How to handle abstraction

[yaxigeigei]

I was quite lost during the lecture when Joshua introducing concepts like action space, loss function, risk function, and many other concepts in previous lectures... probably because I didn't have enough mathematical training before. I think now I have a pretty clear idea about them after learning from different sources with the help of concrete examples after class. Many of you guys have a lot of experiences in mathematics. I would like to know how do you handle abstract concepts and descriptions? Do you rely on concrete examples? If not necessarily, what is the process/training that enable you to think freely in an abstract way?

[ghost]

I definitely start by getting comfortable with the abstract concept using concrete examples. After that I try to pay attention to patterns and relate back to the example as needed. Pattern recognition and getting familiar with notation and definitions helps me a lot.

[SandyaS72]

I definitely start with concrete examples. Especially if it's a whole string of abstract concepts that all relate to each other in some way, I try to think of a set of concrete examples that fit each concept that I can walk through how they relate to each other as an example of what the concepts are. Then I try to think of an example or two for one concept and see if I can fill in the rest accordingly. I like to have a reference example for each thing in my head, so if I ever forget, I can explain it to myself again with that example.

[yaxigeigei]

Thank you for sharing your experiences/tips. I am very encouraged by the fact using concrete examples are quite necessary. I hope we could see more examples from Joshua during the lecture along with introducing new concepts.

[indigorose1]

I'm having trouble with the same thing. What examples did you guys think of? I'm not quite sure how to conceptualize things like action space or a decision rule class.

[mblohr]

I definitely use concrete examples when possible, to learn abstract concepts. But everyone is different. Regarding Statistical Decision Theoretic concepts, I tend to think of them in terms of algorithm development and testing, where Sample Space is the input, Action Space is the output, Decision is the algorithm, Loss is how well the algorithm performed, and Risk is how much we care how well the algorithm performed.