arXiv subjects

Huijie Feng

Publications and source records attributed to Huijie Feng.

4 recordsLinked to original sources

arXiv2023

Test of Significance for High-dimensional Thresholds with Application to Individualized Minimal Clinically Important Difference

This work is motivated by learning the individualized minimal clinically important difference, a vital concept to assess clinical importance in various biomedical studies. We formulate the scientific question into a high-dimensional statistical problem where the parameter of interest lies in an individualized linear threshold. The goal is to develop a hypothesis testing procedure for the significance of a single element in this parameter as well as of a linear combination of this parameter. The difficulty dues to the high-dimensional nuisance in developing such a testing procedure, and also stems from the fact that this high-dimensional threshold model is nonregular and the limiting distribution of the corresponding estimator is nonstandard. To deal with these challenges, we construct a test statistic via a new bias-corrected smoothed decorrelated score approach, and establish its asymptotic distributions under both null and local alternative hypotheses. We propose a double-smoothing approach to select the optimal bandwidth in our test statistic and provide theoretical guarantees for the selected bandwidth. We conduct simulation studies to demonstrate how our proposed procedure can be applied in empirical studies. We apply the proposed method to a clinical trial where the scientific goal is to assess the clinical importance of a surgery procedure.

stat.ME↗

arXiv2022

Inference in High-dimensional Multivariate Response Regression with Hidden Variables

This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient matrix is proposed. Our method first utilizes the multivariate nature of the responses by estimating and adjusting the hidden effect to construct an initial estimator of the coefficient matrix. By further deploying a low-dimensional projection procedure to reduce the bias introduced by the regularization in the previous step, a refined estimator is proposed and shown to be asymptotically normal. The asymptotic variance of the resulting estimator is derived with closed-form expression and can be consistently estimated. In addition, we propose a testing procedure for the existence of hidden effects and provide its theoretical justification. Both our procedures and their analyses are valid even when the feature dimension and the number of responses exceed the sample size. Our results are further backed up via extensive simulations and a real data analysis.

stat.ME↗

arXiv2020

Regularized Training and Tight Certification for Randomized Smoothed Classifier with Provable Robustness

Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded adversarial perturbations. However, how to train a good base classifier that is accurate and robust when smoothed has not been fully investigated. In this work, we derive a new regularized risk, in which the regularizer can adaptively encourage the accuracy and robustness of the smoothed counterpart when training the base classifier. It is computationally efficient and can be implemented in parallel with other empirical defense methods. We discuss how to implement it under both standard (non-adversarial) and adversarial training scheme. At the same time, we also design a new certification algorithm, which can leverage the regularization effect to provide tighter robustness lower bound that holds with high probability. Our extensive experimentation demonstrates the effectiveness of the proposed training and certification approaches on CIFAR-10 and ImageNet datasets.

stat.ML↗

arXiv2019

Nonregular and Minimax Estimation of Individualized Thresholds in High Dimension with Binary Responses

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $θ$ in an individualized linear threshold $θ^T Z$ for a continuous variable $X$, which minimizes the disagreement between $\text{sign}(X-θ^TZ)$ and a binary response $Y$. While the problem can be formulated into the M-estimation framework, minimizing the corresponding empirical risk function is computationally intractable due to discontinuity of the sign function. Moreover, estimating $θ$ even in the fixed-dimensional setting is known as a nonregular problem leading to nonstandard asymptotic theory. To tackle the computational and theoretical challenges in the estimation of the high-dimensional parameter $θ$, we propose an empirical risk minimization approach based on a regularized smoothed loss function. The statistical and computational trade-off of the algorithm is investigated. Statistically, we show that the finite sample error bound for estimating $θ$ in $\ell_2$ norm is $(s\log d/n)^{β/(2β+1)}$, where $d$ is the dimension of $θ$, $s$ is the sparsity level, $n$ is the sample size and $β$ is the smoothness of the conditional density of $X$ given the response $Y$ and the covariates $Z$. The convergence rate is nonstandard and slower than that in the classical Lasso problems. Furthermore, we prove that the resulting estimator is minimax rate optimal up to a logarithmic factor. The Lepski's method is developed to achieve the adaption to the unknown sparsity $s$ and smoothness $β$. Computationally, an efficient path-following algorithm is proposed to compute the solution path. We show that this algorithm achieves geometric rate of convergence for computing the whole path. Finally, we evaluate the finite sample performance of the proposed estimator in simulation studies and a real data analysis.

math.ST↗