, and yet the estimation can be conducted by the maximum likelihood method without selecting hyperparameters. We compare the estimation performance with a previously developed kernel density estimator numerically. In our examples where the true density is log-concave, we demonstrate that our estimator has a smaller integrated squared error when the sample size is large. We also conduct numerical experiments of clustering using the Expectation-Maximization algorithm and compare the results with k-means++ clustering using Fréchet mean.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"10 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139947601","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

Do applied statisticians prefer more randomness or less? Bootstrap or Jackknife? 应用统计学家更喜欢随机性多一些还是少一些？Bootstrap 还是 Jackknife？

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-02-22 DOI: 10.1007/s11222-024-10388-7

Yannis G. Yatracos

{"title":"Do applied statisticians prefer more randomness or less? Bootstrap or Jackknife?","authors":"Yannis G. Yatracos","doi":"10.1007/s11222-024-10388-7","DOIUrl":"https://doi.org/10.1007/s11222-024-10388-7","url":null,"abstract":"Bootstrap and Jackknife estimates, (T_{n,B}^*) and (T_{n,J},) respectively, of a population parameter (theta ) are both used in statistical computations; n is the sample size, B is the number of Bootstrap samples. For any (n_0) and (B_0,) Bootstrap samples do not add new information about (theta ) being observations from the original sample and when (B_0<infty ,) (T_{n_0,B_0}^*) includes also resampling variability, an additional source of uncertainty not affecting (T_{n_0, J}.) These are neglected in theoretical papers with results for the utopian (T_{n, infty }^*, ) that do not hold for (B<infty .) The consequence is that (T^*_{n_0, B_0}) is expected to have larger mean squared error (MSE) than (T_{n_0,J},) namely (T_{n_0,B_0}^*) is inadmissible. The amount of inadmissibility may be very large when populations’ parameters, e.g. the variance, are unbounded and/or with big data. A palliating remedy is increasing B, the larger the better, but the MSEs ordering remains unchanged for (B<infty .) This is confirmed theoretically when (theta ) is the mean of a population, and is observed in the estimated total MSE for linear regression coefficients. In the latter, the chance the estimated total MSE with (T_{n,B}^*) improves that with (T_{n,J}) decreases to 0 as B increases.\u0000","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"54 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139947598","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

Forward stability and model path selection 前向稳定性和模型路径选择

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-02-20 DOI: 10.1007/s11222-024-10395-8

Nicholas Kissel, Lucas Mentch

{"title":"Forward stability and model path selection","authors":"Nicholas Kissel, Lucas Mentch","doi":"10.1007/s11222-024-10395-8","DOIUrl":"https://doi.org/10.1007/s11222-024-10395-8","url":null,"abstract":"Most scientific publications follow the familiar recipe of (i) obtain data, (ii) fit a model, and (iii) comment on the scientific relevance of the effects of particular covariates in that model. This approach, however, ignores the fact that there may exist a multitude of similarly-accurate models in which the implied effects of individual covariates may be vastly different. This problem of finding an entire collection of plausible models has also received relatively little attention in the statistics community, with nearly all of the proposed methodologies being narrowly tailored to a particular model class and/or requiring an exhaustive search over all possible models, making them largely infeasible in the current big data era. This work develops the idea of forward stability and proposes a novel, computationally-efficient approach to finding collections of accurate models we refer to as model path selection (MPS). MPS builds up a plausible model collection via a forward selection approach and is entirely agnostic to the model class and loss function employed. The resulting model collection can be displayed in a simple and intuitive graphical fashion, easily allowing practitioners to visualize whether some covariates can be swapped for others with minimal loss.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"41 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139927157","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

The minimum covariance determinant estimator for interval-valued data 区间值数据的最小协方差行列式估计器

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-02-17 DOI: 10.1007/s11222-024-10386-9

Wan Tian, Zhongfeng Qin

引用次数: 0

Clustering longitudinal ordinal data via finite mixture of matrix-variate distributions 通过矩阵变量分布的有限混合物对纵向序数数据进行聚类

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-02-17 DOI: 10.1007/s11222-024-10390-z

Francesco Amato, Julien Jacques, Isabelle Prim-Allaz

引用次数: 0

Enmsp: an elastic-net multi-step screening procedure for high-dimensional regression Enmsp：用于高维回归的弹性网多步筛选程序