Recent theoretical analyses of a class of unsupervized Hebbian principal component algorithms have identified its local stability conditions. The only locally stable solution for the subspace P extracted by the network is the principal component subspace P∗. In this paper we use the Lyapunov function approach to discover the global stability characteristics of this class of algorithms. The subs...

Manifold regularization is an approach which exploits the geometry of the marginal distribution. The main goal of this paper is to analyze the convergence issues of such regularization algorithms in learning theory. We propose a more general multi-penalty framework and establish the optimal convergence rates under the general smoothness assumption. We study a theoretical analysis of the perform...

Decomposition theorems are useful tools for bounding the convergence rates of Markov chains. The theorems relate the mixing rate of a Markov chain to smaller, derivative Markov chains, defined by a partition of the state space, and can be useful when standard, direct methods fail. Not only does this simplify the chain being analyzed, but it allows a hybrid approach whereby different techniques ...

This thesis describes a new approach to computing mean curvature and mean curvature normals on smooth logically Cartesian surface meshes. We begin by deriving a finite-volume formula for one-dimensional curves embedded in twoor threedimensional space. We show the exact results on curves for specific cases as well as second-order convergence in numerical experiments. We extend this finite-volume...

In this paper we study optimization problems with second-order stochastic dominance constraints. This class of problems allows for the modeling of optimization problems where a riskaverse decision maker wants to ensure that the solution produced by the model dominates certain benchmarks. Here we deal with the case of multi-variate stochastic dominance under general distributions and nonlinear f...

In this note we obtain necessary and sufficient conditions for a convergence space to have a smallest Hausdorff compactification and to have a smallest regular compactification. Introduction. A Hausdorff convergence space as defined in [1] always has a Stone-Cech compactification which can be obtained by a slight modification of the result in [3]. But in general this need not be the largest Hau...

Abstract In this paper, we look at the (Kajii and Ui) mixed equilibrium notion, which has been recognized by previous literature as a natural solution concept for incomplete information games in which players have multiple priors on the space of payoff relevant states. We investigate the problem of stability of mixed equilibria with respect to perturbations on the sets of multiple priors. We fi...

Keywords: Filter Modular space (Modular) filter convergence Rate of convergence Sampling operator Integral operator Urysohn operator Mellin convolution operator a b s t r a c t We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which...

We prove new convergence results for a class of multiscale trust–region algorithms introduced by Gratton et al. in [GST06] to solve unconstrained minimization problems within the Euclidean space R. We will state less restrictive assumptions on the function which has to be minimized and on the iteratively computed trust–region corrections, which allow for proving first– and second–order converge...