Variable dependent features

[s-morten]

First of all, huge thank you again!

It seems like the model, or at least the model definition, works.

@jessegrabowski

I suggest testing all this by generating some labels using scipy.stats.poisson with a known theta, and make sure you can get the right answers in a small test.

That is probably a very good idea. How do I get a known theta? Is it just making it up?

@jessegrabowski

My last comment is that as it’s written, there isn’t really any way for your model to connect one time step to the next

I actually thought I could model this by the \alpha which has the shape T \times k. I read somewhere that you model a temporal process that way.

@jessegrabowski

I would consider adding the t vector into your X vector as another feature

Would that alone be enough to model the dependency between the timesteps?
It probably can’t harm to do that either way, except for an even bigger feature space. So I will add the t to X.

@jessegrabowski

Why not give the time remaining in the match a weight via \beta and let the model decide how important it is?

Because I wanted to start easy (Or as I once thought “easy” )

@jessegrabowski

You might also consider the first lag of R_{i,t},R_{i,t-1} to the feature matrix, since if there are 4 goals to go at time t-1, there’s probably also 4 goals to at time t (alternatively, model s_{i,t}, instead of R_{i,t}).

I dont understand what you mean?

@jessegrabowski

Finally, you could consider putting a Gaussian Random Walk prior on your betas, to let the weights of the features change as the game goes on.

Now that’s the same as the point before, I wanted to start with things I at least half understood. And Gaussian Random Walk isn’t one of them yet. But I will probably look into that next.