Related papers: Generalized Rank Regression
Reduced rank regression (RRR) is a fundamental tool for modeling multiple responses through low-dimensional latent structures, offering both interpretability and strong predictive performance in high-dimensional settings. Classical RRR…
Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still…
In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also,…
In this paper, we introduce the Generalized Mixed Regularized Reduced Rank Regression model (GMR4), an extension of the GMR3 model designed to improve performance in high-dimensional settings. GMR3 is a regression method for a mix of…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
The quasi-maximum likelihood estimation is a commonly-used method for estimating GARCH parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the…
In this paper, we propose the generalized mixed reduced rank regression method, GMR$^3$ for short. GMR$^3$ is a regression method for a mix of numeric, binary, and ordinal response variables. The predictor variables can be a mix of binary,…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…
We study high-dimensional rank regression when data are distributed across multiple machines and the loss is a non-additive U-statistic, as in convoluted rank regression (CRR). Classical communication-efficient surrogate likelihood (CSL)…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…
Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
Reduced rank regression (RRR) is a widely employed model for investigating the linear association between multiple response variables and a set of predictors. While RRR has been extensively explored in various works, the focus has…