Guide for using Mapper for explaining a machine learning model.
We will demonstrate a novel application of Mapper to the domain of explanatory machine learning and show how Mapper can be used to understand not just the shape of data, but also understand a machine learning model.
Fundamental concepts of Mapper and Multiscale Mapper.
In unsupervised learning, one of the main questions we want to answer is what type of structure does this set or shape have? The field of algebraic topology supplies a few tools to help answer this question. We can ask topological questions about the data, such as how many clusters or connected components are there? or are there gaps, holes, or voids in the data?. These question can be easy to answer if the shape is well defined, but in practice, we instead have data sampled from that shape. If…
An introduction to nerves, one of the fundamental building blocks of TDA.
The nerve is a simplicial complex built from a cover. It is a discrete summarization of the cover that captures the interesting topological features. Additionally, if the cover is sufficiently refined, then the nerve is guaranteed to preserve the topological features. A nerve of a cover is constructed in a very straight forward way: An (n-1)-dimensional simplex is added for each nonempty n-way intersection of elements of the cover.
An introduction to towers, an extension of mapper to the world of persistence.
Once we understand the tower, we will show that it plays nice with all of the other definitions we have constructed so far and how it allows us to naturally define a multiscale mapper.
Understanding of mapper from the ground up.
As one of the main tools from the field of Topological Data Analysis, Mapper has been shown to be particularly useful for exploring high dimensional point cloud data. This post will walk through the mapper construction from an intuitive perspective and demonstrate how it can be constructed on a toy example.
A very basic introduction to Topological Data Analysis
The traditional process of the scientific method is to create a hypothesis, design an experiment, collect specific data, and then analyze the results. With modern advances, data collection has become so cheap that it is often collected before we even know what to look for. The scientific method is being flipped on end.Data is being Now, the hard part in the process is sifting through the piles of data and figuring out what to questions to ask. New methods of analysis are emerging to help us…
Machine Learning Engineer focused on agile ML.
I’ve joined OpenSesame as Machine Learning Software Engineer to work on search and recommendation!
I’ve started a new position as Machine Learning Software Engineer at New Relic!
I finished my Masters in Mathematics at Washington State University of Vancouver!
My abstract on Jaccard Filtrations has been accepted to the Young Researchers Forum at SoCG.