Related papers: High-dimensional Ordinary Least-squares Projection…

In ultrahigh dimensional setting, independence screening has been both theoretically and empirically proved a useful variable selection framework with low computation cost. In this work, we propose a two-step framework by using marginal…

Holographic Predictive Search (HPS) is a novel approach to search-based hologram generation that uses a mathematical understanding of the optical transforms to make informed optimisation decisions. Existing search techniques such as Direct…

Best subset selection (BSS) is widely known as the holy grail for high-dimensional variable selection. Nevertheless, the notorious NP-hardness of BSS substantially restricts its practical application and also discourages its theoretical…

Variable selection is a challenging problem in high-dimensional sparse learning, especially when group structures exist. Group SLOPE performs well for the adaptive selection of groups of predictors. However, the block non-separable group…

A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To…

In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…

We consider the problem of variable screening in ultra-high dimensional generalized linear models (GLMs) of non-polynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a…

We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…

Prompt learning has gained significant attention as a parameter-efficient approach for adapting large pre-trained vision-language models to downstream tasks. However, when only partial labels are available, its performance is often limited…

Vision-language models such as CLIP are capable of mapping the different modality data into a unified feature space, enabling zero/few-shot inference by measuring the similarity of given images and texts. However, most existing methods…

Selecting interactions from an ultrahigh-dimensional statistical model with $n$ observations and $p$ variables when $p\gg n$ is difficult because the number of candidates for interactions is $p(p-1)/2$ and a selected model should satisfy…

We propose a new method for high-dimensional semi-supervised learning problems based on the careful aggregation of the results of a low-dimensional procedure applied to many axis-aligned random projections of the data. Our primary goal is…

This paper treats the problem of screening for variables with high correlations in high dimensional data in which there can be many fewer samples than variables. We focus on threshold-based correlation screening methods for three related…

Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources,…

Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,…

Two popular variable screening methods under the ultra-high dimensional setting with the desirable sure screening property are the sure independence screening (SIS) and the forward regression (FR). Both are classical variable screening…

Random sampling is a fundamental tool in modern machine learning and numerical linear algebra for reducing the computational cost of large-scale matrix problems. Existing analyses, however, rely primarily on subspace embedding guarantees,…

Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric…

Extracting relevant features from data sets where the number of observations ($n$) is much smaller then the number of predictors ($p$) is a major challenge in modern statistics. Sorted L-One Penalized Estimation (SLOPE), a generalization of…

Self-Supervised Learning (SSL) methods typically rely on random image augmentations, or views, to make models invariant to different transformations. We hypothesize that the efficacy of pretraining pipelines based on conventional random…