Robust Regression Based on Infinitesimal Neighbourhoods

Robust Regression Based on Infinitesimal Neighibourhoods

Histograms of Infinitesimal Neighbourhoods

Image analysis methods that use histograms defined over non-zero-sized local neighbourhoods have been proposed [1-4]. To better understand such methods, one can study the histograms of infinitesimal neighbourhoods. In this paper we show how the properties of such histograms can be derived through limit arguments. We show that in many cases the properties of these histograms are given by simple ...

Building Infinitesimal Neighbourhoods of Varieties

We develop a deformation-type tool for the study of embeddings of a singular variety X . Given a variety X ⊂ Y there is a natural series of schemes X = X0 ⊂ X1 ⊂ X2 . . . ⊂ Y of infinitesimal neighbourhoods of X defined as follows Xn = zero(I n X/Y ). Under certain assumptions, we calculate the obstructions to the existence of infinitesimal neighbourhoods and classify them when they exist.

Robust PLS regression based on simple least median squares regression

Robust Kernel-Based Regression

In this research, a robust optimization approach applied to support vector regression (SVR) is investigated. A novel kernel based-method is developed to address the problem of data uncertainty where each data point is inside a sphere. The model is called robust SVR. Computational results show that the resulting robust SVR model is better than traditional SVR in terms of robustness and generaliz...