Related papers: A Direct Approach for Sparse Quadratic Discriminan…
This study explores the classification error of Mixture Discriminant Analysis (MDA) in scenarios where the number of mixture components exceeds those present in the actual data distribution, a condition known as overspecification. We use a…
Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection,…
We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
We consider high-dimensional quadratic classifiers in non-sparse settings. The target of classification rules is not Bayes error rates in the context. The classifier based on the Mahalanobis distance does not always give a preferable…
We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a \emph{corrupted} set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in…
Data augmentation (DA) techniques aim to increase data variability, and thus train deep networks with better generalisation. The pioneering AutoAugment automated the search for optimal DA policies with reinforcement learning. However,…
Quantizing deep convolutional neural networks for image super-resolution substantially reduces their computational costs. However, existing works either suffer from a severe performance drop in ultra-low precision of 4 or lower bit-widths,…
Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue…
This paper proposes a robust high-dimensional sparse canonical correlation analysis (CCA) method for investigating linear relationships between two high-dimensional random vectors, focusing on elliptical symmetric distributions. Traditional…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
As the adoption of Artificial Intelligence (AI) models expands into critical real-world applications, ensuring the explainability of these models becomes paramount, particularly in sensitive fields such as medicine and finance. Linear…
Question answering (QA) has recently shown impressive results for answering questions from customized domains. Yet, a common challenge is to adapt QA models to an unseen target domain. In this paper, we propose a novel self-supervised…
Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric…
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…
High-dimensional classification and feature selection tasks are ubiquitous with the recent advancement in data acquisition technology. In several application areas such as biology, genomics and proteomics, the data are often functional in…
Self-supervised learning (SSL) has potential for effective representation learning in medical imaging, but the choice of data augmentation is critical and domain-specific. It remains uncertain if general augmentation policies suit surgical…