Selective inference using randomized group lasso estimators for general models
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for overdispersed count data, for example, and allows for categorical or grouped covariates as well as continuous covariates. A randomized group-regularized optimization problem is studied. The added randomization allows us to construct a post-selection likelihood which we show to be adequate for selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood also provides a selective point estimator, accounting for the selection by the group lasso. Confidence regions for the regression parameters in the selected model take the form of Wald-type regions and are shown to have bounded volume. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey while simulations showcase its behaviour and favorable comparison with other methods.
Code (0)
등록된 구현이 없습니다.
Tasks
NutritionSimilar Papers 제목 키워드 기반
Approximate Post-Selective Inference for Regression with the Group LASSO
After selection with the Group LASSO (or generalized variants such as the overlapping, sparse, or standardized Group LASSO), inference for the selected parameters is unreliable in the absence of adjustments for selection…
regressionSelection biasSparse LearningEmpirical Bayes Estimation for Lasso-Type Regularizers: Analysis of Automatic Relevance Determination
This paper focuses on linear regression models with non-conjugate sparsity-inducing regularizers such as lasso and group lasso. Although the empirical Bayes approach enables us to estimate the regularization parameter, l…
regressionSelective Inference and Learning Mixed Graphical Models
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coef…
Model SelectionvalidCollaborative-controlled LASSO for Constructing Propensity Score-based Estimators in High-Dimensional Data
Propensity score (PS) based estimators are increasingly used for causal inference in observational studies. However, model selection for PS estimation in high-dimensional data has received little attention. In these sett…
Causal InferenceModel SelectionMeasuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments
We develop a new, principled algorithm for estimating the contribution of training data points to the behavior of a deep learning model, such as a specific prediction it makes. Our algorithm estimates the AME, a quantity…
Causal Inference