Many datasets are collected from multiple environments (e.g. different labs, perturbations, etc.), and it is often advantageous to learn models and relations that are invariant across environments. Invariance can improve robustness to unknown confounders and improve generalization to new domains. We develop a novel framework -- KL regression -- to reliably estimate regression coefficients in a challenging multi-environment setting, where latent confounders affect the data from each environment. KL regression is based on a new objective of simultaneously minimizing the KL- divergence between a parametric model and the observed data from each environment. We prove that KL regression recovers the true invariant factors under a flexible confounding setup. Moreover, it is computationally efficient as we derive an analytic solution for its global optimum. In systematic experiments, we validate the improved performance of KL regression compared to commonly used approaches.
Variable Selection in Functional Linear Quantile Regression for Identifying Associations between Daily Patterns of Physical Activity and Cognitive Function
University of South Carolina（南卡罗来纳大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
In compositional data, detecting which part of the whole delineates heterogeneity is important. The aim is to propose a procedure to quantify this term in the multivariate regression context without abandoning the data's natural restriction. A single probabilistic model with a hierarchical structure was built for multiple compositional data. An objective criterion based on skewness and kurtosis metrics provides support to characterize each component's performance as well as to assist in choosing one component as a reference avoiding model identifiability issues. The inference procedure was don…
In bioinformatics, the rapid development of sequencing technology has enabled us to collect an increasing amount of omics data. Classification based on omics data is one of the central problems in biomedical research. However, omics data usually has a limited sample size but high feature dimensions, and it is assumed that only a few features (biomarkers) are active, i.e. informative to discriminate between different categories (cancer subtypes, responder/non-responder to treatment, for example). Identifying active biomarkers for classification has therefore become fundamental for omics data an…
Causal decomposition analysis provides a way to identify mediators that contribute to health disparities between marginalized and non-marginalized groups. In particular, the degree to which a disparity would be reduced or remain after intervening on a mediator is of interest. Yet, estimating disparity reduction and remaining might be challenging for many researchers, possibly because there is a lack of understanding of how each estimation method differs from other methods. In addition, there is no appropriate estimation method available for a certain setting (i.e., a regression-based approach …
Identifying Genetic Variants for Obesity: A Knowledge Integration Quantile Regression (KIQR) Approach for Ultra-High-Dimensional Data
Xavier University（泽维尔大学）；City University of Hong Kong（香港城市大学）；University of Cincinnati（辛辛那提大学）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；Yale University（耶鲁大学）
Motivated by a hemodialysis monitoring study, we propose a logistic model with a functional predictor, called the Sparse Functional Logistic Regression (SFLR), where the corresponding coefficient function is {\it locally sparse}, that is, it is completely zero on some subregions of its domain. The coefficient function, together with the intercept parameter, are estimated through a doubly-penalized likelihood approach with a B-splines expansion. One penalty is for controlling the roughness of the coefficient function estimate and the other penalty, in the form of the $L_1$ norm, enforces the lo…
In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the classic log-contrast model is often used where read counts are normalized into compositions. However, zero read counts and the randomness in covariates remain critical issues. In this article, we introduce a surprisingly simple, interpretable, and efficient method for the estimation of compositional data regression through the lens of a novel high-dimensional lo…
Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a governing stochastic dynamical system, from its time-series data of the most probable transition trajectory. By the Onsager-Machlup theory, the most probable transition trajectory satisfies the corresponding Euler-Lagrange equation, which is a second order deterministic ordinary differential equation involving the drift term and diffusion coefficient. We first e…
