High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It links a problem of classification with a problem of nonparametric regression. We giv…
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48 results for “High-Dimensional Classification”
Linear classification has been widely used in many high-dimensional applications like text classification. To perform linear classification for large-scale tasks, we often need to design distributed learning methods on a cluster of multiple machines. In this paper, we propose a new distributed learning method, called f…
Boosting ridge regression for high-dimensional data classification reduces computational cost and improves learning time.
problem High computational demand of inverting regularised covariance matrix in ridge regression for high-dimensional problems.
method Train an ensemble of ridge regressors in randomly projected subspaces, then combine them using adaptive boosting.
result Effective in terms of learning time and improved predictive performance in some cases.
Novel method converts time series data into functional data for high dimensional classification.
problem Small sample size problem in high dimensional time series data.
method Classwise Functional Principal Component Analysis (PCA) followed by Bayesian linear classifier.
result Demonstrated efficacy on synthetic and real data sets.
Paper proposes sparse classification method for high-dimensional data.
problem Sparse classification in high-dimensional data with positive-confidence samples.
method Developed a novel sparse-penalization framework using L1, SCAD, and MCP penalties for convex and non-convex shrinkage.
result Proved near minimax-optimal sparse recovery rates under Restricted Strong Convexity condition.
Centroid Decision Foreststat.ML
CDF uses centroids to split features for high-dimensional classification.
problem High-dimensional classification problems with complex class structures.
method CDF introduces a centroid-driven splitting strategy in decision trees.
result CDF outperforms conventional methods in high-dimensional classification.
This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (IIS) approach based on transforming the original -dimensional feature vector is propose…
Novel algorithm SAODE improves high-dimensional stream classification in seasonal data.
problem Handling seasonal concept drift in high-dimensional stream classification.
method SAODE classifier that includes time as a super parent to handle seasonal drift.
result SAODE consistently outperforms other methods in stream and concept drift classification.
Regularization helps improve classification of noisy high-dimensional data.
problem Classifying high-dimensional noisy Gaussian mixture with limited oracle knowledge.
method Analysis of regularized convex classifiers including ridge, hinge, and logistic regression.
result Regularization can reach Bayes-optimal performance under certain conditions.
We study high-dimensional Gaussian mixture classification using statistical physics methods.
problem Classifying high-dimensional Gaussian mixture with general covariance matrices.
method Replica method from statistical physics for asymptotic analysis of convex classifiers.
result Construction and validation of a de-biased estimator for variable selection.
Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background material, this paper introduces a technique we call slicing for obtaining a nonsingular …
Study shows how to approximate and estimate high-dimensional classification functions without the curse of dimensionality.
problem Approximating and estimating classification functions in high-dimensional spaces.
method Modified existing results to show that functions can be approximated by neural networks with bounded weights. Proved the existence of a neural network with bounded weights approximating a classification function. Leveraged these bounds to quantify estimation rates.
result Neural networks can approximate functions without the curse of dimensionality, leading to efficient estimation rates.
Prevalidated ridge regression simplifies logistic regression for high-dimensional data.
problem Efficient probabilistic classification in high-dimensional data with logistic regression.
method Developed a prevalidated ridge regression model that matches logistic regression's performance but is more computationally efficient.
result Prevalidated ridge regression achieves similar classification error and log-loss to logistic regression for high-dimensional data.
Develops a new tensor classification method for high-dimensional data.
problem Efficient learning algorithms exploiting tensorial structure in high-dimensional multi-way arrays.
method Tensor Train Multi-way Multi-level Kernel (TT-MMK) combining Canonical Polyadic decomposition, Dual Structure-preserving Support Vector Machine, and Tensor Train approximation.
result The TT-MMK method provides higher prediction accuracy and is more reliable computationally compared to other techniques.
SGD's training dynamics align with Hessian and gradient spectra in high-dimensional classification tasks.
problem Understanding the spectra of Hessian and gradient matrices in high-dimensional classification tasks.
method Rigorous analysis of SGD dynamics and spectra of Hessian and gradient matrices.
result SGD trajectory and emergent outlier eigenspaces align with a common low-dimensional subspace in multi-class high-dimensional mixtures and neural networks.
