Nearly Optimal Bernoulli Factories for Linear Functions

Optimal linear Bernoulli factories for small mean problems

Suppose a coin with unknown probability p of heads can be flipped as often as desired. A Bernoulli factory for a function f is an algorithm that uses flips of the coin together with auxiliary randomness to flip a single coin with probability f(p) of heads. Applications include perfect sampling from the stationary distribution of certain regenerative processes. When f is analytic, the problem ca...

nearly optimal linear programming and its application in farm management

linear programming has been employed in many areas of constrained optimization including in agricultural planning for a long time. one of the most important disadvantages of such a method is that there is only one optimum solution for a given objective function and constraints set. another method named nearly optimal linear programming has been developed for solving the problem. this method can...

Nearly Optimal Minimax Estimator for High Dimensional Sparse Linear Regression

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints (`q constraint with 0 < q ≤ 1) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic ...

FME ® Functions and Factories

Sample-Optimal Density Estimation in Nearly-Linear Time

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let f be the density function of an arbitrary univariate distribution, and suppose that f is OPT close in L1-distance to an unknown piecewise polynomial function with t interval pieces and degree d. Our algorithm draws n = O(t(d+...