Related papers: Asymptotic Normality of Support Vector Machine Var…
In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…
Typically, nonlinear Support Vector Machines (SVMs) produce significantly higher classification quality when compared to linear ones but, at the same time, their computational complexity is prohibitive for large-scale datasets: this…
Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) \citep{jacot2018neural}. Under the squared loss, the infinite-width NN trained…
Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of classification tasks. In this work, we consider extending classical SVMs with quantum kernels and applying them to satellite data analysis.…
We propose $\ell_1$ norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish their desired theoretical properties, including the existence and uniqueness of the optimal…
We review the concept of support vector machines (SVMs) and discuss examples of their use. One of the benefits of SVM algorithms, compared with neural networks and decision trees is that they can be less susceptible to over fitting than…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
The support vector machines (SVM) algorithm is a popular classification technique in data mining and machine learning. In this paper, we propose a distributed SVM algorithm and demonstrate its use in a number of applications. The algorithm…
This paper presents a review on methods for class-imbalanced learning with the Support Vector Machine (SVM) and its variants. We first explain the structure of SVM and its variants and discuss their inefficiency in learning with…
A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding tasks where neural variability may…
Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma_n Z_i$ and the $Y$'s and $Z$'s are independent. Assume that the $Y$'s are unobservable and that they have the density $f$ and also that the $Z$'s have a known density $k.$…
The support vector machine (SVM) is a powerful and widely used classification algorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into the behavior of SVM. These insights…
The huge amount of available data nowadays is a challenge for kernel-based machine learning algorithms like SVMs with respect to runtime and storage capacities. Local approaches might help to relieve these issues and to improve statistical…
This article studies global testing of the slope function in functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The…
This paper develops asymptotic normality results for individual coordinates of robust M-estimators with convex penalty in high-dimensions, where the dimension $p$ is at most of the same order as the sample size $n$, i.e, $p/n\le\gamma$ for…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…
We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
Software defect prediction is an essential task during the software development Lifecycle as it can help managers to identify the most defect-proneness modules. Thus, it can reduce the test cost and assign testing resources efficiently.…