arXiv subjects

Patrick Laurie Davies

Publications and source records attributed to Patrick Laurie Davies.

2 recordsLinked to original sources

arXiv2018

Unsupervised nonparametric detection of unknown objects in noisy images based on percolation theory

We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes and sizes in the presence of nonparametric noise of unknown level. The noise density is assumed to be unknown and can be very irregular. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove strong consistency and scalability of our method in this setup with minimal assumptions.

math.ST↗

arXiv2016

On stepwise regression

Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$ is large then some other procedure must be use. Stepwise regression and the lasso are two such procedures but they both assume a linear model with error term. A different approach is taken here which does not assume a model. A covariate is included if it is better than random noise. This defines a procedure which is simple both conceptually and algorithmically

math.ST↗