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Balancing covariates is critical for credible and efficient randomized experiments. Rerandomization addresses this by repeatedly generating treatment assignments until covariate balance meets a prespecified threshold. By shrinking this…
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…
In high-dimensional regression, we attempt to estimate a parameter vector $\beta_0\in\mathbb{R}^p$ from $n\lesssim p$ observations $\{(y_i,x_i)\}_{i\leq n}$ where $x_i\in\mathbb{R}^p$ is a vector of predictors and $y_i$ is a response…
We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for…
Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is…
In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
Consider the use of $\ell_{1}/\ell_{\infty}$-regularized regression for joint estimation of a $\pdim \times \numreg$ matrix of regression coefficients. We analyze the high-dimensional scaling of $\ell_1/\ell_\infty$-regularized quadratic…
We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion…
In this paper, a Mixed Data Sampling (MIDAS) model is studied when both low and high frequency variables are contaminated with measurement error. It is shown that the profile likelihood estimator becomes inconsistent in the presence of…
Multivariate network time series are ubiquitous in modern systems, yet existing network autoregressive models typically treat nodes as scalar processes, ignoring cross-variable spillovers. To capture these complex interactions without the…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted…