31 add support for conformalized bayes

[pat-alt]

No description provided.

[codecov-commenter]

Codecov Report

Merging #32 (7dd1b4b) into main (479b94f) will decrease coverage by 8.27%.
The diff coverage is 10.00%.

@@            Coverage Diff             @@
##             main      #32      +/-   ##
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- Coverage   99.32%   91.04%   -8.28%     
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  Files           6        7       +1     
  Lines         297      324      +27     
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  Hits          295      295              
- Misses          2       29      +27     

Impacted Files	Coverage Δ
src/ConformalModels/inductive_bayes.jl	0.00% <0.00%> (ø)
src/ConformalModels/inductive_classification.jl	98.41% <100.00%> (ø)

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[pat-alt]

Some very early-stage work on this.

Initially attempted to just standardize/streamline the existing code base, which broadly distinguishes between regressors and classifiers. I thought that to deal with Bayesian models that can produce predictive densities, I'd just need to respecify the the score function as $s(x,y)=-f(y|x,D)$ following Section 2.4 in Angelopoulus (2021). The idea was to then be able to use all existing approaches to regression and classification as before with this new score function.

Unfortunately, this after all seems a little more difficult than anticipated for various reasons. For example, in the case of regression, one can no longer just form intervals based on the quantile $q(\{ s(x_i,y_i) \} _n)$ since the scores represent densities, not residuals. In fact, it seems that one needs to rely on discretization of the output space $\mathcal{Y}$, which can be done efficiently by just sampling from the predictive posterior (see here).

It seems that it will be easier to treat Conformalized Bayes as a separate task for now with separate constructors.