Varying Coefficient Linear Discriminant Analysis for Dynamic Data

• URL: http://arxiv.org/abs/2203.06371v2
• Date: Tue, 15 Mar 2022 02:54:38 GMT
• Title: Varying Coefficient Linear Discriminant Analysis for Dynamic Data
• Authors: Yajie Bao and Yuyang Liu
• Abstract summary: This paper investigates the varying coefficient LDA model for dynamic data. By deriving a new discriminant direction function parallel with Bayes' direction, we propose a least-square estimation procedure. For high-dimensional regime, the corresponding data-driven discriminant rule is more computationally efficient than the existed dynamic linear programming rule.
• Score: 5.228711636020666
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Linear discriminant analysis (LDA) is a vital classification tool in statistics and machine learning. This paper investigates the varying coefficient LDA model for dynamic data, with Bayes' discriminant direction being a function of some exposure variable to address the heterogeneity. By deriving a new discriminant direction function parallel with Bayes' direction, we propose a least-square estimation procedure based on the B-spline approximation. For high-dimensional regime, the corresponding data-driven discriminant rule is more computationally efficient than the existed dynamic linear programming rule. We also establish the corresponding theoretical results, including estimation error bound and the uniform excess misclassification rate. Numerical experiments on synthetic data and real data both corroborate the superiority of our proposed classification method.

Related papers

• Induced Covariance for Causal Discovery in Linear Sparse Structures [55.2480439325792]
  Causal models seek to unravel the cause-effect relationships among variables from observed data. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships.
  arXiv  Detail & Related papers  (2024-10-02T04:01:38Z)
• Adaptive debiased SGD in high-dimensional GLMs with streaming data [4.704144189806667]
  We introduce a novel approach to online inference in high-dimensional generalized linear models. Our method operates in a single-pass mode, significantly reducing both time and space complexity. We demonstrate that our method, termed the Approximated Debiased Lasso (ADL), not only mitigates the need for the bounded individual probability condition but also significantly improves numerical performance.
  arXiv  Detail & Related papers  (2024-05-28T15:36:48Z)
• Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification [72.77513633290056]
  We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model. Our method captures intricate patterns and relationships, enhancing classification performance.
  arXiv  Detail & Related papers  (2024-02-14T16:10:42Z)
• Regularized Linear Discriminant Analysis Using a Nonlinear Covariance Matrix Estimator [11.887333567383239]
  Linear discriminant analysis (LDA) is a widely used technique for data classification. LDA becomes inefficient when the data covariance matrix is ill-conditioned. Regularized LDA methods have been proposed to cope with such a situation.
  arXiv  Detail & Related papers  (2024-01-31T11:37:14Z)
• Minimally Informed Linear Discriminant Analysis: training an LDA model with unlabelled data [51.673443581397954]
  We show that it is possible to compute the exact projection vector from LDA models based on unlabelled data. We show that the MILDA projection vector can be computed in a closed form with a computational cost comparable to LDA.
  arXiv  Detail & Related papers  (2023-10-17T09:50:31Z)
• A Bi-level Nonlinear Eigenvector Algorithm for Wasserstein Discriminant Analysis [3.4806267677524896]
  Wasserstein discriminant analysis (WDA) is a linear dimensionality reduction method. WDA can account for both global and local interconnections between data classes. A bi-level nonlinear eigenvector algorithm (WDA-nepv) is presented.
  arXiv  Detail & Related papers  (2022-11-21T22:40:43Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• A Doubly Regularized Linear Discriminant Analysis Classifier with Automatic Parameter Selection [24.027886914804775]
  Linear discriminant analysis (LDA) based classifiers tend to falter in many practical settings where the training data size is smaller than, or comparable to, the number of features. We propose a doubly regularized LDA classifier that we denote as R2LDA. Results obtained from both synthetic and real data demonstrate the consistency and effectiveness of the proposed R2LDA approach.
  arXiv  Detail & Related papers  (2020-04-28T07:09:22Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)
• Saliency-based Weighted Multi-label Linear Discriminant Analysis [101.12909759844946]
  We propose a new variant of Linear Discriminant Analysis (LDA) to solve multi-label classification tasks. The proposed method is based on a probabilistic model for defining the weights of individual samples. The Saliency-based weighted Multi-label LDA approach is shown to lead to performance improvements in various multi-label classification problems.
  arXiv  Detail & Related papers  (2020-04-08T19:40:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.