Multiple Models for Multi-Output Regression

Regression problems involve predicting a numerical value given an input example.

Typically, a single output value is predicted. Nevertheless, there are regression problems where multiple numeric values must be predicted for each input example. These problems are referred to as multiple-output regression problems.

  • Multiple-Output Regression : Predict two or more numeric outputs given an input.

Models can be developed to predict all target values at once, although a multi-output regression problem is another example of a problem that can be naturally divided into subproblems.

Like binary classification in the previous section, most techniques for regression predictive modeling were designed to predict a single value. Predicting multiple values can pose a problem and requires the modification of the technique. Some techniques cannot be reasonably modified for multiple values.

One approach is to develop a separate regression model to predict each target value in a multi-output regression problem. Typically, the same algorithm type is used for each model. For example, a multi-output regression with three target values would involve fitting three models, one for each target.

When a prediction is required, the same input pattern is provided to each model and the specific target for each model is predicted and together represent the vector output of the method.

  • Multi-Output Regression : A technique where one regression model is used for each target in a multi-output regression problem.

Another related approach is to create a sequential chain of regression models. The difference is that the output of the first model predicts the first output target value, but this value is used as part of the input to the second model in the chain in order to predict the second output target value, and so on.

As such, the chain introduces a linear dependence between the regression models, allowing the outputs of models later in the chain to be conditional on the outputs of prior models in the chain.

  • Regression Chain : A technique where a sequential chain of regression models is used to predict each target in a multi-output regression problem, one model later in the chain uses values predicted by models earlier in the chain.In each case, multiple regression models are used, just like an ensemble.

A possible difference from ensembles is that the predictions made by each model are not combined directly. We could stretch the definition of “combining predictions” to cover this approach, however. For example, the predictions are concatenated in the case of multi-output regression models and indirectly via the conditional approach in chained regression.

The key difference from ensemble learning methods is that no contributing ensemble member can solve the prediction problem alone. A solution can only be achieved by combining the predictions from all members.