On 24.12.2009, at 05:18, jim wrote:
> I was looking at the probability monad today and think this definition
> of m-bind might be easier to understand.
>
> (defmonad dist-m
> [m-result (fn m-result-dist [v]
> {v 1})
> m-bind (fn m-bind-dist [mv f]
> (reduce (partial merge-with +)
> (for [[x p] mv
> [y q] (f x)]
> {y (* q p)})))
> ])
>
> What do you think?
I agree. In fact, I had reinvented merge-with because I wasn't aware
of its existence.
> Also, I was thinking about cond-dist-m. What if dist-m was redefined
> to be this
>
> (defmonad dist-m
> [m-result (fn m-result-dist [v]
> {v 1})
> m-bind (fn m-bind-dist [mv f]
> (if (empty? mv)
> {}
> (reduce (partial merge-with +)
> (for [[x p] mv
> [y q] (f x)]
> {y (* q p)}))))
> m-zero {}
> m-plus (fn m-plus-dist [& mvs]
> (if-let [mv (first (drop-while empty? mvs))]
> mv
> {}))
> ])
>
> I think that would roll cond-dist-m into dist-m, eliminating the need
> for a seperate monad. Don't know if you'd thought of that and
> discarded it or not.
At first glance I doubt that this works. Did you try it?
Your m-bind looks equivalent to the one of my original dist-m, with
just an optimization for the case of an empty map. If that is true,
then your dist-m can't include the features of cond-dist-m, which
require a different m-bind.
It is in fact essential for cond-dist-m not to eliminate invalid
values from the distributions immediately, but to accumulate their
weights into the map entry for some special value (nil in my
implementation). Otherwise the probabilities come out wrong for multi-
step computations containing more than one :when clause.
Konrad.
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