The Deepest Recorded Fishes

The Deepest Regression Method

Deepest regression (DR) is a method for linear regression introduced by Rousseeuw and Hubert [20]. The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with breakdown value that converges almost surely to 1/3 in any dimension. We construct an approximate algorithm for fast computation of DR in more than two dim...

Deepest Neural Networks

This paper shows that a long chain of perceptrons (that is, a multilayer perceptron, or MLP, with many hidden layers of width one) can be a universal classifier. The classification procedure is not necessarily computationally efficient, but the technique throws some light on the kind of computations possible with narrow and deep MLPs.

Asymptotics Of The Deepest Line

Implications of the Deepest Freshest Lunar Craters

Lunar Topographic Orthophoto maps (LTO) at 1:250 k scale have been used as a basis to measure the depth (dr and ds), diameter (D), and rim height (Hr) for 359 fresh Lunar craters in the diameter range of .08 – 131 km along the Apollo metric camera ground tracks. This study used LTO maps with high enough sun angle photography to permit deep crater depth measurements. This includes an area of ~ 3...

Deepest Regression in Analytical Chemistry

Recently the concept of regression depth has been introduced [1]. The deepest regression (DR) is a method for linear regression which is defined as the fit with the best depth relative to the data. In this paper we explain the properties of the DR and give some applications of deepest regression in analytical chemistry which involve regression through the origin, polynomial regression, the Mich...