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# Alex's concepts deck

2.11MB. 0 audio & 26 images. Updated 2020-12-01.
The author has shared 1 other item(s).

## Description

Not guaranteed to make any sense to people who are not me.

## Sample (from 139 notes)

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 Front What is an algebra over sets of a space $$\Omega$$? Back A set of sets which is closed under complements, finite unions and intersections, and which contains $$\emptyset$$ and $$\Omega$$. $$\sigma$$-algebra if the operations can be countable. Ajouter le verso Tags
 Front When is a metric space complete / Banach? Back When every Cauchy sequence converges to something in the space Ajouter le verso Tags
 Front In the context of statistical learning theory, what is a teaching set? Motivate why this is useful, and give an example of concepts which have a large minimum teaching set. Back Consider a set of concepts $$C$$ (like, "dog", "cat", "1", etc). Let $$X$$ be a finite set of examples. $$S \subseteq X$$ is a teaching set for concept $$c\in C$$ when $$\forall c' \neq c: \exists s \in S: c'(s)\neq c(s)$$. In other words, the teaching set gives us a chance of distinguishing between concepts. However, the rule may not help us generalize: imagine a teaching set for the concepts which classify the RGB value of the top-left pixel of an image. We might have a lot of trouble finding the right hypothesis, even given a teaching set. The teaching set concept seems good as a necessary condition: if you want to train a loss-minimizing discrete classifier, you need to at least give it a teaching set for the label space!$$S$$ is a minimal teaching set for $$c$$ when it's as small as possible. A large minimal teaching set would be, say, concepts corresponding to animal types, and a set of example photos where each had to contain at least 50 different kinds of animals. Ajouter le verso Tags

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