The curse of dimensionality

On Bias, Variance, 0/1 - Loss, and the Curse of Dimensionality

The purpose of this document is to summarize the main points from the paper, “On Bias, Variance, 0/1 Loss, and the Curse of Dimensionality”, written by Jerome H.Friedman(1997).

Several Approaches to Break the Curse of Dimensionality

Using Randomization to Break the Curse of Dimensionality

This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the “curse of dimensionality” for a subclass of MDPs known as discrete decision processes (DDPs).

Curse of Dimensionality and k-NN

High Dimensional Integration: New Weapons Fighting the Curse of Dimensionality

Remember the Curse of Dimensionality: The Case of Goodness-of-Fit Testing in Arbitrary Dimension

Despite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions, there is no mention there of any curse of dimensionality. In fact, in some publications, a parametric rate is derived. As we discuss below, this is because a directional alternative is considered. Indeed, even in dimension one, Ingster (1987) has shown that the minimax rate is not param...