L3-SVMs clusters data, reduces dimensions, and learns linear models.
problem Capturing non-linearities and scaling to large datasets.
method Clusters input space, projects data onto landmarks, learns linear combination of local models.
result L3-SVMs achieves generalization guarantees and competitive performance. Paper develops distributed inference for SVM binary classification.
problem Challenges in modern data size for existing statistical inference.
method Proposes MDL estimator for linear SVM, computationally efficient.
result MDL estimator achieves optimal statistical efficiency.
Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a great deal of samples as well as a large number of features. In this paper, thus…
This paper presents a unified framework to tackle estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The use of SVMs in estimation problems has been traditionally limited to its mere use as a black-box model. Noting such limitations in the literature, we take advantage of sever…
A quantum-inspired classical algorithm speeds up LS-SVM classification.
problem Big data challenge in SVM classification.
method Improved indirect sampling technique for LS-SVM.
result Algorithm achieves logarithmic runtime for low rank data matrices.
Exact solver speeds up Weston-Watkins SVM subproblem significantly.
problem Improving performance of Weston-Watkins multiclass SVM.
method Novel reparametrization for exact subproblem solving.
result Significant speed-up over state-of-the-art solvers for large number of classes.
GADGET SVM uses gossip-based distributed learning for scalable SVMs.
problem Scalability issues in traditional SVM algorithms for large datasets.
method Gossip-based distributed learning for the primal SVM formulation.
result Performance comparable to centralized and online SVM algorithms.
Faster algorithms for structured SVMs reduce computation time.
problem Efficiently solving quadratic programming problems with specific structures.
method Designing nearly-linear time algorithms for quadratic programs with low-rank factorizations and few linear constraints.
result First nearly-linear time algorithms for solving quadratic programs with specific structures.
Localized SVMs maintain SVM's consistency properties for large datasets.
problem Inefficient computational requirements of global SVMs for large data sets.
method Localized SVMs apply different hyperparameters to different regions of the input space.
result Localized SVMs inherit Lp- and risk consistency from global SVMs. Extends linear classification framework to nonlinear SVM-based ranking problems.
problem Maximizing performance on relevant samples in ranking problems.
method Dualization, kernel addition, componentwise dual ascent method.
result General framework for nonlinear classifiers in ranking problems.
Tropical SVM tackles phylogenomics by classifying multi-locus data.
problem Classifying multi-locus data sets for phylogenetic analysis.
method Proposes tropical support vector machines (SVMs) for phylogenomics, formulated as linear programming problems.
result Developed methods for hard and soft margin tropical SVMs, proving necessary and sufficient conditions for separation.
AdaGrad on linear problems converges to SVM direction.
problem Understanding AdaGrad's implicit bias on linear classification.
method Characterizing AdaGrad's convergence direction as a quadratic optimization problem.
result AdaGrad converges to a direction similar to SVM's solution.
When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection techniques have been successfully used in the SVM to perform automatic variable selec…
Quantum SVM uses fewer features for faster training.
problem Training high-dimensional SVMs efficiently.
method Quantum linear programming for sparse SVM training.
result Quantum sparse SVM can be trained in sublinear time.
This paper uses MIO to select features for kernel SVM classification.
problem Feature selection for kernel SVM classification.
method Mixed-integer optimization (MIO) for feature subset selection.
result The MIO approach can often outperform linear-SVM-based methods in prediction performance.
Paper addresses SVM bias in high-dimension, low-sample-size settings.
problem Bias in SVM performance in high-dimension, low-sample-size settings.
method Proposes a bias-corrected SVM (BC-SVM) to improve SVM performance.
result BC-SVM gives preferable performances in high-dimension, low-sample-size settings.
Paper shows SVMs can interpolate data in various settings.
problem Understanding SVM performance and generalization.
method Flexible analysis framework for proving SVM interpolation in diverse settings.
result Support vector machines can interpolate data in many cases not previously covered.
