<p style='text-indent:20px;'>We study the problem of minimizing sum two functions. The first function is average a large number nonconvex component functions and second convex (possibly nonsmooth) that admits simple proximal mapping. With diagonal Barzilai-Borwein stepsize for updating metric, we propose variable metric stochastic variance reduced gradient method in mini-batch setting, na...

We consider space-cutoff P (φ)2 models with a variable metric of the form

Nearest-neighbour interpolation algorithms have many useful properties for applications to learning, but they often exhibit poor generalization. In this paper, it is shown that much better generalization can be obtained by using a variable interpolation kernel in combination with conjugate gradient optimization of the similarity metric and kernel size. The resulting method is called variable-ke...

We define the notions of unilateral metric derivatives and “metric derived numbers” in analogy with Dini derivatives (also referred to as “derived numbers”) and establish their basic properties. We also prove that the set of points where a path with values in a metric space with continuous metric derivative is not “metrically differentiable” (in a certain strong sense) is σsymmetrically porous ...

We consider the problem of the global convergence of gradient-based optimization algorithms for interstitial high-dose-rate (HDR) brachytherapy dose optimization using variance-based objectives. Possible local minima could lead to only sub-optimal solutions. We perform a configuration space analysis using a representative set of the entire non-dominated solution space. A set of three prostate i...

Current findings from genetic studies of complex human traits often do not explain a large proportion of the estimated variation of these traits due to genetic factors. This could be, in part, due to overly stringent significance thresholds in traditional statistical methods, such as linear and logistic regression. Machine learning methods, such as Random Forests (RF), are an alternative approa...

In this article, we give a perspective on several results, old and new, concerning geometric structures of moduli spaces of Riemann surfaces with respect to the L2 metric (Weil-Petersson metric) on deformations of hyperbolic metrics. In doing so, we aim to demonstrate that the Weil-Petersson metric is suited to account for the geometry of moduli spaces while the topological type, genus in parti...

In some applications of statistical process monitoring, a quality characteristic can be characterized by linear regression relationships between several response variables and one explanatory variable, which is referred to as a “multivariate simple linear profile.” It is usually assumed that the process parameters are known in Phase II. However, in most applications, this assumption is viola...