arXiv subjects

Seunghyun Min

Publications and source records attributed to Seunghyun Min.

3 recordsLinked to original sources

arXiv2021

Constructing confidence sets after lasso selection by randomized estimator augmentation

Although a few methods have been developed recently for building confidence intervals after model selection, how to construct confidence sets for joint post-selection inference is still an open question. In this paper, we develop a new method to construct confidence sets after lasso variable selection, with strong numerical support for its accuracy and effectiveness. A key component of our method is to sample from the conditional distribution of the response $y$ given the lasso active set, which, in general, is very challenging due to the tiny probability of the conditioning event. We overcome this technical difficulty by using estimator augmentation to simulate from this conditional distribution via Markov chain Monte Carlo given any estimate $\tildeμ$ of the mean $μ_0$ of $y$. We then incorporate a randomization step for the estimate $\tildeμ$ in our sampling procedure, which may be interpreted as simulating from a posterior predictive distribution by averaging over the uncertainty in $μ_0$. Our Monte Carlo samples offer great flexibility in the construction of confidence sets for multiple parameters. Extensive numerical results show that our method is able to construct confidence sets with the desired coverage rate and, moreover, that the diameter and volume of our confidence sets are substantially smaller in comparison with a state-of-the-art method.

stat.ME↗

arXiv2017

Uncertainty Quantification Under Group Sparsity

Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons, we demonstrate that our bootstrap method performs much better than popular competitors, highlighting its practical utility. The theoretical result is generalized to other block norm penalization and sub-Gaussian errors, which further broadens the potential applications.

math.ST↗

arXiv2016

Estimator Augmentation with Applications in High-Dimensional Group Inference

To make inference about a group of parameters on high-dimensional data, we develop the method of estimator augmentation for the block Lasso, which is defined via the block norm. By augmenting a block Lasso estimator $\hatβ$ with the subgradient $S$ of the block norm evaluated at $\hatβ$, we derive a closed-form density for the joint distribution of $(\hatβ,S)$ under a high-dimensional setting. This allows us to draw from an estimated sampling distribution of $\hatβ$, or more generally any function of $(\hatβ,S)$, by Monte Carlo algorithms. We demonstrate the application of estimator augmentation in group inference with the group Lasso and a de-biased group Lasso constructed as a function of $(\hatβ,S)$. Our numerical results show that importance sampling via estimator augmentation can be orders of magnitude more efficient than parametric bootstrap in estimating tail probabilities for significance tests. This work also brings new insights into the geometry of the sample space and the solution uniqueness of the block Lasso.

stat.ME↗