llasram
Joined 15 years ago
Joined 15 years ago
I haven't worked these all the way through, but I'm slightly skeptical or at least confused by a few details:
1. Another way to frame P(D|B=b) would be to have the old vs new side draws be beta-binomial distributed, in which case we should then have binomial coefficients for each of the draw side probabilities for the number of possible orderings of the observations. Do they end up cancelling out somewhere? [ed: Oh yes, of course -- D includes that in each case we observe exactly one of the C(n,k) orderings.]
2. I think your expected conditional entropy code is treating the imputed new observations as independent from the past observations, though even if that's the case it may not affect it much in this model. If it does though, it might be worth explicitly unit-testing the naive vs efficient calculations to ensure they match.
Anyway, thanks for sharing!
I look forward to reading this book when finished and hope they find success with this presentation of the core ideas. As a practitioner I see a fair amount of "I have a hammer; now I just need this problem to be a nail" type thinking with regard to using off-the-shelf techniques.
In the intro to this book the authors have an example with Kalman filters. A similar example is how Latent Dirichlet Allocation (LDA) is treated by different communities. In a certain chunk of the CS-dominated topic-modeling literature and in the data science blogosphere LDA is this recieved atomic technique; a black-box tool for modeling documents. In the Stan manual, it is one fairly boring example of a mixture model, only worth talking about explicitly because so many people ask about it.
I find that this is a theme which runs through a number of Chiang's stories. If you haven't read it, you might find "Exhalation" interesting: http://www.lightspeedmagazine.com/fiction/exhalation/ . You may also find it nihilst, but makes the positive, celabratory element even more explicit.