New classifiers for HDLSS data classify without tuning, robustly.
problem Classification of high-dimensional data with small samples.
method Data-adaptive energy distance classifiers, free of tuning parameters.
result Perfect classification in HDLSS asymptotic regime under general conditions.
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a bridge to connect the estimation error of the mean difference and the misclassificat…
New method for tensor classification with missing data.
problem Handling incomplete tensor data in high-dimensional classification.
method High-dimensional tensor linear discriminant analysis with TGMM and Tensor LDA-MD.
result Established convergence rates and minimax optimal bounds for misclassification rate.
High-dimensional classification problems with Barron regular boundaries under margin conditionscs.LG
Neural networks can approximate high-dimensional classifiers with ReLU networks under margin conditions.
problem Approximating high-dimensional discontinuous classifiers with neural networks.
method Using ReLU neural networks with three hidden layers, approximating a classifier with a Barron-regular decision boundary.
result High-dimensional discontinuous classifiers can be approximated with a rate of under strong margin conditions.
The paper optimizes hyperplanes for binary classification in high-dimensional data with latent Gaussian mixtures.
problem Binary classification in high-dimensional data with latent Gaussian mixtures.
method Generalized least squares estimator for estimating the direction of the optimal separating hyperplane. Simple correction for intercept estimation.
result The procedure is minimax optimal in many scenarios and can retain the interpolation property.
A new QDA classifier for high-dimensional data with spiked covariance.
problem Classifying high-dimensional data with distinct covariance matrices.
method Proposes a novel quadratic classification technique with parameters chosen to maximize the fisher-discriminant ratio.
result The proposed classifier outperforms classical R-QDA and requires lower computational complexity.
Classification is an important topic in statistics and machine learning with great potential in many real applications. In this paper, we investigate two popular large margin classification methods, Support Vector Machine (SVM) and Distance Weighted Discrimination (DWD), under two contexts: the high-dimensional, low-sa…
Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.
problem Lack of inference procedures for identifying driving factors in high-dimensional classification with non-differentiable surrogate losses.
method Kernel-smoothed decorrelated score and cross-fitted version for hypothesis tests and interval estimators.
result Valid and superior inference methods for high-dimensional classification with non-differentiable surrogate losses.
The paper develops a method for optimal projection selection in high-dimensional classification.
problem High-dimensional classification with latent variable structure.
method Formulates a latent-variable model and proposes a computationally efficient classifier.
result Explicit rates of convergence for excess risk of the proposed classifier are derived and shown to be optimal.
Weakly Supervised-Based Oversampling for High Imbalance and High Dimensionality Data Classificationcs.LG
This paper tackles imbalanced classification with weakly supervised oversampling.
problem Imbalanced classification in high-dimensional datasets.
method Weakly supervised SMOTE, cost-sensitive NCA, bootstrap ensemble.
result Improved classification performance on synthetic and real-world datasets.
A new algorithm efficiently selects features for functional data classification.
problem Feature selection and classification of functional data in high-dimensional spaces.
method Developed a novel optimization problem integrating logistic loss and functional features. Employed functional principal components and a new adaptive Dual Augmented Lagrangian algorithm for efficient minimization.
result FSFC outperforms other methods in computational time and classification accuracy.
The paper improves classification accuracy by leveraging a shared signal across domains in high-dimensional classification.
problem Improving classification accuracy in high-dimensional data with shared signals across domains.
method Transfer learning for linear discriminant analysis, decomposing mean differences into common and domain-specific components.
result Deterministic limits for transfer performance, leading to optimal weights and corrections for bias.
Paper analyzes multiclass classification with high-dimensional data.
problem Understanding statistical properties and behavior of multiclass classification algorithms.
method Asymptotic analysis of linear multiclass classification.
result Test error varies significantly across different training algorithms and data distributions.
Study reveals how high-dimensional models are vulnerable to consistent adversarial attacks.
problem Understanding the vulnerability of high-dimensional linear classifiers to adversarial attacks.
method Introducing a new error metric to quantify model vulnerability, and rigorously characterizing these metrics in asymptotic settings.
result As models become more overparameterized, their vulnerability to label-preserving perturbations increases.
Trans-GCR uses GCR model for node classification, providing theoretical guarantees and superior performance.
problem Challenges in obtaining node classification labels in real-world scenarios.
method Graph Convolutional Multinomial Logistic Regression (GCR) model and transfer learning method based on GCR.
result Trans-GCR provides superior empirical performance and theoretical guarantees.
