Multiple purchases per sessions ?

[SebDub]

Hi,

First of all, thanks for the great package,

I was wondering how you would go about having multiple purchase in a sessions (this can happen in some context).

I thought about it and got two ideas:

1. Rework the maths (hugh...) to replace equation seven from here P(Er = 1|Sr-1=0 ) =0 by something like P(Er = 1|Sr-1=0 ) = gamma_2 . This would means that despite being satisfied there is still a chance you continue to evaluate the next items. I didn't work the full math out because i wanted first to ask your opinions on this. Do you think this would work ?
2. Much more simple hack: consider session with multiple purchase as separated sessions (either incorporating the first purchase in the second sessions as simple click with no purchase or simply not incorporating it)

Any chance to get your opinion on this ?

Thanks.

[WillianFuks]

Hi @SebDub ,

This is definitely an interesting idea!

But I suppose the only valid approach here would be your option 1. Unfortunately all the mathematics behind the Bayesian Net would have to be redefined which is a lot of work (one should be prepared for doing so).

If you want to implement something and send a PR it would be very welcome. The only requirements I'd ask is to fully cover it with unit tests (you could use the ones that were already implemented in this package as reference).

Best Regards,

Will

[SebDub]

Hi @WillianFuks,

Yeap that's what I was thinking.
Could I know the source of the DBN update rules derivation with purchase (didn't find it) ? Or did you derive it yourself ?
In any case, I'll try to work on it in the next days.

Thanks

[WillianFuks]

Sounds cool!

I did have to derive all the equations. I used this book as main reference. I wrote down a medium post as well with most of the ideas behind its development, might be helpful as well.

[SebDub]

So,
I tried to do the first part with the examination probability, expanding it to have this gamma_2 when the user is satisfied (and renaming gamma to gamma_1).
I think i got it right but wanted to double check. I know it's the easy part ...

The bottom is just the 'development' on how i get to the second part (the first part being the same as you).

[WillianFuks]

Nice work! I just derived the equations here as well and found the same result. So far it seems you're on the right track.

I'd recommend you to write down those equations in a notebook as well, you could fork this repo and in the notebooks folder create another file, maybe called EDBN.py (Enhanced Dynamic Bayesian Network) or a name that best suits your taste.

As you advance on finding the structure of the network you'll already have all equations in on place so if you want to write an article and so on it might be easier. Also you could send a PR and then we'd have two equations implemented on this repo.

Let me know how it's going :)

Best,

Will