![]() The second generalizes the subgaussian technique to other Orlicz norms. The first enables one to replace the independence assumption by appropriate strong mixing. We give two extensions of the basic concentration result. If you are working in an abstract metric space, without any assumed vector space structure. In some sense, you replace xn < M x n < M with d(x,xn) < M d ( x, x n) < M. This yields a novel risk bound for some regularized metric regression algorithms. A sequence is bounded if it is contained in a ball, so x X, M > 0 x X, M > 0 such that (xn) BM(x) ( x n) B M ( x ). Keywords Boundary regularity Metric space p-Harmonic function Semibarrier. As an application, we give apparently the first generalization bound in the algorithmic stability setting that holds for unbounded loss functions. pharmonic functions on unbounded sets in metric spaces. Our technique provides an alternative approach to that of Kutin and Niyogi’s method of weakly difference-bounded functions, and yields nontrivial, dimension-free results in some interesting cases where the former does not. To this end, we introduce the notion of the \em subgaussian diameter, which is a distribution-dependent refinement of the metric diameter. TI - Concentration in unbounded metric spaces and algorithmic stabilityīT - Proceedings of the 31st International Conference on Machine LearningĭP - Proceedings of Machine Learning ResearchĪB - We prove an extension of McDiarmid’s inequality for metric spaces with unbounded diameter. ![]() ![]() This yields a novel risk bound for some regularized metric regression algorithms. As an application, we give apparently the first generalization bound in the algorithmic stability setting that holds for unbounded loss functions. ![]() %X We prove an extension of McDiarmid’s inequality for metric spaces with unbounded diameter. %C Proceedings of Machine Learning Research %B Proceedings of the 31st International Conference on Machine Learning %T Concentration in unbounded metric spaces and algorithmic stability A flow field is defined by the superposition of a linear flow field and a. The trichotomy between regular, semiregular, and strongly irregular boundary points for (p)-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a (p)-Poincaré inequality, (1 space whose elements are points, and between any two of which a non-negative real number can be defined as the distance between the points ….a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the.A Distance Metric Space is a 2-tuple \displaystyle for a metric space if it is clear from the context what metric is used.
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