Conventional SVM-based image coding methods are founded on independently restricting the distortion in every image coefficient at some particular image representation. Geometrically, this implies allowing arbitrary signal distortions in an n-dimensional rectangle defined by the ε-insensitivity zone in eac…
Introduces Soft-SVM for binary classification bridging logistic and SVM.
problem Data separability issues in binary classification.
method Soft-SVM regression using convex relaxation of hinge loss with softness and class-separation parameters.
result Soft-SVM performs well in classification and prediction errors.
SVM and linear regression models coincide in high dimensions.
problem Understanding the connection between SVM and linear regression in high-dimensional data.
method Analyzing feature models and proving lower bounds on dimensionality.
result A sharp phase transition in Gaussian feature models, with support vector proliferation occurring only in very high dimensions.
Paper proposes a novel SVM method for creating survival trees.
problem Creating non-linear survival trees for right-censored data.
method L2-regularized dipole splitting criteria with kernel methods.
result Non-linear splits using polynomial and Gaussian kernels show similar predictive power but often smaller tree sizes.
Enhances SVM interpretability by integrating data priors.
problem Lack of interpretability in black-box models.
method Integrates data-based priors into soft-margin SVM to enhance interpretability.
result Proposes an interpretable SVM optimization model and solves it as a nonlinear quadratic programming problem.
SFM uses linear models in extended feature spaces to avoid kernel issues.
problem Difficulty in interpreting SVM solutions and limitations of single kernel types.
method Support Feature Machines (SFM) use linear models in extended feature spaces.
result SFM provides at least as good results as kernel-based SVMs without interpretation, scaling, and convergence issues.
The paper uses KKT conditions to reveal new insights into SVM behavior.
problem Understanding SVM behavior and tuning.
method Using Karush-Kuhn-Tucker conditions to explore SVM connections with other classifiers.
result SVM can be seen as a cropped version of mean difference and maximal data piling direction classifiers.
New algorithms solve L1-regularized SVMs and related LPs, outperforming existing methods.
problem Solving large-scale L1-regularized SVMs and related linear programs.
method Combining column/constraint generation with first-order methods for non-smooth convex optimization.
result Our approach significantly outperforms commercial solvers and specialized implementations.
This work simplifies SVM parameter selection using S&S ratio.
problem SVM parameter tuning for optimal performance.
method S&S ratio to model SVM performance; automatic RP, kernel, and parameter selection.
result Optimized SVM parameters with reduced computational complexity.
Recently, fully-connected and convolutional neural networks have been trained to achieve state-of-the-art performance on a wide variety of tasks such as speech recognition, image classification, natural language processing, and bioinformatics. For classification tasks, most of these "deep learning" models employ the so…
Proposes SVM-based Deep Stacking Network for improved deep learning.
problem Improving deep learning performance and interpretability.
method Uses stacked SVM classifiers within a DSN architecture and a BP-like layer tuning scheme.
result Demonstrates superior performance compared to benchmark models on image and text data.
The paper improves SVM and localized SVM stability under triple perturbations.
problem Stability of SVMs and localized SVMs under triple perturbations.
method Generalizes and improves existing results, considering simultaneous variations in probability measure, regularization parameter, and kernel.
result Improved stability of SVMs and localized SVMs under triple perturbations.
This paper improves SVM prediction uncertainty quantification methods.
problem Lack of comprehensive UQ methods for SVM predictions.
method Developed SSVQR model for sparse PI estimation and feature selection algorithm.
result Proposed SSVQR model achieves sparse solutions and improves PI quality.
A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method can be viewed as a hybrid of SVM and DWD that finds the classification directio…
In this paper, we propose to (seamlessly) integrate b-bit minwise hashing with linear SVM to substantially improve the training (and testing) efficiency using much smaller memory, with essentially no loss of accuracy. Theoretically, we prove that the resemblance matrix, the minwise hashing matrix, and the b-bit minwise…
One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that train SVMs on many small chunks of large data sets separately have been proposed in…
This paper compares TFC and LS-SVM for solving DEs, showing TFC is faster and more accurate.
problem Solving differential equations efficiently and accurately.
method Theory of Functional Connections (TFC) integrated with LS-SVM.
result TFC is faster and more accurate than LS-SVM for solving DEs.
Efficiently solves large-scale SVMs with sparse semismooth Newton method.
problem Numerical difficulties in solving large-scale SVMs.
method Sparse semismooth Newton based augmented Lagrangian method.
result Outperforms state-of-the-art solvers for large-scale SVMs.
Improved SRHT for linear SVM classification with higher accuracy.
problem Inefficient random projection methods for high-dimensional data.
method Importance sampling and deterministic top-r sampling for effective low-dimensional embedding. result Higher classification accuracy on real-life datasets.
Support vector machine (SVM) training is an active research area since the dawn of the method. In recent years there has been increasing interest in specialized solvers for the important case of linear models. The algorithm presented by Hsieh et al., probably best known under the name of the "liblinear" implementation,…
Paper proposes methods to improve SVM classifiers in noisy data scenarios.
problem Improving SVM classifiers when training data contains label noise.
method Mixed Integer Linear and Non Linear models with relabeling and clustering.
result Effective methods improve SVM performance in noisy data scenarios.
Paper tackles efficient SVM classification over decentralized networks.
problem Efficiently classifying high-dimensional data over decentralized networks.
method Convolution-based smoothing technique for nonsmooth hinge loss function, combined with an efficient ADMM algorithm.
result Provable linear convergence of the ADMM algorithm and near-optimal statistical convergence of the sparse estimator.
Algorithm improves SVM classification in non-Euclidean spaces.
problem Limitations of traditional SVM in non-Euclidean spaces.
method Covariance-adjusted SVM using Cholesky Decomposition.
result Cholesky-SVM outperforms traditional SVM in non-Euclidean spaces.
Optimal posterior distributions improve SVM classifiers and parameter selection.
problem Improving SVM classifiers and selecting optimal regularization parameters.
method PAC-Bayesian approach with optimal posterior identification for stochastic classifiers.
result Optimal posteriors yield tight risk bounds and improved SVM performance.
Improves SVM speed by 2 orders of magnitude for 12 out of 17 datasets.
problem Slowness of kernel classifiers like SVM for large problems.
method Piecewise linear classifier trained from kernel-based classifier.
result Improves classification speed by up to 2 orders of magnitude.
Paper proposes SVM-based methods for inferring interaction networks.
problem Modeling interaction between variables in time series and high dimensions.
method Two approaches: neighborhood SVM and restricted Bayesian network for time series.
result Efficiency demonstrated through simulations with linear and nonlinear data.
Paper proposes semi-supervised method for dictionary learning.
problem Learning from both labeled and unlabeled data.
method Uses semi-supervised dictionary learning with LLE for manifold preservation.
result Significant improvements over other methods demonstrated.
Support vector machines (SVMs) rely on the inherent geometry of a data set to classify training data. Because of this, we believe SVMs are an excellent candidate to guide the development of an analytic feature selection algorithm, as opposed to the more commonly used heuristic methods. We propose a filter-based feature…
Spatial SVM decompositions improve training and testing speed.
problem Expensive SVM optimization for large datasets.
method Spatially defined data chunks for decomposition.
result Decomposition significantly faster during testing and reduces test error.
SVM generalizes well even with many support vectors in high dimensions.
problem Generalization of SVM in high-dimensional spaces with many support vectors.
method Identified new deterministic equivalences and proved conditions for support vector proliferation.
result Broadened conditions for SVM generalization in high-dimensional settings and proved converse result.
Analyzes SVM classifier behavior with different parameters and data types.
problem Tuning SVM parameters for balanced and imbalanced data.
method Behavioral analysis of SVM with different parameters and data types, proposing a novel search algorithm.
result Proposed search algorithm reduces computational time and provides expected kernel function range.