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Introductory Mathematics

Machine learning uses mathematics to describe data, make predictions, and improve those predictions. Those calculations are much easier to follow when we understand what they are doing. We will work through statistics, linear algebra, and calculus from small examples, so you don't need to arrive with that background.

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Introductory Mathematics

  1. 01Statistics & Probability PrimerA collection of measurements does not explain itself. We need ways to describe what is typical, how much the values differ, and how much confidence we should place in the patterns we observe.
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  2. 02Linear Algebra PrimerA model often needs to work with many measurements at once. Vectors and matrices let us organise those numbers and repeat useful calculations without writing a separate rule for every example.
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  3. 03Calculus PrimerIf we change a model's setting a little, does its error improve or get worse? Calculus gives us a way to describe that change and use it to decide what to adjust next.
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Reasoning From Uncertain Evidence

An observation can change what we believe, but we need to keep track of the group we are talking about. We will follow an alarm back to its possible causes, then compare rules that could have produced a recorded sequence.

  1. 04What Does an Alarm Tell Us?An alarm may catch most faulty sensors and still be wrong surprisingly often. We need to know how common faults are before deciding what an alarm means.
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  2. 05Which Rule Could Have Produced These Observations?A probability rule predicts possible observations. Likelihood holds the observations fixed and compares the rules that might have produced them. That distinction connects probability to fitting a model.
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