Related papers: Learning a hyperplane regressor by minimizing an e…
Support vector machines (SVM) can classify data sets along highly non-linear decision boundaries because of the kernel-trick. This expressiveness comes at a price: During test-time, the SVM classifier needs to compute the kernel…
Since Hamming distances can be calculated by bitwise computations, they can be calculated with less computational load than L2 distances. Similarity searches can therefore be performed faster in Hamming distance space. The elements of…
Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is…
Model predictive control (MPC) has established itself as the primary methodology for constrained control, enabling general-purpose robot autonomy in diverse real-world scenarios. However, for most problems of interest, MPC relies on the…
Hyperdimensional computing (HDC) is a method to perform classification that uses binary vectors with high dimensions and the majority rule. This approach has the potential to be energy-efficient and hence deemed suitable for…
Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…
We derive an objective function that can be optimized to give an estimator of the Vapnik- Chervonenkis dimension for model selection in regression problems. We verify our estimator is consistent. Then, we verify it performs well compared to…
Explaining the unreasonable effectiveness of deep learning has eluded researchers around the globe. Various authors have described multiple metrics to evaluate the capacity of deep architectures. In this paper, we allude to the radius…
Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Furthermore, the conic-segmentation SVM (CS-SVM) is a natural multiclass analogue of the standard binary SVM, as CS-SVM models are dealing…
We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its…
We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to…
Considering the classification problem, we summarize the nonparallel support vector machines with the nonparallel hyperplanes to two types of frameworks. The first type constructs the hyperplanes separately. It solves a series of small…
Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…
Relevance Vector Machine (RVM) is a supervised learning algorithm extended from Support Vector Machine (SVM) based on the Bayesian sparsity model. Compared with the regression problem, RVM classification is difficult to be conducted because…
This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…
Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…
Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…
Hyperplane hashing aims at rapidly searching nearest points to a hyperplane, and has shown practical impact in scaling up active learning with SVMs. Unfortunately, the existing randomized methods need long hash codes to achieve reasonable…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…