His old book did just that: https://www.amazon.com/Machine-Learning-Probabilistic-Perspe...

In retrospect, my other comment was stupidly obtuse. Both too technical (in the sense of specificity) and too unstructured (in the sense of presentation order). A more appropriate path from CS might be analogous (well, inverse if anything) to the path Robert Goldblatt has taken. It dips into nonstandard analysis, but not totally without reason. Some subset of the following, with nLab and Wikipedia supplementing as necessary:

0. Milewski's "Category Theory for Programmers"[0]

1. Goldblatt's "Topoi"[1]

2. McLarty's "The Uses and Abuses of the History of Topos Theory"[2] (this does not require [1], it just undoes some historical assumptions made in [1] and, like everything else by McLarty, is extraordinarily well-written)

3. Goldblatt's "Lectures on the Hyperreals"[3]

4. Nelson's "Radically Elementary Probability Theory"[4]

5. Tao's "Ultraproducts as a Bridge Between Discrete and Continuous Analysis"[5]

6. Some canonical machine learning text, like Murphy[6] or Bishop[7]

7. Koller/Friedman's "Probabilistic Graphical Models"[8]

8. Lawvere's "Taking Categories Seriously"[9]

From there you should see a variety of paths for mapping (things:Uncertainty) <-> (things:Structure). The Giry monad is just one of them, and would probably be understandable after reading Barr/Wells' "Toposes, Triples and Theories"[10].

The above list also assumes some comfort with integration. Particularly good books in line with this pedagogical path might be:

9. Any and all canonical intros to real analysis

10. Malliavin's "Integration and Probability"[11]

11. Segal/Kunze's "Integrals and Operators"[12]

Similarly, some normative focus on probability would be useful:

12. Jaynes' "Probability Theory"[13]

13. Pearl's "Causality"[14]

---

[0] https://bartoszmilewski.com/2014/10/28/category-theory-for-p...

[1] https://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathe...

[2] http://www.cwru.edu/artsci/phil/UsesandAbuses%20HistoryTopos...

[3] https://www.amazon.com/Lectures-Hyperreals-Introduction-Nons...

[4] https://web.math.princeton.edu/%7Enelson/books/rept.pdf

[5] https://www.youtube.com/watch?v=IS9fsr3yGLE

[6] https://www.amazon.com/Machine-Learning-Probabilistic-Perspe...

[7] https://www.amazon.com/Pattern-Recognition-Learning-Informat...

[8] https://www.amazon.com/Probabilistic-Graphical-Models-Princi...

[9] http://www.emis.de/journals/TAC/reprints/articles/8/tr8.pdf

[10] http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf

[11] https://www.springer.com/us/book/9780387944098

[12] https://www.amazon.com/Integrals-Operators-Grundlehren-mathe...

[13] http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

[14] https://www.amazon.com/Causality-Reasoning-Inference-Judea-P...

Some good books on Machine Learning:

Machine Learning: The Art and Science of Algorithms that Make Sense of Data (Flach): http://www.amazon.com/Machine-Learning-Science-Algorithms-Se...

Machine Learning: A Probabilistic Perspective (Murphy): http://www.amazon.com/Machine-Learning-Probabilistic-Perspec...

Pattern Recognition and Machine Learning (Bishop): http://www.amazon.com/Pattern-Recognition-Learning-Informati...

There are some great resources/books for Bayesian statistics and graphical models. I've listed them in (approximate) order of increasing difficulty/mathematical complexity:

Think Bayes (Downey): http://www.amazon.com/Think-Bayes-Allen-B-Downey/dp/14493707...

Bayesian Methods for Hackers (Davidson-Pilon et al): https://github.com/CamDavidsonPilon/Probabilistic-Programmin...

Doing Bayesian Data Analysis (Kruschke), aka "the puppy book": http://www.amazon.com/Doing-Bayesian-Data-Analysis-Second/dp...

Bayesian Data Analysis (Gellman): http://www.amazon.com/Bayesian-Analysis-Chapman-Statistical-...

Bayesian Reasoning and Machine Learning (Barber): http://www.amazon.com/Bayesian-Reasoning-Machine-Learning-Ba...

Probabilistic Graphical Models (Koller et al): https://www.coursera.org/course/pgm http://www.amazon.com/Probabilistic-Graphical-Models-Princip...

If you want a more mathematical/statistical take on Machine Learning, then the two books by Hastie/Tibshirani et al are definitely worth a read (plus, they're free to download from the authors' websites!):

Introduction to Statistical Learning: http://www-bcf.usc.edu/~gareth/ISL/

The Elements of Statistical Learning: http://statweb.stanford.edu/~tibs/ElemStatLearn/

Obviously there is the whole field of "deep learning" as well! A good place to start is with: http://deeplearning.net/

Murphy's is probably most current, and an excellent text (read first review). OTW there's lots of stuff on the web for various levels of rigor

http://www.amazon.com/Machine-Learning-Probabilistic-Perspec...

http://metaoptimize.com/qa/questions/186/good-freely-availab...

http://www.p-value.info/2012/11/free-datascience-books.html

http://www.kaggle.com/wiki/Tutorials