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Maths for Machine Learning

This Wiki Site is basically somewhere where we can maintain a list of required maths for machine learning research. Basically if you are probably going to need to use it sometime, it should go in here.

The aim is to collate stuff at this stage. Then we will sort it and work through it. Though possibly unlikely, we may end up sorting this out and publishing it. So at the moment anything posted may be used by someone else to aid or as part of a publication that is not in your name. Basically if you want to maintain copyright don't put it on here. Realistically though that is unlikely to be an issue. Really a list of things we think people need to know (at all levels) would be useful.

e.g.

How to integrate scalar fields over submanifolds, and hence how to deduce the probability density that is induced by a higher dimensional distribution on a conditioned submanifold -- P(s|P(x),x=f(s)) -- for s,x vectors in R^m,R^n, m<n. See http://www.math.duke.edu/~wka/math204/intman.pdf. Avoid the usual 3D restriction stuff.

Basic vector calculus without the physics: vector calculus without any focus on 3 Dimensions (mainly ignore cross product stuff). But possibly with 3D examples to help with intuition.

Differentiation of vectors matrices wrt vectors matrices etc. The use of summation convention and a systematic overview of shortcuts. A quick introduction to mathematica for this purpose.

An optimization handbook. Different types of optimization scenarios, and pointers to methods for solution without going into gory details (e.g. Interior point versus other methods). Basically what method set to use when. Pointers to actual working implementations.

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-- AmosStorkey - 02 Nov 2007