When it comes to building models based on collected data, there is much more to consider than just fitting the observations. The challenge lies in selecting the best model among the many possibilities. This general problem, known as model selection, goes beyond regression and applies to various types of models.
In the previous section, we discussed evaluating the error of a model by measuring the difference between each data point and the model’s prediction. This method helps us determine how well a model predicts the available data. However, as the complexity of the dataset increases, fitting more and more models to the data may lead to overfitting.
Overfitting occurs when a model becomes too complex, fitting the training data exceptionally well but failing to generalize to new data. To tackle this issue, we need a cure for overfitting that applies to all types of models. Enter validation, a powerful concept that assesses a model’s performance based on new, unseen data.
When we collect data, we typically want our model to predict the outcome of future experiments. Therefore, the assessment of a model’s performance should be based on its ability to predict new data, not the data used for training. This approach ensures that the model’s predictive capabilities are properly evaluated.
To demonstrate this concept, let’s revisit a simple example of fitting a polynomial model to five data points. We’ll imagine collecting additional data points and plot them as red crosses alongside the original data points. Next, we’ll evaluate the errors of three polynomial models using the new data.
The linear model, with a moderate amount of error, remains consistent when evaluated on the new data. However, the quadratic model’s error increases significantly compared to the linear model. Surprisingly, the magenta fourth-degree polynomial, which perfectly fits the original data points, no longer has zero error and no longer performs the best among the three models.
By performing validation and assessing the models using new data, we obtain a different answer regarding the best model. In this case, the linear model, which also happens to be the simplest, emerges as the winner with the smallest validated error.
It’s crucial to note that the model selection process involves comparing different models rather than finding the single best model. While we can’t claim that the linear model is the definitive model for the dataset, we can confidently say that it outperforms the other evaluated models.
This validation approach is not limited to polynomial models; it extends to models of various complexities and types. Whether it’s logistic regression or classification, the concept of using validation to assess models using unseen data holds true. It provides a valuable method for comparing models with different numbers of parameters, offering a data-driven approach to combatting overfitting and making informed model selection decisions.
In conclusion, when it comes to model selection and validation, relying on unseen data is the key. By using this method, you can avoid overfitting and choose the most appropriate model for your data. Remember, in the ever-changing world of models, validation is the secret ingredient that brings out the true potential of your predictions.
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