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Forward regression is a crucial methodology for automatically identifying important predictors from a large pool of potential covariates. In contexts with moderate predictor correlation, forward selection techniques can achieve screening…

This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…

Over the past two decades, shrinkage priors have become increasingly popular, and many proposals can be found in the literature. These priors aim to shrink small effects to zero while maintaining true large effects. Horseshoe-type priors…

Mirror Descent is a popular algorithm, that extends Gradients Descent (GD) beyond the Euclidean geometry. One of its benefits is to enable strong convergence guarantees through smooth-like analyses, even for objectives with exploding or…

Domain generalization (DG) strives to address distribution shifts across diverse environments to enhance model's generalizability. Current DG approaches are confined to acquiring robust representations with continuous features, specifically…

The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysis-of-variance dimensional…

Discovering temporal lagged and inter-dependencies in multivariate time series data is an important task. However, in many real-world applications, such as commercial cloud management, manufacturing predictive maintenance, and portfolios…

Domain generalization(DG) endeavors to develop robust models that possess strong generalizability while preserving excellent discriminability. Nonetheless, pivotal DG techniques tend to improve the feature generalizability by learning…

Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such…

Weak-to-strong generalization (W2SG) has emerged as a promising paradigm for stimulating the capabilities of strong pre-trained models by leveraging supervision from weaker supervisors. To improve the performance of the strong model,…

Implicit neural representations (INRs) enable fast video compression and effective video processing, but a single model rarely offers scalable decoding across rates and resolutions. In practice, multi-resolution typically relies on…

Recorrupted-to-Recorrupted (R2R) has emerged as a methodology for training deep networks for image restoration in a self-supervised manner from noisy measurement data alone, demonstrating equivalence in expectation to the supervised squared…

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained…

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to autoregressive generation by enabling parallel token prediction. However, practical dLLM decoding still suffers from high inference latency, which limits…

In multivariate statistics, estimating the covariance matrix is essential for understanding the interdependence among variables. In high-dimensional settings, where the number of covariates increases with the sample size, it is well known…

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…

This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances,…

Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to…

Generative diffusion models for end-to-end autonomous driving often suffer from mode collapse, tending to generate conservative and homogeneous behaviors. While DiffusionDrive employs predefined anchors representing different driving…

We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…