Grassmannian diffusion maps based dimension reduction and classification for high-dimensional datacs.LG
GDMaps reduces high-dimensional data to lower dimensions for better classification.
problem High-dimensional data classification and representation.
method Grassmannian Diffusion Maps technique for nonlinear dimensionality reduction.
result GDMaps effectively identifies intrinsic subspace structures in high-dimensional data.
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are considered. Focusing on the fundamental problem of separating a two-class Gauss…
New methods implement manifold scattering transform for high-dimensional point cloud data.
problem Classifying data on complex, non-linear manifolds.
method Adapting diffusion maps theory for numerical implementation.
result Effective for signal and manifold classification tasks.
A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work quite accurately; the structure of the data in such problems is easy to uncover wi…
Classifies hyperbolic manifolds with specific automorphism groups.
problem Classifying Kobayashi-hyperbolic manifolds with high-dimensional automorphism groups.
method Analyzes manifolds of dimension with automorphism groups of dimensions or .
result Completes the classification for automorphism groups and .
Proposes a novel classification criterion for high-dimensional data with few samples.
problem Challenges in classifying high-dimensional data with limited samples.
method Tolerance similarity criterion and No-separated Data Maximum Dispersion classifier (NPDMD).
result NPDMD outperforms state-of-the-art methods in various real-world applications.
SEDA improves RLDA for high-dimensional data.
problem Inconsistent performance of RLDA in high-dimensional scenarios.
method Developed a non-asymptotic approximation of misclassification rate, derived new theoretical results on eigenvectors, and proposed SEDA algorithm.
result SEDA achieves higher classification accuracy and dimensionality reduction compared to existing LDA methods.
New framework classifies high-dimensional shapes using ray intersections, establishing data requirements.
problem Classifying high-dimensional shapes in real-world data.
method Ray-based classification (RBC) framework using intersections of one-dimensional representations (rays) with shape boundaries.
result Established bounds on the number of rays necessary for shape classification, defined by key angular metrics.
New Hard-thresholding Rules based on Data Splitting in High-dimensional Imbalanced Classificationstat.ME
New method improves classification accuracy in imbalanced high-dimensional data.
problem Imbalanced classification in high-dimensional data.
method Data splitting and hard-thresholding rules for LDA.
result Proposed method reduces misclassification rates in minority class.
A new PCA-based imputation method for high-dimensional data.
problem Missing data in high-dimensional datasets.
method Principal Component Analysis Imputation (PCAI) framework.
result PCAI significantly speeds up imputation and maintains high accuracy.
A new method for high-dimensional data classification reduces misclassification errors.
problem High-dimensional data classification with limited samples.
method Compressive Regularized Discriminant Analysis (CRDA) using joint-sparsity promoting hard thresholding and regularized covariance matrix estimators.
result CRDA gives fewer misclassification errors than competitors and accurately selects features.
Paper tackles imbalanced time series classification with a novel oversampling method.
problem Imbalanced time series classification challenges due to high dimensionality and correlation.
method Density-ratio based clustering followed by shrinkage technique for covariance estimation, then generating synthetic samples.
result OHIT outperforms state-of-the-art methods in F1, G-mean, and AUC metrics.
We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contribu…
For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important problem of estimating high dimensional covariance matrix. Then we explore some …
Characterizes uncertainty in high-dimensional linear classification models.
problem Assessing uncertainty in high-dimensional linear classification models.
method Approximate message passing algorithm for posterior marginals, closed-form formula for joint statistics.
result Closed-form formula for joint statistics between logistic classifier, Bayesian uncertainty, and ground-truth probit uncertainty.
The paper develops a statistical theory explaining overfitting in imbalanced classification.
problem Overfitting in high-dimensional imbalanced classification.
method Developed a statistical theory for support vector machines and logistic regression.
result Overfitting is more severe for the minority class due to truncation or skewing effects in high-dimensional data.
Quantum machine learning model for binary classification.
problem Efficiency in high-dimensional binary classification tasks.
method Quantum-classical hybrid algorithm and quantum computer for inference.
result Quantum discriminator achieves 99% accuracy on Iris dataset.
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability bounds on the estimated sparsity as well as on the excess misclassification ris…