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Chris Cave

Publications and source records attributed to Chris Cave.

6 recordsLinked to original sources
arXiv2021

An Approach to Symbolic Regression Using Feyn

In this article we introduce the supervised machine learning tool called Feyn. The simulation engine that powers this tool is called the QLattice. The QLattice is a supervised machine learning tool inspired by Richard Feynman's path integral formulation, that explores many potential models that solves a given problem. It formulates these models as graphs that can be interpreted as mathematical equations, allowing the user to completely decide on the trade-off between interpretability, complexity and model performance. We touch briefly upon the inner workings of the QLattice, and show how to apply the python package, Feyn, to scientific problems. We show how it differs from traditional machine learning approaches, what it has in common with them, as well as some of its commonalities with symbolic regression. We describe the benefits of this approach as opposed to black box models. To illustrate this, we go through an investigative workflow using a basic data set and show how the QLattice can help you reason about the relationships between your features and do data discovery.

cs.LG↗
arXiv2017

Exactness of locally compact groups

We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact second countable group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.

math.GR↗
arXiv2014

Embeddings of locally compact hyperbolic groups into Lp-spaces

In the last years, there has been a large amount of research on embeddability properties of finitely generated hyperbolic groups. In this paper, we elaborate on the more general class of locally compact hyperbolic groups. We compute the equivariant $L_p$-compression in a number of locally compact examples, such as the groups $SO(n,1)$: by proving that the equivariant $L_p$-compression of a locally compact compactly generated group is minimal for $p=2$, we calculate all equivariant $L_p$-compressions of $SO(n,1)$. Next, we show that although there are locally compact, non-discrete hyperbolic groups $G$ with Kazhdan's property ($T$), it is true that any locally compact hyperbolic group admits a proper affine isometric action on an $L_p$-space for $p$ larger than the Ahlfors regular conformal dimension of $\partial G$. This answers a question asked by Yves de Cornulier. Finally, we elaborate on the locally compact version of property $(A)$ and show that, as in the discrete case, a locally compact second countable group has property (A) if its non-equivariant compression is greater than 1/2.

math.GR↗
arXiv2013

Embeddability of generalized wreath products and box spaces

Given two finitely generated groups that coarsely embed into a Hilbert space, it is known that their wreath product also embeds coarsely into a Hilbert space. We introduce a wreath product construction for general metric spaces X,Y,Z and derive a condition, called the (delta-polynomial) path lifting property, such that coarse embeddability of X,Y and Z implies coarse embeddability of X\wr_Z Y. We also give bounds on the compression of X\wr_Z Y in terms of delta and the compressions of X,Y and Z. Next, we investigate the stability of the property of admitting a box space which coarsely embeds into a Hilbert space under the taking of wreath products. We show that if an infinite finitely generated residually finite group H has a coarsely embeddable box space, then G\wr H has a coarsely embeddable box space if G is finitely generated abelian. This leads, in particular, to new examples of bounded geometry coarsely embeddable metric spaces without property A.

math.GR↗