相关论文: On the dimension effect of regularized linear disc…
This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An $l_1$ minimization method is used to select the…
This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized…
Domain alignment (DA) has been widely used in unsupervised domain adaptation. Many existing DA methods assume that a low source risk, together with the alignment of distributions of source and target, means a low target risk. In this paper,…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…
Data augmentation (DA) is a powerful workhorse for bolstering performance in modern machine learning. Specific augmentations like translations and scaling in computer vision are traditionally believed to improve generalization by generating…
Quadratic discriminant analysis (QDA) is a widely used method for classification problems, particularly preferable over Linear Discriminant Analysis (LDA) for heterogeneous data. However, QDA loses its effectiveness in high-dimensional…
The family of rank estimators, including Han's maximum rank correlation (Han, 1987) as a notable example, has been widely exploited in studying regression problems. For these estimators, although the linear index is introduced for…
In supervised classification problems, the test set may contain data points belonging to classes not observed in the learning phase. Moreover, the same units in the test data may be measured on a set of additional variables recorded at a…
Latent Dirichlet allocation (LDA) obtains essential information from data by using Bayesian inference. It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been…
Dimension reduction and variable selection are performed routinely in case-control studies, but the literature on the theoretical aspects of the resulting estimates is scarce. We bring our contribution to this literature by studying…
We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of…
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…
This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on…
In current research, machine and deep learning solutions for the classification of temporal data are shifting from single-channel datasets (univariate) to problems with multiple channels of information (multivariate). The majority of these…
This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix $\O$ and the difference $\de$ of the mean vectors, we…
Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its own importance, as it is a keystone in human knowledge about statistical…
The difference-in-differences (DID) design is one of the most popular methods used in empirical economics research. However, there is almost no work examining what the DID method identifies in the presence of a misclassified treatment…
Regularization is a fundamental technique to prevent over-fitting and to improve generalization performances by constraining a model's complexity. Current Deep Networks heavily rely on regularizers such as Data-Augmentation (DA) or…
Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. Previous studies have also extended the binary-class case into multi-classes. However, many applications, such as object detection…