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Identifying the relevant variables for a classification model with correct confidence levels is a central but difficult task in high-dimension. Despite the core role of sparse logistic regression in statistics and machine learning, it still…

Modern machine learning models are highly expressive but notoriously difficult to analyze statistically. In particular, while black-box predictors can achieve strong empirical performance, they rarely provide valid hypothesis tests or…

In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in…

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Uniform random rotations (URRs) are a common preprocessing step in modern quantization approaches used for gradient compression, inference acceleration, KV-cache compression, model weight quantization, and approximate nearest-neighbor…

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…

Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus thus far has been on studying the proportional asymptotic regime, $n \asymp d$,…

Recent advances in machine learning have been achieved by using overparametrized models trained until near interpolation of the training data. It was shown, e.g., through the double descent phenomenon, that the number of parameters is a…

The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…

This paper proposes two distributed random reshuffling methods, namely Gradient Tracking with Random Reshuffling (GT-RR) and Exact Diffusion with Random Reshuffling (ED-RR), to solve the distributed optimization problem over a connected…

In this work, we introduce kernels with random Fourier features in the meta-learning framework to leverage their strong few-shot learning ability. We propose meta variational random features (MetaVRF) to learn adaptive kernels for the…

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter…

Random Reshuffling (RR), which is a variant of Stochastic Gradient Descent (SGD) employing sampling without replacement, is an immensely popular method for training supervised machine learning models via empirical risk minimization. Due to…

Sampling-based algorithms, such as Rapidly Exploring Random Trees (RRT) and its variants, have been used extensively for motion planning. Control barrier functions (CBFs) have been recently proposed to synthesize controllers for…

We propose a new method named the Conditional Randomization Rank Test (CRRT) for testing conditional independence of a response variable Y and a covariate variable X, conditional on the rest of the covariates Z. The new method generalizes…

Completely random measures (CRMs) are fundamental to Bayesian nonparametric models, with applications in clustering, feature allocation, and network analysis. A key quantity of interest is the Laplace exponent, whose asymptotic behavior…

We propose a novel approach for sampling-based and control-based motion planning that combines a representation of the environment obtained via a modified version of optimal Rapidly-exploring Random Trees (RRT*), with landmark-based…

Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…

In multi-view medical diagnosis, deep learning-based models often fuse information from different imaging perspectives to improve diagnostic performance. However, existing approaches are prone to overfitting and rely heavily on…