Related papers: Nonparametric Reduced Rank Regression
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm based relaxed…
In this paper, we introduce a novel high-dimensional Factor-Adjusted sparse Partially Linear regression Model (FAPLM), to integrate the linear effects of high-dimensional latent factors with the nonparametric effects of low-dimensional…
Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness…
Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large language models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA…
Reduced-Rank (RR) regression is a powerful dimensionality reduction technique but it overlooks any possible group configuration among the responses by assuming a low-rank structure on the entire coefficient matrix. Moreover, the temporal…
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…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
This paper tackles the challenge of performing multiple quantile regressions across different quantile levels and the associated problem of controlling the familywise error rate, an issue that is generally overlooked in practice. We propose…
Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…
We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant…
We present a novel Bayesian nonparametric regression model for covariates X and continuous, real response variable Y. The model is parametrized in terms of marginal distributions for Y and X and a regression function which tunes the…
Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive…
This paper investigates the partial linear model by Least Absolute Deviation (LAD) regression. We parameterize the nonparametric term using Deep Neural Networks (DNNs) and formulate a penalized LAD problem for estimation. Specifically, our…
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…
In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the…
Homogeneity, low rank, and sparsity are three widely adopted assumptions in multi-response regression models to address the curse of dimensionality and improve estimation accuracy. However, there is limited literature that examines these…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification,…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…