[ENH] Support for discrete output distributions and probabilistic classification

[fkiraly]

Even though scikit-learn supports probabilistic classification and, thus, discrete output distributions, it has a few problems:

• the predict_proba API is inconsistent with the skpro regression API, as it returns a numpy array and not a distribution object
• there is no API for multivariate probabilistic classification, or ordinal regression.

It was suggested by @felipeangelimvieira to add a skpro native probabilistic classifier API that can represent a wider range of return distributions.

Someone working on this should give more details about the API design first.

As a starting point, I suggest:

• a new module classification
• a base class BaseProbaClassifier with methods fit, predict and predict_proba
• if ordinal classification is also covered, then predict_quantiles and predict_interval may also make sense, in this case a capability tag for ordinal classification
• a distribution DiscreteClass used for the output
• a scikit-learn adapter that allows to expose any sklearn probabilistic classifier under the modified API

[ANANYA542]

Hi @fkiraly, I'd like to work on this I went through BaseProbaRegressor, BaseSurvReg, and the BaseDistribution hierarchy to align with existing patterns. Here's my proposed design:
Module layout:
skpro/classification/
├── base/_base.py # BaseProbaClassifier
├── adapters/_sklearn.py # SklearnProbaClassifier
└── tests/
skpro/distributions/categorical.py # new distribution

BaseProbaClassifier — extends BaseEstimator directly (not BaseProbaRegressor, since outputs differ fundamentally):

1. fit(X, y) → stores classes_ from training labels
2. predict(X) → pd.DataFrame of predicted labels (default: mode of predict_proba)
3. predict_proba(X) → Categorical distribution object, not a numpy array
   Optional predict_interval / predict_quantiles for ordinal classification, gated behind a capability:ordinal tag — but I'd defer this to a follow-up.

Categorical distribution — distr:measuretype = "discrete", parameterized by p (n_samples × n_classes) and classes:

1. pmf(x) — vectorized per-sample probability for given class labels
2. sample() — draws class labels according to stored probabilities
3. mean() — well-defined only for numeric classes (sum(p_i * class_i)); for non-numeric, would raise or fall back to mode. Happy to discuss the right convention here.

SklearnProbaClassifier adapter:
clf = SklearnProbaClassifier(RandomForestClassifier())
clf.fit(X_train, y_train)
d = clf.predict_proba(X_test) # → Categorical distribution
d.pmf("class_A") # per-sample P(class_A)

PR plan:

1. Categorical distribution + tests
2. BaseProbaClassifier + sklearn adapter + tests
3. (follow-up) ordinal classification support

One naming question: the issue mentions DiscreteClass — I used Categorical to match scipy/PyTorch/TF conventions, but happy to rename. Would love your feedback on the design

[Ironankit525]

i would like to work on it,can you plz assign it to me.