作者：Talay, D; Vaillant, O
作者单位：Inria
摘要：We are interested in statistical solutions of McKean-Vlasov-Fokker-Planck equations. An example of motivation is the Navier-Stokes equation for the vorticity of a two-dimensional incompressible fluid flow. We propose an original and efficient numerical method to compute moments of such solutions. It is a stochastic particle method with random weights. These weights are defined through nonparametric estimators of a regression function and convey the uncertainty on the initial condition of the c...
作者：Penrose, MD; Yukich, JE
作者单位：Durham University; Lehigh University
摘要：Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly nonuniform) density of the point process. The general result is applied to the minimal spanning tree, the k-nearest neighbors graph, the Voronoi graph and the sphere of influence graph. Functionals of interest include total edge length with arbitrary weighting, number of vertices of specified degree...
作者：Koltchinskii, V; Panchenko, D; Lozano, F
作者单位：University of New Mexico; Pontificia Universidad Javeriana
摘要：A problem of bounding the generalization error of a classifier f is an element of conv(H), where H is a base class of functions (classifiers), is considered. This problem frequently occurs in computer learning, where efficient algorithms that combine simple classifiers into a complex one (such as boosting and bagging) have attracted a lot of attention. Using Talagrand's concentration inequalities for empirical processes, we obtain new sharper bounds on the generalization error of combined clas...
