The mathematics behind Shapley Values

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Shapley values are a fair way to divide the value of a game amongst its players. We explain the mathematics behind the Shapley value formula. To understand why it is fair, we also discuss the Shapley value axioms that the formula is derived from. The formula may seem scary but you will find it has an intuitive explanation.
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Опубликовано:

26 мар 2023

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Комментарии : 64

@adataodyssey 5 месяцев назад

*NOTE*: You will now get the XAI course for free if you sign up (not the SHAP course) SHAP course: adataodyssey.com/courses/shap-with-python/ XAI course: adataodyssey.com/courses/xai-with-python/ Newsletter signup: mailchi.mp/40909011987b/signup

@abstractqqq Год назад

Good job sir. Very few in the ML (industry) will go this deep. Seeing more like-minded people always feel great.

@adataodyssey Год назад

Thank you! I always feel a bit uncomfortable if I don't have some sort of an understanding of the theory :)

@HenryCagnini 5 месяцев назад

That's a great video to explain the concept of Shapley values. Many thanks!

@adataodyssey 5 месяцев назад

Thanks Henry! I’m glad you found it useful :)

@umarkhan-hu7yt 4 месяца назад

Dear Odyssey you are doing great. Keep continue and hit hard on all XAI models for a layman.

@adataodyssey 4 месяца назад

Thank you Umar! Will do :)

@santizdr 2 месяца назад

Best channel to dig deep into XAI. It would be great a video about the state of art of XAI applied on LLMs.

@adataodyssey Месяц назад

Thanks Santi! I will consider this however my interests are more in computer vision at the moment

@mugiwxrx6282 Год назад

thank you sir, that seems more clear in my mind !

@adataodyssey Год назад

I’m glad it helped!

@muhammadawais581 Месяц назад

hats off to you for such a nice explanation.

@adataodyssey Месяц назад

Thanks Muhammad!

@shadmohammed618 5 месяцев назад

Great explanation, thanks very much. 🙂

@adataodyssey 5 месяцев назад

No problem Shad! I’m glad you found it useful

@Ericfrodrigues Месяц назад

Sou outra pessoa depois de conhecer Shap Values!! ----> I'm a different person after getting to know Shap Values!! Thanks a lot!

@adataodyssey Месяц назад

I agree Eric! It is an interesting topic :)

@miguelgarciaortegon 4 месяца назад

Great explanation, thank you!

@adataodyssey 4 месяца назад

I'm glad you found it useful Miguel :)

@yelancho 3 месяца назад

Appreciate a lot Prof Odyssey！Shaply values is now a more clear concept in my mind!

@adataodyssey 3 месяца назад

Thanks Ye! I'm glad you found it useful :)

@smithanair787 Год назад

Great video! Can you make a video on how exactly the Kernel SHAP and TreeSHAP works?

@adataodyssey Год назад

Thank you Smitha! I will consider that. But, to be honest, it will take me some time to fully understand the algorithms first.

@smithanair787 Год назад

@@adataodyssey Thank you!

@adataodyssey Год назад

@@smithanair787 by the way, the course goes into a bit more detail on the difference between kernelSHAP and treeSHAP. Otherwise you might find this article helpful: towardsdatascience.com/kernelshap-vs-treeshap-e00f3b3a27db

@v-ba 2 месяца назад

Great explanation, thank you very much

@adataodyssey 2 месяца назад

Thanks!

@silver_soul98 4 месяца назад

Bro that was a nice explanation. thanks so much.

@adataodyssey 4 месяца назад

No problem :) I’m glad it was useful

@lakshman587 8 месяцев назад

The time machine thing really got me hahaha!! I was wondering how can individual values be calculated!! Thanks for clear explanation!!

@adataodyssey 8 месяцев назад

No problem Lakshman! Are there any other related concepts you're interested in learning about?

@lakshman587 8 месяцев назад

@@adataodyssey I would like to learn about ChatGPT like how transformers work.

@adataodyssey 8 месяцев назад

@@lakshman587 This is a bit out of my comfort zone tbh. My content is more aimed towards computer vision and explainable AI. I was considering doing a tutorial on how you can use the GPT API though!

@lakshman587 8 месяцев назад

@@adataodyssey Ok No problem, can we have a video about how diverse counterfacuals work under the hood, we currently are using DiCE package from interpretml repo. I would like to know how these counterfacuals are getting generated!

@adataodyssey 8 месяцев назад

@@lakshman587 will look into that!

@Empobaer Год назад

Great video, formula was well explained! Though, I do have a question. What is the Intuition behind P(C1-C0) = 2/6 at 7:11 ? Because intuitively I would have thought there is only one way how player 1 can start its new coalition and thus I would have thought the weight should be 1/6. I see that if we look into the formula on how to calculate the weights, we obtain (p-|S|-1)!=2 and thus (1*2)/6=1/3, but I still miss the intuition behind why we need the (p-|Sl-1)!. Where am I thinking wrong?

