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mml-book / mml-book.github.io

Companion webpage to the book "Mathematics For Machine Learning"
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Examples or references #549

Open mml-nitkkr opened 4 years ago

mml-nitkkr commented 4 years ago

Is your feature request related to a problem? Please describe. In the Draft (2019-10-20), Chapter 5, Section 5.5 and page 158, there are some identities related to the gradient. It does not give a clue how to verify or understand them. The book you referenced (Petersen and Pedersen, 2012) contains proofs and that is not easy for beginners. I think some intermediate thing like examples may be shared, especially for 5.101,102,103

Describe the solution you'd like May be one example for each identity will help a lot. For an early solution, you can give some links so that things can be looked there

mpd37 commented 4 years ago

The list of identities on p. 158 is thought more of a lookup table, no proofs. These partial derivatives are relatively advanced, and we do not think that a detailed derivation is helpful here, and we decided to leave them out. We refer to the matrix cookbook, where there are some derivations, but we are aware that things require some more detailed knowledge and tricks. This is beyond what we wanted to do in our book.

vbartle commented 4 years ago

Pages 145 through 165 are definitely the weakest link, or at least driest section of Part 1 of the book.

Compared to the rest of Part 1 of the book, pages 145 through 165 contain the least amount of graphical figures, proportional to page count, and the examples are rarely fully worked, numerical examples, see 5.12,3. In the chapters leading up to 5, one would find a worked numerical example or graphical figure, roughly in 5 page increments.

In the same vein of having back to back identities as in 5.5, Pages 145-165 also bare the quality of having back to back examples, with no text in-between (5.9,10,11; 5.12,13), which indicates a bigger disconnect than in other chapters, between the text and the examples.

Regarding links, the authors reference 3b1b as an additional recommended resource, for which Grant of 3b1b does have some content on multivariable calculus, although it's not on his youtube account, but through his work at Khan Academy; and he also has this youtube video on partial derivatives. These videos might help you gain an intuition for gradients and partial derivatives.

Pages 145-165 could be helped with a matplotlib built graph akin to what Grant does in those videos, such as input 25 in here, or at least a reference to Grant's content.