Related papers: Sure Independence Screening for Ultra-High Dimensi…
A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of…
We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between the features and the labels. The key idea is that good features should maximise such…
Feature screening is useful and popular to detect informative predictors for ultrahigh-dimensional data before developing proceeding statistical analysis or constructing statistical models. While a large body of feature screening procedures…
Establishing reliable image correspondences is essential for many robotic vision problems. However, existing methods often struggle in challenging scenarios with large viewpoint changes or textureless regions, where incorrect cor-…
Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the so-called $\textit{safe rules}$ for the Lasso.…
Fused Lasso was proposed to characterize the sparsity of the coefficients and the sparsity of their successive differences for the linear regression. Due to its wide applications, there are many existing algorithms to solve fused Lasso.…
Sparse variable selection improves interpretability and generalization in high-dimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale…
Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more…
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
The Dantzig selector (Candes and Tao, 2007) is a popular l1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to…
Monitoring the performance of classification models in production is critical yet challenging due to strict labeling budgets, one-shot batch acquisition of labels and extremely low error rates. We propose a general framework based on…
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…
Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we…
We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high…
Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace…
Single image super-resolution (SISR) is a notoriously challenging ill-posed problem, which aims to obtain a high-resolution (HR) output from one of its low-resolution (LR) versions. To solve the SISR problem, recently powerful deep learning…
This paper proposes a model-free and data-adaptive feature screening method for ultra-high dimensional datasets. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This…
We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus…
Consider a linear model $Y=X\beta+z$, $z\sim N(0,I_n)$. Here, $X=X_{n,p}$, where both $p$ and $n$ are large, but $p>n$. We model the rows of $X$ as i.i.d. samples from $N(0,\frac{1}{n}\Omega)$, where $\Omega$ is a $p\times p$ correlation…