Learning curves help understand the evolution of a model's performance with the amount of data used to train that model. They can be used for instance to know whether more data would help the model be better or not. They also enable you to know whether the model is a good fit, underfitting, or overfitting.
What is a learning curve
To produce a learning curve, many models are trained using a different proportion of the data available for training. For each proportion, the model performance metric (mean square error in our case) will be calculated. In some cases, to avoid having too much variability in the results, it is possible to train multiple models for the same proportion of data and get an average (see curve on test data on the left).
On the Figure shown below for instance, you can see that training a model with more data will improve the model's performance as the mean square error (MSE) keeps going down for the test data. Point 1 shows the MSE when the model is trained on 50% of the available data, and point 2 shows the MSE when the model is trained on 100% of the available data.
How to read a learning curve?
In the examples below, we trained 3 models (linear regression, polynomial regression and decision tree regression) on the same data and we plotted the learning curve for each model:
Example for an underfitting model: Linear regression
 
Example for a suitable model: Polynomial regression
 
Example for an overfitting model: Decision Tree Regression

Read here to find out what “less” or “more complex” means in practical.
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