Regression

Regression analysis is a machine learning process for estimating the relationships among different fields in your data, then making further predictions based on these relationships.

For example, suppose we are interested in finding the relationship between apartment size and monthly rent in a city. Our imaginary data set consists of three data points:

After the model determines the relationship between the apartment size and the rent, it can make predictions such as the monthly rent of a hundred square meter-size apartment.

This is a simple example. Usually regression problems are multi-dimensional, so the relationships that regression analysis tries to find are between multiple fields. To extend our example, a more complex regression analysis could take into account additional factors such as the location of the apartment in the city, on which floor it is, and whether the apartment has a riverside view or not, and so on. All of these factors can be considered features; they are measurable properties or characteristics of the phenomenon we’re studying.

When you perform regression analysis, you must identify a subset of fields that you want to use to create a model for predicting other fields. We refer to these fields as feature variables and dependent variables, respectively. Feature variables are the values that the dependent variable value depends on. If one or more of the feature variables changes, the dependent variable value also changes. There are three different types of feature variables that you can use with our regression algorithm:

Regression is a supervised machine learning method, which means that you need to supply a labeled training data set that has some feature variables and a dependent variable. The regression algorithm identifies the relationships between the feature variables and the dependent variable. Once you’ve trained the model on your training data set, you can reuse the knowledge that the model has learned to make inferences about new data.

The relationships between the feature variables and the dependent variable are described as a mathematical function. Regression analysis tries to find the best prediction for the dependent variable by combining the predictions from multiple base learners – algorithms that generalize from the data set. The performance of an ensemble is usually better than the performance of each individual base learner because the individual learners will make different errors. These average out when their predictions are combined.

Regression works as a batch analysis. If new data comes into your index, you must restart the data frame analytics job.

The ensemble learning technique that we use in the Elastic Stack is a type of boosting called extreme gradient boost (XGboost) which combines decision trees with gradient boosting methodologies.

Feature importance is calculated for supervised machine learning methods such as regression and classification. This value provides further insight into the results of a data frame analytics job and therefore helps interpret these results. As we mentioned, there are multiple features of a data point that are analyzed during data frame analytics. These features are responsible for a particular prediction to varying degrees. Feature importance shows to what degree a given feature of a data point contributes to the prediction. The feature importance value of a feature can be either positive or negative depending on its effect on the prediction. If the feature reduces the prediction value, the value is negative. If the feature increases the prediction, the feature importance value positive. The magnitude of the feature importance value shows how significantly the feature affects the prediction both locally (for a given data point) or generally (for the whole data set).

Feature importance in the Elastic Stack is calculated using the SHAP (SHapley Additive exPlanations) method as described in Lundberg, S. M., & Lee, S.-I. A Unified Approach to Interpreting Model Predictions. In NeurIPS 2017.

By default, feature importance values are not calculated. To generate this information, when you create a data frame analytics job you must specify the num_top_feature_importance_values property. The feature importance values are stored in the destination index in fields prefixed by ml.feature_importance.

You can measure how well the model has performed on your training data set by using the regression evaluation type of the evaluate data frame analytics API. The mean squared error (MSE) value that the evaluation provides you on the training data set is the training error. Training the regression model means finding the combination of model parameters that produces the lowest possible training error.

Another crucial measurement is how well your model performs on unseen data points. To assess how well the trained model will perform on data it has never seen before, you must set aside a proportion of the training data set for testing. This split of the data set is the testing data set. Once the model has been trained, you can let the model predict the value of the data points it has never seen before and compare the prediction to the actual value. This test provides an estimate of a quantity known as the model generalization error.

Two concepts describe how well the regression algorithm was able to learn the relationship between the feature variables and the dependent variable. Underfitting is when the model cannot capture the complexity of the data set. Overfitting is when the model is too specific to the training data set and is capturing details which do not generalize to new data. A model that overfits the data has a low MSE value on the training data set and a high MSE value on the testing data set. For more information about the evaluation metrics, see Regression evaluation.