A parsimonious personalized dose-finding model via dimension reduction

Model Approximation via Dimension Reduction

In the initial stages of refining a mathematical model of a real-world dynamical system, one is often confronted with many more variables and coupled differential equations than one intuitively feels should be sufficient to describe the system. Yet none of the variables may seem so irrelevant as to be excludable nor so dominant as to explain the overall dynamics. Part of the problem might even ...

Efficiently Finding the Most Parsimonious Phylogenetic Tree Via Linear Programming

Reconstruction of phylogenetic trees is a fundamental problem in computational biology. While excellent heuristic methods are available for many variants of this problem, new advances in phylogeny inference will be required if we are to be able to continue to make effective use of the rapidly growing stores of variation data now being gathered. In this paper, we introduce an integer linear prog...

Dimension reduction via principal variables

For many large-scale datasets it is necessary to reduce dimensionality to the point where further exploration and analysis can take place. Principal variables are a subset of the original variables and preserve, to some extent, the structure and information carried by the original variables. Dimension reduction using principal variables is considered and a novel algorithm for determining such p...

Dimension Reduction via Colour Refinement

Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into “colour classes” in such a way that all vertices in the same colour class have the same number of neighbours in every colour class. Tinhofer [27], Ramana, Scheinerman, and Ullman [23] and Godsil [12] est...

A mixture model for dimension reduction