Related papers: A New Angle on L2 Regularization
Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional…
We assess the possibility of determining the Hubble constant H_0 by measuring time delays between multiple images of supernovae gravitationally lensed by rich clusters of galaxies and combining these delay measurements with detailed…
We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…
Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…
We find a relation between the spectrum of solitons of massive $N=2$ quantum field theories in $d=2$ and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions…
The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds in dimension 2, and is asymptotically tight in fixed…
For many years it had been believed that steric compatibility of helix interfaces could be the source of the observed preference for particular angles between neighbouring helices as emerging from statistical analysis of protein databanks.…
Recently determined atomistic scale structures of near-two dimensional bilayers of vitreous silica (using scanning probe and electron microscopy) allow us to refine the experimentally determined coordinates to incorporate the known local…
Lenses are a mathematical structure for maintaining consistency between a pair of systems. In their ongoing research program, Johnson and Rosebrugh have sought to unify the treatment of symmetric lenses with spans of asymmetric lenses. This…
We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The…
The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise due to spatial clustering of the galaxies…
The localization length has been derived for one-dimensional bi-layered structures with random perturbations in the refractive indices for each type of layers. Main attention is paid to the comparison between conventional materials and…
Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model…
In this paper the usual $Z_2$ graded Lie algebra is generalized to a new form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there exists close connections between the $Z_{2,2}$ graded Lie algebra and parastatistics, so…
The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points in the plane with which are associated directions. At time 0, each line-segment starts…
A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
Understanding the formation and evolution of high mass star clusters requires comparisons between theoretical and observational data to be made. Unfortunately, while the full phase space of simulated regions is available, often only partial…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
In supersymmetric models, scalar top quarks, or stops, generically have parity-violating couplings to top quarks. As a result, tops produced in stop decays should be polarized. In this paper, we will argue that this effect may be observable…