Currently, BaseDistribution descendants support up-broadcasting of arguments, but not up-broadcasting of results, if arguments with additional dimensions are given. Mathematically, this is related to taking outer products instead of element-wise products, in scalar or vector cases
This is a natural feature to offer, for instance tensorflow.probability functions in this way, and cyclic-boosting also has the feature.
There are a few obstacles for adding this:
expectations on public inputs and outputs being pd.DataFrame
numpy.ndarray-s - where are not a supported input type
unclear target interface, e.g., cyclic-boosting has an extra argument that controls elementwise vs outer product, which I find cumbersome and somewhat unintuitive.
Imo the most elegant way to allow this is as follows:
allow numpy.ndarray and coercibles as input to all distribution methods. These must have shape of the distribution or 1, for dimensions present in the distribution. Inputs that are currently valid - up to 2D coercibles for array distributions, and flots for scalar distributions - are not coerced and treated as presently.
If a numpy.ndarray is passed, dimensions that are not present in the distribution will lead to output upcasting, special case is outer product mode for scalar distributions.
Examples:
For a scalar distribution n = Normal(0, 1), passing n.pdf([1, 2, 3, 4, 5]) will lead to evaluation at 5 points, and return a np.ndarray of shape (5,).
For an array distribution n = Normal([[0, 1], [2, 3]], 1), calling n.pdf([[[1, 2, 3, 4, 5]]]) leads to a return np.ndarray of shape (2, 2, 3) - upcasting happens along the 3rd dimension of length 5 that the argument introduces.
VascoSch92
commented
4 months ago
Design issue related to adding outer product evaluation mode to distribution methods.
Related to comments of @felixwick in https://github.com/sktime/skpro/pull/327#discussion_r1603946431.
Currently,
BaseDistributiondescendants support up-broadcasting of arguments, but not up-broadcasting of results, if arguments with additional dimensions are given. Mathematically, this is related to taking outer products instead of element-wise products, in scalar or vector casesThis is a natural feature to offer, for instance
tensorflow.probabilityfunctions in this way, andcyclic-boostingalso has the feature.There are a few obstacles for adding this:
pd.DataFramenumpy.ndarray-s - where are not a supported input typecyclic-boostinghas an extra argument that controls elementwise vs outer product, which I find cumbersome and somewhat unintuitive.Imo the most elegant way to allow this is as follows:
numpy.ndarrayand coercibles as input to all distribution methods. These must have shape of the distribution or 1, for dimensions present in the distribution. Inputs that are currently valid - up to 2D coercibles for array distributions, and flots for scalar distributions - are not coerced and treated as presently.numpy.ndarrayis passed, dimensions that are not present in the distribution will lead to output upcasting, special case is outer product mode for scalar distributions.Examples:
n = Normal(0, 1), passingn.pdf([1, 2, 3, 4, 5])will lead to evaluation at 5 points, and return anp.ndarrayof shape(5,).n = Normal([[0, 1], [2, 3]], 1), callingn.pdf([[[1, 2, 3, 4, 5]]])leads to a returnnp.ndarrayof shape(2, 2, 3)- upcasting happens along the 3rd dimension of length 5 that the argument introduces.Thoughts, @setoguchi-naoki, @felixwick, @vascosch92, @ShreeshaM07 ?