Any good math-theory-focused books on neural networks and data science?

Click For Summary

Discussion Overview

The discussion centers around the search for mathematically rigorous books on data science and neural networks, with a focus on theoretical aspects such as optimization theorems and efficient layer structures. Participants express a desire for resources that delve deeper into the mathematical foundations rather than providing superficial coverage.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for books that emphasize mathematical rigor in data science and neural networks.
  • Another participant suggests "Algorithms for Optimization" by Kochenderfer, noting its practical examples in Julia, but indicates it may not meet the desired rigor.
  • Additional recommendations include Burkov's "100 page ML book" and Geron's "Hands-on ML with Scikit-Learn, Keras and Tensorflow," with a similar caveat regarding their mathematical depth.
  • A participant mentions "Data Mining" by Witten et al., acknowledging its coverage but criticizing its lack of rigor compared to traditional math analysis texts.
  • Another participant points out that many relevant theoretical insights are still primarily found in research papers, providing links to several arXiv papers on function approximation, gradient descent effectiveness, and error estimation.

Areas of Agreement / Disagreement

Participants generally agree on the lack of rigor in available books and the preference for more mathematically focused resources. However, there is no consensus on specific texts that fully meet the rigorous criteria sought.

Contextual Notes

Participants note the rapid development of the field may contribute to the scarcity of rigorous texts, and there is an acknowledgment that many foundational concepts are still being explored in academic papers rather than comprehensive books.

s00mb
Messages
33
Reaction score
10
Hi. I'm looking for books on data science, preferably leaning towards neural networks, that focus on mathematical rigor. For example, theorems on optimization, minimum number of layers to accomplish a task efficiently, etc. Most books I've seen seem to hand wave this stuff. Anyone know any juicy books on the topic?
 
Physics news on Phys.org
There's a rather recent book by Kochenderfer called Algorithms for Optimization with many examples written in Julia, a hot programming language from MIT that folks are using for numerical work in diverse fields including ML and Data Science.

https://www.amazon.com/dp/0262039427/?tag=pfamazon01-20

There's also the 100 page ML book by Burkov:

https://www.amazon.com/dp/199957950X/?tag=pfamazon01-20

which is available online as a try and buy book.

Lastly, Geron's book Hands-on ML with Scikit-Learn, Keras and Tensorflow:

https://www.amazon.com/dp/1492032646/?tag=pfamazon01-20

All are good books that discuss the math behind the ML although not at the rigor you're looking for.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
6K
  • · Replies 5 ·
Replies
5
Views
7K
  • · Replies 13 ·
Replies
13
Views
5K
Replies
10
Views
5K
  • · Replies 11 ·
Replies
11
Views
10K
Replies
15
Views
41K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
10
Views
3K