@ 8:40 ??? why these sub intervals have equal probabilities of 20%? isnt it better to assign prob with their MAE range which they take(ofc I know for last subInterval we would have a problem that it would get infinite)? what if we had another point with .16 MAE loss(note we have .15 MAE also), so it would have created another subInterval with same prob as others?
@@MLBoost first of all I thought `exchangeability of data` means that the orders of (x,y) pairs doesnt matter, I dont know where but it was in the video and I think it needs to be explained (intuitive if possible) more why exchangeability is correct, complement the explanation with my question of if there is 5 points and they have [.15, .16, .31, .46, .67] losses, why exchangeability still makes sense to assume all intervals equal probable. ofc I know in practice they might be more points and this may or may not happen but if this exchangeability and taking intervals equal probable, is a principle, so it should make sense in this case also
Great questions and I am really glad to see videos are being watched in detail. You are correct that exchangeability means order does not matter and yes that was mentioned in one of the videos. Number of points does not really matter. As long as exchangeability is satisfied intervals are equi-probable. The theoretical proof of why that is the case is in the original conformal papers or the book by original developers of the method but I may prepare a video addressing that.
Good work
Thank you! Cheers!
@ 8:40
??? why these sub intervals have equal probabilities of 20%? isnt it better to assign prob with their MAE range which they take(ofc I know for last subInterval we would have a problem that it would get infinite)? what if we had another point with .16 MAE loss(note we have .15 MAE also), so it would have created another subInterval with same prob as others?
because of exchangeability as discussed @8:42
@@MLBoost first of all I thought `exchangeability of data` means that the orders of (x,y) pairs doesnt matter, I dont know where but it was in the video
and I think it needs to be explained (intuitive if possible) more why exchangeability is correct, complement the explanation with my question of if there is 5 points and they have [.15, .16, .31, .46, .67] losses, why exchangeability still makes sense to assume all intervals equal probable. ofc I know in practice they might be more points and this may or may not happen but if this exchangeability and taking intervals equal probable, is a principle, so it should make sense in this case also
Great questions and I am really glad to see videos are being watched in detail.
You are correct that exchangeability means order does not matter and yes that was mentioned in one of the videos.
Number of points does not really matter. As long as exchangeability is satisfied intervals are equi-probable. The theoretical proof of why that is the case is in the original conformal papers or the book by original developers of the method but I may prepare a video addressing that.
@@MLBoost without any doubt these videos are top notch content so they worth to be watched carefully