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The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…
In many conventional scientific investigations with high or ultra-high dimensional feature spaces, the relevant features, though sparse, are large in number compared with classical statistical problems, and the magnitude of their effects…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least…
This paper proposes a new method and algorithm for predicting multivariate responses in a regression setting. Research into classification of High Dimension Low Sample Size (HDLSS) data, in particular microarray data, has made considerable…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
Hyperspectral images (HSI) classification is a high technical remote sensing tool. The main goal is to classify the point of a region. The HIS contains more than a hundred bidirectional measures, called bands (or simply images), of the same…
Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC),…
The all-relevant problem of feature selection is the identification of all strongly and weakly relevant attributes. This problem is especially hard to solve for time series classification and regression in industrial applications such as…
This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear…
We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…
High dimensional classification has been highlighted for last two decades and much research has been conducted in order to circumvent challenges encountered in high dimensions. While existing methods have focused mainly on developing…
Recent advancements in instruction tuning for large language models (LLMs) suggest that a small, high-quality dataset can significantly equip LLMs with instruction-following capabilities, outperforming large datasets often burdened by…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…
High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…
Feature selection has evolved to be an important step in several machine learning paradigms. In domains like bio-informatics and text classification which involve data of high dimensions, feature selection can help in drastically reducing…
The automated discovery of constitutive models from data has recently emerged as a promising alternative to the traditional model calibration paradigm. In this work, we present a fully automated framework for constitutive model discovery…