机器学习中常用的数学知识（英文）
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2018-07-13
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Math for Machine Learning
Author: Parameswaran Raman
January 25, 2015
Abstract
In this post, I want to discuss the connections between Machine Learning and various other fields (especially
Mathematics), citing specific examples where they come up. I have given very high-level explanations below
and cut corners at several places as I do not want to get into the depth. My intention here is not to explain any
concept precisely, but to merely lay down enough of them on the table to emphasize the role of Mathematics
in this fast growing area.
1 Ok, why so much Math?
Machine Learning is an incredibly modern field that borrows heavily from several areas of Mathematics. Having
evolved as an inter-disciplinary field which is very applied (driven by data), it has captured concepts, intuition and
theory from several places. Being at such an intersection of diverse areas of mathematics and computer science is
what makes research in Machine Learning so exciting and challenging!
At this point, I would like to mention Physics as an analogy. I consider Machine Learning to be very similar
to Physics as a discipline, primarily because both are applied areas by nature, governed by deep mathematical
foundations. It turns out, much of the pre-requisite Math for Machine Learning (Multi-variable calculus, linear
algebra) applies to Physics too. Another similarity between the two fields is their philosophy and connection to the
real world. In both cases, we try to model the real world phenomena by coming up with hypothesis and backing
it up with experiments. While we might not be able to fit most of the happenings in the real world exactly, we
try to get as accurate as possible. This in turn leads us to a better understanding of the black-box that generates
events in the real world (or data in case of machine learning).
”Imagine being in a battlefield without knowing how to use the weapons you have, (or worse still, not having the
weapons at all)!”
That’s exactly how it feels when you set out to do research in machine learning without knowing enough about
the fundamental areas underlying it. Without the right intuition, it becomes very hard to build new algorithms
or extend existing ones.
Below are the key useful areas:
1.1 Algorithms & Complexity
Knowledge of basic data structures such as arrays/trees/hash tables, programming techniques like dynammic pro-
gramming, graphs, space and time complexity requirements for a given method, randomized algorithms, sublinear
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