Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning high-dimensional statistics area. We obtain sharper constants-specified for sum independent sub-Weibull random variables, which leads to a mixture two tails: sub-Gaussian small deviations large from mean. These bounds are new improve existing with constants. In ad...

LetG be a Polish group, τ a Polish topology on a spaceX, G acting continuously on (X, τ), with B ⊂ X G-invariant and in the Borel algebra generated by τ . Then there is a larger Polish topology τ ⊃ τ on X so that B is open with respect to τ, G still acts continuously on (X, τ), and τ has a basis consisting of sets that are of the same Borel rank as B relative to τ . 1

Occam’s razor is the principle that, given two hypotheses consistent with the observed data, the simpler one should be preferred. Many machine learning algorithms follow this principle and search for a small hypothesis within the version space. The principle has been the subject of a heated debate with theoretical and empirical arguments both for and against it. Earlier empirical studies lacked...

The Korkine–Zolotareff (KZ) reduction and its generalisations, are widely used lattice strategies in communications cryptography. KZ constant Schnorr’s were defined by Schnorr 1987. can be to quantify some useful properties of reduced matrices. characterize the output quality his block 2k-reduction is define semi 2k-reduction, which was also developed Hermite’s constant, a fundamental has many ...

Digital hydrographic maps have transformed global environmental studies and resource management. A major database update will provide even clearer more complete views of Earth’s waterways.