Related papers: Data-Driven Random Projection and Screening for Hi…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…
Correlation among the observations in high-dimensional regression modeling can be a major source of confounding. We present a new open-source package, plmmr, to implement penalized linear mixed models in R. This R package estimates…
This paper presents two novel algorithms for approximately projecting symmetric matrices onto the Positive Semidefinite (PSD) cone using Randomized Numerical Linear Algebra (RNLA). Classical PSD projection methods rely on full-rank…
This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Logistic regression is a ubiquitous method for probabilistic classification. However, the effectiveness of logistic regression depends upon careful and relatively computationally expensive tuning, especially for the regularisation…
Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection,…
Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear…
For finite samples with binary outcomes penalized logistic regression such as ridge logistic regression (RR) has the potential of achieving smaller mean squared errors (MSE) of coefficients and predictions than maximum likelihood…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
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…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the L0-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield…
Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…
For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…
Gradient-based methods for instance-based explanation for large language models (LLMs) are hindered by the immense dimensionality of model gradients. In practice, influence estimation is restricted to a subset of model parameters to make…
The big data trend has inspired feature-driven learning tasks, which cannot be handled by conventional machine learning models. Unstructured data produces very large binary matrices with millions of columns when converted to vector form.…