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We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
Image classifiers often rely overly on peripheral attributes that have a strong correlation with the target class (i.e., dataset bias) when making predictions. Due to the dataset bias, the model correctly classifies data samples including…
Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…
Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…
Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…
Deep neural networks often struggle to learn robust representations in the presence of dataset biases, leading to suboptimal generalization on unbiased datasets. This limitation arises because the models heavily depend on peripheral and…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Spectral methods have myriad applications in high-dimensional statistics and data science, and while previous works have primarily focused on $\ell_2$ or $\ell_{2,\infty}$ eigenvector and singular vector perturbation theory, in many…
Measurement error arises through a variety of mechanisms. A rich literature exists on the bias introduced by covariate measurement error and on methods of analysis to address this bias. By comparison, less attention has been given to errors…
We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
High-dimensional regression models with regularized sparse estimation are widely applied. For statistical inferences, debiased methods are available about single coefficients or predictions with sparse new covariate vectors (also called…
Several prior studies have suggested that word frequency biases can cause the Bert model to learn indistinguishable sentence embeddings. Contrastive learning schemes such as SimCSE and ConSERT have already been adopted successfully in…
Regression is fundamental in computer vision and is widely used in various tasks including age estimation, depth estimation, target localization, \etc However, real-world data often exhibits imbalanced distribution, making regression models…
Dataset bias is a critical challenge in machine learning since it often leads to a negative impact on a model due to the unintended decision rules captured by spurious correlations. Although existing works often handle this issue based on…
Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…
Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting…
Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the…
Concept-based explanation approach is a popular model interpertability tool because it expresses the reasons for a model's predictions in terms of concepts that are meaningful for the domain experts. In this work, we study the problem of…