Great initiative. I really appreciate the attempt to standardize and identify common interfaces. Currently, I have three issues:

- Abstraction of Multilabel

The distinguish between classification and regression seems to be natural and also the abstraction of a multi-label makes sense to me. The simplest multi-label approach that I can think of is a collection of binary classifiers. Do you plan to support also mixtures of multi-labels (regression / multinomial classification)? If so, does it makes sense to distinguish between ``MultilabelClassifier`` and ``MultilabelRegressor``? Isn't it then just a list of Estimators?

- Model-based vs. memory-based

I am wondering if it is worth to distinguish between memory-based (e.g., k-nearest neighbour, kernel-machines,...) and model-based predictions (Decision trees, NN, Naive Bayes, GLMs)? Or more general, how does k-nearest neighbour fit into that framework?

- Model vs. Estimator Abstraction

Currently, the main distinction is between classification and regression. However, many methods are similar because they have the same modelling rather than they have the same prediction type. I am wondering how the functional similarities can be reflected in that hierarchy. I tried to follow a bottom-up approach and applied these abstractions to different learning methods. Here are two examples:

Decision trees are trained with some recursive algorithm as ID3 or C4.5 and the predicition is obtained by traversing the tree. The difference between classification and regression plays rather a minor role. So, intuitively, there is a DecisionTree estimator that can be, e.g., ID3 or C4.5. Then, the DecisionTreeClassifier is a DecisionTree with classification criteria; it returns a DecisionTree.Model (the tree) with a predictClass function (Classifier.Model?). The DecisionTreeRegresser is a DecisionTree with regression criteria and it returns a DecisionTree.Model with a predictScore function (Regressor.Model?). Formally, it looks like

- DecisionTree extends Estimator
- DecisionTreeClassifier extends DecisionTree with Classifier
- DecisionTreeRegressor extends DecisionTree with Regressor

- DecisionTree.Model extends Transformer
- DecisionTreeClassifier.Model extends DecisionTree.Model with Classifier.Model
- DecisionTreeRegressor.Model extends DecisionTree.Model with Regressor.Model

Methods like LogReg, SVM, RidgeRegression, ... maintain a weight vector (one probably could summarize them to GLMs). The inner product with the example vector results naturally in a regression score for each prediction; a binary classification is then derived by thresholding that score. The underlying optimization problem for all consists of a sum over loss functions and a regularization term (regularized empirical risk minimization) that can be solved by different solvers, e.g., SGD, LBFGS... So to exploit this structure, I would expect something like this:

- RegularizedEmpiricalRiskMinimizer extends Estimator

// LogisticRegression and SupportVectorMachine could be an automatic selection between the binomial and multinomial version
- BinomialLogisticRegression extends RegularizedEmpiricalRiskMinimizer
- MultinomialLogisticRegression extends RegularizedEmpiricalRiskMinimizer
- BinomialSupportVectorMachine extends RegularizedEmpiricalRiskMinimizer
- RidgeRegression extends RegularizedEmpiricalRiskMinimizer

- LinearModel extends Transformer
- BinomialLinearModel extends LinearModel with Classifier.Model
- MultinomialLinearModel extends LinearModel with Classifier.Model
- BinomialLogisticRegression.Model extends BinomialLinearModel with ProbabilisticClassificationModel
- MultinomialLogisticRegression.Model extends MultinomialLinearModel with ProbabilisticClassificationModel
- BinomialSupportVectorMachine.Model extends BinomialLinearModel // actually it is a binomial linear model
- RidgeRegression.Model extends LinearModel // actually it is a linear model

So isn't the Classifier.Model more a trait than an abstract class? Perhaps, I just missed something, but I think it is helpful to consider the interfaces for specific instances. I am really interested in discussing the pros/cons.

I'm closing this and calling it fixed. This JIRA was scoped a bit too large, and I'm cutting it off to limit it to classification and regression abstractions. I've created a new umbrella SPARK-10817 under which we can do further work on abstractions.