Course talk:CPSC522/Probability

Nice work Junyuan, Samprity, Ke Dai and Arthur Sun. A very good page on the basics of probability. The concepts are well written, the use of examples were great and there is much depth in the material though the page is not unnecessarily long at all. I have a couple of suggestions that I believe would make the page even better. You did mention about the page being regarding the finite case. If it is possible, a small description of what is the finite case and what is the infinite case might make the page even better. One more thing that I would like to mention is that in the subsection 3.1.3(Event), the probability of an event was given based on notations of probability measure which was introduced on the next sections(3.1.4).This can be a bit convoluted for someone who does not have much idea about probability. However, I can also see why you might have done that, since you have used the notion of events to define probability measure. One way this issue could be solved is, to divide the subsection (3.1.3) into two: Event and Event Space. Then, I believe, the notation problem can be avoided. Or you can simply mention the probability after you have defined the probability measure notations. Thank you and I hope this feedback would help you.

Hi Abed,

Thank you for your feedback, I will try to modify the section 3.1.4 and section 3.1.3.

Thank you for your help!

Sincerely,

Junyuan Zheng

Hi Junyuan,

I like your work, it is every organized, clear and the examples that you added are easy to understand, makes a deeper understanding of the material. Even for beginners, those are very usful.

But do you think it is possible and necessary to add some more concepts or practical applications related to AI? I mean this page is so well organized, but suitable for any courses, like Stats, Discrete mathematics, etc.. Can you make it more related to AI? All the examples that you gave are too Math. Show us something intelligent!

Hi Dandan Wang,

Thank you for your feedback, I see the problem now, and I have added another AI related example.

Sincerely,

Junyuan Zheng

A very good piece of work by Junyuan. I do agree with other two critics that the page provides good examples, is well organized, extends both breadth to depth, and could be very easily understood by a novice. But I think you missed to connect the dots between probability and AI. Dutch book example that you gave is very nice and a good application of probability theory, but it's not specific to AI.

Hi Tanuj,

Thank you for your reply!

I add an AI example, it's a Content-Based Recommendation Service, with a simple example to explain the Naïve Bayesian Classifier.

Sincerely,

Junyuan Zheng

Hi Junyuan, I like how you have presented the information lucidly and tried to cover all the related topics. A few comments I had are: In the section Event, there seems to be a typo: sample space of a deck of cards would be 52. (13*4) -I would’ve liked if you had given a probabilistic aspect to concepts in AI rather than treating it as an individual concept even though as a standalone page it provides a very comprehensive guide. -I really like the geometric visualization of Bayes theorem -I found the Dutch book example really interesting and it made me think for sometime (which is great!). So what I am unable to figure out is that mathematically how does implied probability lower than one relate to getting profit in the same ratio. I understand from the example how its working but i was wondering if you had some sort of mathematical proof/verification to this. Really enjoyed the example. Thank you for sharing this with us. Warm regards, Ritika

Hi Ritika,

Thank you for your feedback! I will try to use plain English to explain the Dutch Book. I also add an AI Example.

Sincerely,

Junyuan Zheng