Hello, I am trying to implement Sequential Line search, but is not sure what’s the right way to do so.
Simply speak, the model approximates the user preference g over a parameter space (think about photo editing with all the parameters), given a user interaction with slider using [Bradley–Terry model] (https://en.wikipedia.org/wiki/Bradley–Terry_model) (User picks a point over the two ends of the slider, probability of user choosing an arbitrary point in the slider is formulated as g_chosen/(g_start + g_end). In the paper, they assume the user preference to each choice as latent variable, and use MAP estimation to maximize the posterior. I am aware that pyro is capable of doing MAP but the only information I can find is an opening issue and a closed PR.
In particular, I don’t understand
- where should I compute the posterior distribution? As I go through all the tutorials, the posterior seems to be defined in the guide, but it is not quite sure how should I feed it to the SVI object since the model, guide in many tutorials never return anything.
- In case of MAP estimation, in the issue on github it says that we should use a delta distribution as a posterior but I am not exactly sure the reason behind this. In my understand MAP tries to Maximize a Posterior, meaning that we are capable of evaluating the posterior in closed form anyway, why do we need to set it as a delta distribution?
- The problem (I think) can be formulated as an SVI problem but I don’t know how to systematically convert a MAP problem to an SVI one.
Any help will be appreciated.