Related papers: A New Angle on L2 Regularization
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
Clustering aims to divide a set of points into groups. The current paradigm assumes that the grouping is well-defined (unique) given the probability model from which the data is drawn. Yet, recent experiments have uncovered several…
In these notes we study hyperplane arrangements having at least one logarithmic derivation of degree two that is not a combination of degree one logarithmic derivations. It is well-known that if a hyperplane arrangement has a linear…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
This paper is a continuation of an earlier one, and completes a classification of the configurations of points in a plane lattice that determine angles that are rational multiples of ${\pi}$. We give a complete and explicit description of…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
We investigate high-order harmonic spectra from aligned diatomic molecules in intense driving fields whose components have orthogonal polarizations. We focus on how the driving-field ellipticity influences structural interference patterns…
Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…
This is the second installment of an exposition of an ACL2 formalization of elementary linear algebra. It extends the results of Part I, which covers the algebra of matrices over a commutative ring, but focuses on aspects of the theory that…
It seems that the literature suggests to go in two opposing directions simultaneously. On the one hand, many papers construct basis-independent quantities, since exactly these quantities appear in the expressions for observables. This means…
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing…
A formal link between regression and classification has been tenuous. Even though the margin maximization term $\|w\|$ is used in support vector regression, it has at best been justified as a regularizer. We show that a regression problem…
This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of $\pi$. We shall study how many such angles may appear in a given lattice and in which positions, allowing the…
General expressions for the double-lepton polarizations in the (B -> K l^+ l^-) decay are obtained, using model independent effective Hamiltonian, including all possible interactions. Correlations between the averaged double-lepton…
We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…
The curvature on codimension-two and higher branes is not regular for arbitrary matter sources. Nevertheless, the low-energy theory for an observer on such a brane should be well-defined and independent to any regularization procedure. This…
Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…