Overfitting in regression models

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Are you wondering whether overfitting is a problem in regression models? Or maybe you are more interested in learning how to address overfitting in regression models? Well either way, you are in the right place!

In this article, we tell you everything you need to know about overfitting and how it relates to regression models. Specifically, we will talk about how overfitting relates to linear regression models and generalized linear models, such as logistic regression models. First, we discuss what overfitting is and why overfitting is a problem. After that, we discuss how to identify whether a regression model is overfitting. Finally, we discuss whether overfitting is a common problem with regression models and how to prevent regression models from overfitting.

What is overfitting?

What is overfitting? Overfitting is a phenomenon that occurs when a machine learning model focuses too much on granular details of the dataset it was trained on. Specifically, it occurs when the model focuses on specific details that are characteristic of the training dataset itself, but are not generalizable to other datasets. This means that the model will be able to make accurate predictions on observations it saw during training, but it will not be able to make accurate predictions on observations that were not seen during training.

Two examples of how different machine learning models might fit to the same data. In one example, there is no overfitting. In the other there is overfitting.

Why is overfitting a problem?

Why is overfitting a problem? It is a problem when a model overfits to the dataset it was trained on because that means that the model will not be able to make good predictions on new observations that were not seen during training. Machine learning models are generally trained with the specific purpose of being able to make predictions on observations that have not been seen before, so that means that machine learning models that have overfit to the training dataset cannot fulfill their main purpose.

How to recognize when a model is overfitting

How do you recognize when a machine learning model, such as a regression model, is overfitting? The best way to identify when a machine learning model is overfitting is to compare the predictions that the model makes on the data it was trained on to the predictions the model makes on a dataset it was not trained on. If the predictions that the model makes on the dataset it was trained on are much better than the predictions the model makes on a dataset that was not seen during training, then the model is likely overfitting.

Do regression models overfit?

Is overfitting common in regression models like linear regression and logistic regression? Overfitting is a problem that can happen when you are training models like linear regression models and logistic regression models. That means that you should always evaluate how your model performs on data that was not seen during training when you are building a regression model to predict an outcome.

With that being said, we will note that regression models like linear regression and logistic regression are less likely to overfit than many other types of machine learning models. This is because complex models with many parameters that need to be fit are more likely to overfit than simple models with fewer parameters. Regression models are relatively simple and have only a few parameters that need to be fit so they are less likely to overfit than a more complex model, such as a neural network model.

An example of what prediction error on the test data and training data might look like as model complexity increases if a model is overfitting.

How to prevent overfitting in regression models?

How do you prevent a regression model like a linear regression model or a logistic regression model from overfitting? Here are a few examples of strategies you can take to prevent a regression model from overfitting.

  • Reduce the number of features. The first option you have when you see that your regression model is overfitting is to reduce the number of features that are being used in the model. Each feature that is added to the model introduces a new parameter that needs to be fit, so reducing the number of features that are used in a model will reduce the number of parameters that need to be fit and therefore the overall complexity of the model.
  • Use more data to train the model. Another option you can turn to when you see that a regression model is overfitting is increasing the amount of data that you are using to train the model. Overfitting often happens not just because there are too many parameters that need to be fit, but also because there is not enough data to be able to estimate those parameters in a way that can generalize to other datasets. Increasing the amount of data you are using to train your model can help to ameliorate this problem.
  • Add regularization. Another popular option you can turn to when you see that your regression model is overfitting is introducing some regularization into your model. When you add regularization to a model, you add a penalty that puts constraints on how fast model parameters or coefficients that are associated with different features can grow. What happens, many of the parameters shrink to zero or to a value that is close to zero. This effectively eliminates those features from the model and reduces complexity. There are few different types of regularization that can be used in regression models. To learn more about the differences between different regularized regression models, check out our articles on LASSO models and ridge regression models.

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