降维空间中用于联合二元逻辑回归的MELODIC族

Confidence Bands for the Logistic and Probit Regression Models Over Intervals

This article presents methods for the construction of two-sided and one-sided simultaneous hyperbolic bands for the logistic and probit regression models when the predictor variable is restricted to a given interval. The bands are constructed based on the asymptotic properties of the maximum likelihood estimators. Past articles have considered building two-sided asymptotic confidence bands for the logistic model, such as Piegorsch and Casella (1988). However, the confidence bands given by Piegorsch and Casella are conservative under a single interval restriction, and it is shown in this articl…

联合核范数和ℓ1正则化的逻辑矩阵回归及其在脑成像中的应用

Joint Nuclear and $\ell_1$ Regularization for Logistic Matrix Regression with Applications to Brain Imaging

提出一种结合核范数和ℓ1惩罚的凸优化框架，用于逻辑标量-矩阵回归，以同时实现系数矩阵的低秩和稀疏结构，并应用于脑成像数据分析。

Logistic Biplots for Ordinal Data with an Application to Job Satisfaction of Doctorate Degree Holders in Spain

Biplot Methods allow for the simultaneous representation of individuals and variables of a data matrix. For Binary or Nominal data, Logistic biplots have been recently developed to extend the classical linear representations for continuous data. When data are ordinal, linear, binary or nominal logistic biplots are not adequate and techniques as Categorical Principal Component Analysis (CATPCA) or Item Response Theory (IRT) for ordinal items should be used instead. In this paper we extend the Biplot to ordinal data. The resulting method is termed Ordinal Logistic Biplot (OLB). Row scores are co…

Robust Parametric Classification and Variable Selection by a Minimum Distance Criterion

We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, that is shrink towards the zero vector. Thus, using LASSO-like penalties to perform variable selection in the presence of outliers can result in missed detections of relevant covariates. We show that by choosing a minimum distance criterion together with an Elastic Net penalty, we…

高维Logistic回归中的稳健自适应Lasso

Robust adaptive Lasso in high-dimensional logistic regression

针对高维惩罚Logistic回归中似然损失对数据污染敏感的问题，提出基于密度幂散度损失与自适应加权LASSO的稳健估计量，推导了其稳健性与渐近性质，并在癌症分类真实数据中验证了其基因选择与分类的准确性和稳健性。

Logistic Network Regression for Scalable Analysis of Networks with Joint Edge/Vertex Dynamics

Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Though early studies of such processes were primarily descriptive, recent work on this topic has increasingly turned to formal statistical models. While showing great promise, many of these modern dynamic models are computationally intensive and scale very poorly in the size of the network under study and/or the number of time points considered. Likewise, currently employed models focus on edge dynamics, with little support for endog…

基于逻辑回归和图像序列拓扑分析的贝叶斯变点检测

Bayesian changepoint detection via logistic regression and the topological analysis of image series

本文提出BCLR方法，将贝叶斯变点检测与逻辑回归结合，利用Pólya-gamma增广的Gibbs采样进行推断，并结合拓扑特征嵌入有效检测图像序列中的拓扑变化。

多变化点分析的通用贝叶斯方法

A generalized Bayesian approach to multiple changepoint analysis

本文提出一种通用贝叶斯方法用于多变化点分析，通过受多项逻辑回归启发的损失函数，无需指定数据生成过程，避免对变化点性质的限制，同时推断变化点位置和多项逻辑回归系数，通过模拟和应用展示其准确性和可解释性。

网络依赖下的高维逻辑回归

High Dimensional Logistic Regression Under Network Dependence

本文提出一种带二次交互项的高维逻辑回归框架，用惩罚最大伪似然法同时估计网络同伴效应与高维协变量效应，在稀疏参数下达到经典高维一致性速率。

面向二分类数据的贝叶斯融合Lasso建模

Bayesian Fused Lasso Modeling for Binary Data

针对二分类数据的变量选择与分组问题，提出带拉普拉斯先验的贝叶斯融合lasso二项逻辑回归模型，还引入马蹄形先验提升融合灵活性，通过Gibbs采样估计参数，经模拟和真实数据验证与现有方法对比。

Principled Drug-Drug Interaction Terms for Bayesian Logistic Regression Models of Drug Safety in Oncology Phase I Combination Trials

In Oncology, trials evaluating drug combinations are becoming more common. While combination therapies bring the potential for greater efficacy, they also create unique challenges for ensuring drug safety. In Phase-I dose escalation trials of drug combinations, model-based approaches enable efficient use of information gathered, but the models need to account for trial complexities: appropriate modeling of interactions becomes increasingly important with growing numbers of drugs being tested simultaneously in a given trial. In principle, we can use data from multiple arms testing varying combi…

Clinical Prediction Models to Predict the Risk of Multiple Binary Outcomes: a comparison of approaches

Clinical prediction models (CPMs) are used to predict clinically relevant outcomes or events. Typically, prognostic CPMs are derived to predict the risk of a single future outcome. However, with rising emphasis on the prediction of multi-morbidity, there is growing need for CPMs to simultaneously predict risks for each of multiple future outcomes. A common approach to multi-outcome risk prediction is to derive a CPM for each outcome separately, then multiply the predicted risks. This approach is only valid if the outcomes are conditionally independent given the covariates, and it fails to expl…

A Hierarchical Bayesian Framework for Constructing Sparsity-inducing Priors

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant. In this context, Bayesian variable selection techniques involving Markov chain Monte Carlo exploration of the posterior distribution over models can be prohibitively computationally expensive and so there has been attention paid to quasi-Bayesian approaches such as maximum a posteriori (MAP) estimation using priors that induce sparsity in such estimates. We…

Efficient Penalized Generalized Linear Mixed Models for Variable Selection and Genetic Risk Prediction in High-Dimensional Data

Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an attractive alternative to principal components (PC) adjustment to account for population structure and relatedness in high-dimensional penalized models. However, their use in binary trait GWAS rely on the invalid assumption that the residual variance does not depend on the estimated regression coefficients. Moreover, LMMs use a single spectral decomposition …