@adataodyssey Год назад

Great question! Keep in mind that to receive the full value of the game all 3 players need to participate. So, after P1 joins, there are 2 ways for the full coalition to form -- P2 joins then P3 or P3 joins then P2. In other words, there will be 2 scenarios where P1 makes a marginal contribution to a team of no players. Does that make sense?

@adataodyssey Год назад

If not, then this article may help. It calculates the values in a slightly different way which may be more intuitive to you. www.analyticsvidhya.com/blog/2019/11/shapley-value-machine-learning-interpretability-game-theory/

@Empobaer Год назад

@@adataodyssey Thank you for your fast reply, indeed the blog post was very useful for an intuitive understanding! Anyways your series on SHAP and Shapley values was a very helpful introduction. Now I only need to fully understand Kernel SHAP, which will probably take a bit longer :)!

@hasnainayub2369 5 месяцев назад

Great explanation! I have a question though. Why don't the shap values for each feature (from the waterfall plot) add up to the predicted output at that particular observation?

@adataodyssey 5 месяцев назад

They do if you also add the average prediction across all the instances in the dataset: f(x) = E[f(x)] + sum(shap values) You can see the average prediction, i.e. E[f(x)], on the bottom of the waterfall plot :)

@hasnainayub2369 5 месяцев назад

Got it ! Thanks mate @@adataodyssey

@dennisestenson7820 8 месяцев назад

I really don't like that this subject is presented and studied as "games" when the underlying math is so incredibly enlightening and important.

@adataodyssey 8 месяцев назад

This is a term that comes from "game theory". Rest assured that the "games" it deals with are very serious! Perhaps the example I've chosen is a bit silly but I was hoping that it would help the target audience relate to the concepts :)

@elenagolovach384 Год назад

Thanks very much

@adataodyssey Год назад

No problem, Elena!

@mathieucordier9248 10 месяцев назад

Does Shap Value is adapted for imbalanced data set ? Because one assumption is that we consider equality of chance for players combination (at 6:00).

@adataodyssey 10 месяцев назад

That's a good question! I haven't really thought about that. In ML we don't assume equal chance for all feature values. We use the empirical distributions of the features. So you don't have to worry about that assumption for unbalanced features. For unbalanced targets, I'd say you should be fine as long as the model is still making accurate predictions. E.g. if it is always predicting one class then the SHAP values won't be meaningful.

@adityababel3998 9 месяцев назад

Hello, can you make a video explaining the calculation of TreeSHAP??

@adataodyssey 9 месяцев назад

Hi Aditya, this is already on my list of videos to do! I want to make a video about both Kernel SHAP and tree SHAP that go more in-depth into the algorithms.

@abdelbaki8625 2 месяца назад

what is the article reference for this information i need it for my studies emergency, please

@adataodyssey 2 месяца назад

ru-vid.com?event=video_description&redir_token=QUFFLUhqbktFYXFNVHVzc3NsTWpaYkc4Y3l3alZ0N3dmZ3xBQ3Jtc0trX2c3WmlOUVQwYW1USmJsaDh4YnpLV191dk5tOEdnOUtnVF9vZm5BbG8yTmRTaU56RXZNSE12Nkh2MjRITUZSLUZINUNPWmM3WFRlbnVGZWlscDFLZnFOZy1Xb0JiYm1RMnlQbVU2MEJ4R0hoUmJxMA&q=https%3A%2F%2Ftowardsdatascience.com%2Ffrom-shapley-to-shap-understanding-the-math-e7155414213b%3Fsk%3D329a1f042a0167162487f7bb3f0ffd46&v=UJeu29wq7d0

@QuantizedFields 9 месяцев назад

This is a very good explanation. However, I found it a bit confusing when you were referring to "Player-1" as "You". Because it is not clear who I am from the animation, am I "Player-1" or "Player-2" ? It would be better if you simply refer to the animation/picture and say "Player-1" or "Player-2" instead of "You". Thanks for your great work!

@adataodyssey 8 месяцев назад

Thanks for the input Daniya! When it comes to technical content, it is difficult to strike a balance between making it interesting and easy to understand. My goal was to get the audience engaged but I see how this can be confusing.

@hasnainayub2369 5 месяцев назад

Could you please explain P(C1-C0) = 1/3 ? (at 7:12). The rest is very well explained.

@adataodyssey 5 месяцев назад

Remember, to get the prize money all players must eventually join the coalition. So, there are 2 ways that P1 can contribute to a coalition with no players (i.e. C0): - P1 joins then P2 then P3 - P1 joins the P3 then P2 So they make the marginal contribution C1 - C0 in 2/6 = 1/3 ways the coalition of 3 players can form.

@hasnainayub2369 5 месяцев назад

@@adataodyssey thank you so much ! How did i not see that :/

@adataodyssey 5 месяцев назад

@@hasnainayub2369 don't stress! It took me forever to understand