Related papers: Optimal Feature Selection in High-Dimensional Disc…
This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection,…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
Simultaneous variable selection and statistical inference is challenging in high-dimensional data analysis. Most existing post-selection inference methods require explicitly specified regression models, which are often linear, as well as…
We propose and analyze a variant of Sparse Polyak for high dimensional M-estimation problems. Sparse Polyak proposes a novel adaptive step-size rule tailored to suitably estimate the problem's curvature in the high-dimensional setting,…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
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…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sparse representation of the regression function in a…
Given $m$ $d$-dimensional responsors and $n$ $d$-dimensional predictors, sparse regression finds at most $k$ predictors for each responsor for linear approximation, $1\leq k \leq d-1$. The key problem in sparse regression is subset…
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
Hilbert-Schmidt Independence Criterion (HSIC) has recently been used in the field of single-index models to estimate the directions. Compared with some other well-established methods, it requires relatively weaker conditions. However, its…