Related papers: Naive imputation implicitly regularizes high-dimen…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

Marginal imputation, which consists of imputing each item requiring imputation separately, is often used in surveys. This type of imputation procedures leads to asymptotically unbiased estimators of simple parameters such as population…

Handling missing values in tabular datasets presents a significant challenge in training and testing artificial intelligence models, an issue usually addressed using imputation techniques. Here we introduce "Not Another Imputation Method"…

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…

Time series are all around in real-world applications. However, unexpected accidents for example broken sensors or missing of the signals will cause missing values in time series, making the data hard to be utilized. It then does harm to…

In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…

In many application settings, the data have missing entries which make analysis challenging. An abundant literature addresses missing values in an inferential framework: estimating parameters and their variance from incomplete tables. Here,…

Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…

The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…

Missing data in supervised learning is well-studied, but the specific issue of missing labels during model evaluation has been overlooked. Ignoring samples with missing values, a common solution, can introduce bias, especially when data is…

Nonconvex penalties are utilized for regularization in high-dimensional statistical learning algorithms primarily because they yield unbiased or nearly unbiased estimators for the parameters in the model. Nonconvex penalties existing in the…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit…

Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…

Regularized linear regression is a promising approach for binary classification problems in which the training set has noisy labels since the regularization term can help to avoid interpolating the mislabeled data points. In this paper we…

BACKGROUND: As databases grow larger, it becomes harder to fully control their collection, and they frequently come with missing values: incomplete observations. These large databases are well suited to train machine-learning models, for…

We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…