RFC: Allow DiscreteNonParametric to have non-Real support

[DilumAluthge]

Description

Let vs denote the list of support values used when creating an instance of DiscreteNonParametric. Currently, we require that:

• vs::Ts where Ts<:AbstractVector{T} and T<:Real.

This pull request relaxes the requirement so that it is now:

• vs::Ts where Ts<:AbstractVector{T}

This allows you to create instances of DiscreteNonParametric that have non-Real support.

All of the existing DiscreteNonParametric tests are preserved, to show that this change is backwards compatible and will have no effect on DiscreteNonParametric when T<:Real.

I also add some tests for DiscreteNonParametric when T is String.

Motivation

Suppose you have trained a multiclass classifier, and you would now like run the classifier on a single sample. For each of the classes, the classifier will output the probability of that class. For example, the output might be setosa=0.1, versicolor=0.7, verginica=0.2.

Since the output of a multiclass classifier (when run on a single sample) is a discrete non-parametric distribution on the set of classes, it would be natural to store it in a DiscreteNonParametric. However, currently DiscreteNonParametric requires that the support be a list of real values. This pull request relaxes the requirement and allows you to create a DiscreteNonParametric where the support values can be of any type (such as String).

[codecov-io]

Codecov Report

Merging #916 into master will increase coverage by 2.35%.
The diff coverage is 100%.

@@            Coverage Diff            @@
##           master    #916      +/-   ##
=========================================
+ Coverage   73.94%   76.3%   +2.35%     
=========================================
  Files         107     107              
  Lines        5269    5114     -155     
=========================================
+ Hits         3896    3902       +6     
+ Misses       1373    1212     -161

Impacted Files	Coverage Δ
src/samplers/discretenonparametric.jl	100% <100%> (ø)	⬆️
src/univariate/discrete/discretenonparametric.jl	98.07% <100%> (+8.79%)	⬆️
src/univariates.jl	65.69% <100%> (+1.24%)	⬆️
src/multivariate/mvtdist.jl	52.74% <0%> (+0.57%)	⬆️
src/univariate/discrete/binomial.jl	73.4% <0%> (+0.77%)	⬆️
...c/univariate/continuous/generalizedextremevalue.jl	88.18% <0%> (+0.79%)	⬆️
src/matrix/wishart.jl	58.82% <0%> (+1.13%)	⬆️
src/multivariates.jl	79.03% <0%> (+1.25%)	⬆️
src/univariate/continuous/beta.jl	62.65% <0%> (+1.47%)	⬆️
... and 34 more

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[DilumAluthge]

Bump. Any thoughts on this?

[richardreeve]

Not that I have any say, but this looks like a good idea to me. However, am I right in thinking that DiscreteNonParametric currently rounds to integers? If so, then that seems like a slightly crazy restriction in its own right, and your code doesn't fix it... e.g.

logcdf(d::DiscreteUnivariateDistribution, x::Real) = logcdf(d, floor(Int,x))

[DilumAluthge]

I wanted this pull request to be backwards-compatible, which is why I didn't make any changes to the behavior of DiscreteNonParametric when the support is Real.

I imagine that removing those calls to round, floor, etc. would probably be a breaking change.

[richardreeve]

True, but only to people doing some seriously crazy stuff!

[DilumAluthge]

Closing in favor of #941