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A Fully Polynomial Approximation Scheme for Approximating a Sum of Random Variables
Threshold probability Tail probability Approximate counting Counting knapsack FPTAS
2016/1/22
Given n independent integer-valued random variables X 1 , X 2 ,..., X n and an integer C, we study the fundamental problem of computing the probability that the sum X = X 1 + X 2 +···+ X n is at most ...
Efficient Density Estimation via Piecewise Polynomial Approximation
Efficient Density Estimation Piecewise Polynomial Approximation
2013/6/14
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary dis...
Polynomial Approximation in Sobolev Spaces on the Unit Sphere and the Unit Ball
Polynomial Sobolev Spaces Unit Sphere Unit Ball
2010/11/18
This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial ap...