Let’s assume we have a hypothesis or model m that we fit on our training data. In machine learning, the training performance — for example, accuracy — is what we measure and optimize during training time. Let’s call this training accuracy ACCtrain(m).

Now, what we really care about in machine learning is to build a model that generalizes well to unseen data, that is, we want to build a model that has a high accuracy on the whole distribution of data; let’s call this ACCpopulation(m). (Typically, we use cross-validation techniques and a separate, independent test set to estimate the generalization performance.)

Now, overfitting occurs if there’s an alternative model m’ from the algorithm’s hypothesis space where the training accuracy is better and the generalization performance is worse compared to model m – we say that m overfits the training data.

Learning Curves

As a rule of thumb, a model is more likely to overfit if it is too complex given a fixed number of training samples. The figure below shows the training and validation accuracies of a SVM model on a certain dataset. Here, I plotted the accuracy as a function of the inverse regularization parameter C – the larger the value of C the larger the penalty term against complexity.

We observe a larger difference between training and test accuracy for increasing values of C (more complex models). Based on the plot, we can say that the model at < 10^-1 underfit the training data whereas the models > 10^-1 overfit the training data.

Remedies

Remedies against overfitting include

  1. Choose a simpler model by adding bias and/or reducing the number of parameters
    1. Adding regularization penalties
    2. Reducing the dimensionality of the feature space
  2. Collecting more training data



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