Ŷi vs. f_w,b(xi) [Are they interchangeable?]

Course Q&A Machine Learning Specialization Supervised ML: Regression and Classification
1

I am trying to discern whether the f_w,b(xi) notation for the regression model is the same as ŷi.

I’ve done regression analysis in stats, and the model was referred to as ŷi.

In this course, I’ve seen f_w,b(xi) used to refer to the model, but I’ve also seen ŷi mentioned.

Any idea?

2

@stcampione

Welcome to the community.

You are right.
\hat{y}^{(i)} = f_{w,b}(x^{(i)})

3

Thank you!, my intuition was correct. One more notation question: can superscript (i) be subscribed alongside j such as in the instances below?

\hat{y}^{(i)}_{j} \to \hat{y}_{ij}

f_{w,b}(x^{(i)}) \to f_{w,b}(x_i)

Thanks again -Sam

4

@stcampione

I would strongly advise against it.

Atleast as it pertains to Prof. Andrew’s courses (not limited to this specialization alone), he is maintaining a certain set of standards and conventions, and it could lead to a lot of confusion if we deviate from it.

To give you an idea about the conventions followed:
x_n or a_n (in case of neural networks) stands for the n^{th} feature or unit or node.
x^{(i)} or a^{(i)} stands for the i^{th} sample
a^{[l]} stands for the l^{th} layer - Layers are introduced in the context of neural networks in Course 2.

All put together we have a_n^{[ l ](i)} - Each of the subscripts and superscripts already having a fixed meaning associated with it. So I leave it to your imagination, what can happen if we dont maintain consistency with these conventions :slightly_smiling_face:

1 Like
5

This is great. I needed this explanation.

Makes sense.

Thank you :smiling_face:

6

You are most welcome @stcampione :blush: