منابع مشابه
Geometric Inference for Probability Measures
Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (e.g., Betti numbers, normals) of this subset from the approximating point cloud data. It appears that the study of distance functions allows to address many of these questions successfully. However...
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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 non-uniform) 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...
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Statistics arising in geometric probability can often be expressed as sums of stabilizing functionals, that is functionals which satisfy a local dependence structure. In this note we show that stabilization leads to nearly optimal rates of convergence in the CLT for statistics such as total edge length and total number of edges of graphs in computational geometry and the total number of particl...
متن کاملAlgebraic Geometric Comparison of Probability Distributions
We propose a novel algebraic algorithmic framework for dealing with probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by tr...
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We use differential geometry techniques to estimate the class probability P (y = l|x) for learning both binary and multiclass plug-in classifiers. We propose a geometric regularization technique to find the optimal submanifold corresponding to the estimator of P (y = l|x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces fast osci...
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ژورنال
عنوان ژورنال: Mathematical Modelling
سال: 1980
ISSN: 0270-0255
DOI: 10.1016/0270-0255(80)90047-0