Decision Tree

Consider a dataset consisting of 10 examples, 6 of which are Yes and 4 of which are No. Below given is the formula for determining the dataset's entropy before splitting:

For example, let's consider that feature "X" divides the dataset in half:

Subset 1: 4  Yes and 1 No

Subset 2: 2 Yes and 3 No

First, we determine the information gain from dividing the dataset along feature "X" and then we compute the entropy for every subdivision.

In order to obtain the Information Gain, the weighted average of the subsets' entropies is calculated and then subtracted from the original dataset's entropy.

Infinite Number of Trees

Given a dataset's rich range of attributes and the various ways those features can be partitioned, it is theoretically feasible to construct an endless number of trees. Multiple tree topologies can be generated from a limited set of features depending on the selection on where to split (for continuous features) and how to combine (for categorical or boolean features). With the stopping conditions influencing the final tree structure—for example, the maximum depth of the tree, minimum samples at a leaf node, or minimal information gain for a split—the number of alternative trees is practically unlimited.

For supervised learning models in particular, data preparation is an essential part of the machine learning process. Labeled data, which includes both input attributes and the right output, is used to train supervised learning algorithms. This labelled data is used by the model to train it to predict the output given the input. Predictions on previously unseen data are possible after the model has been trained.

Key Steps in Data Preparation for Supervised Learning:

•  Acquiring Labeled Data: Collecting a dataset with the right outputs labeled for each occurrence is the initial stage. The model will train itself to anticipate this label.

• Creating Separate Data Sets for Training and Testing: Two parts make up the labeled dataset:

 The Training Set is what we need to construct or train the model. This data is used by the model to learn.

 The Testing Set: This is where the model's accuracy is checked. This set is utilized to assess the model's ability to generalize its predictions from the training data to fresh data; the model does not see this set during training.

In order to evaluate the model's generalizability, it is essential to test its accuracy on data it has never seen before; this can only be achieved by dividing the data.

The Importance of Separating Training and Testing Data Sets:

To evaluate the model's efficacy, the training and testing sets should not be related. Because the model has "seen" the data during training, its performance on the testing set may be inflated if there is an overlap. The model's ability to generalize to new data would not be accurately measured in this case.

The data which is intended to utilize contains characteristics that are pertinent to the prediction of future motorsport championships, such as measures for driver performance and team performance. Each race or season's results (such as the champion) are labeled in the data.

Assembling Data Sets for Training and Evaluation:

To make sure the two sets of data are really representative of the whole dataset, the split is usually done at random. Nevertheless, in order to maintain the temporal order of events, the split might be executed chronologically for time-series data, such as results from motorsports. Typically, 70–80% of the data is set aside for training and 20–30% is set aside for testing.

The Full Decision Tree which the model utilized to predict future champions is visualized above. It may be difficult to interpret each detail here because of the tree's depth and complexity. Next, we'll see the tree in its pruned form to understand it better. Pruning the tree involves limiting its depth to simplify the model and focus on the most significant decision paths.

Pruned Tree with Max Depth of 3: This tree highlights the most important choices based on feature importance and offers a higher-level perspective of the decision-making process. It makes it simpler to understand how important decisions are made by reducing the complexity of the model.

Pruned Tree with Max Depth of 2: This variant concentrates on the most important decision points and provides an even more straightforward perspective. It draws attention to the key characteristics that the model use to distinguish between champions and non-champions.

The way the Decision Tree model prioritizes and decides depending on many features is demonstrated by these pruned trees. Reducing overfitting can also be achieved by limiting the tree's depth, which will improve the model's ability to generalize to new data.

The Decision Tree model demonstrated high accuracy in predicting champions, as evidenced by the performance metrics and the confusion matrix. The display of the decision trees, including both the complete and pruned versions, offers valuable insights into the model's decision-making process and the significance of certain characteristics.

Through the analysis of the trees, we may discern the most relevant attributes for predicting a winner, including total points, total victories, and podium finishes. These insights are important for understanding the primary aspects that contribute to a championship victory in the dataset.

To predict future formula one driver and constructor championships, the dataset was fed into a Decision Tree model, which yielded interesting findings and insights. Based on the results, the following are the main conclusions:

1. Understanding Important Predictors: Certain factors are very important in identifying a champion, as demonstrated by the model's performance and the decision tree visualization. Among these are:

• Total Points: It should come as no surprise that a driver's total points for the season serves as a reliable predictor of their championship status.

• Win totals and podium finishes are important metrics that show both superior performance in races over the season and steady performance.

• Average Finish Position: A measure of general consistency in performance, which is important when trying to win a championship.

• Races Participated: This factor accounts for the driver's experience as well the capacity to compete in several races, which is necessary to get points.

2. High Model Performance: With a very high ROC-AUC score and high accuracy (about 99.13%), the Decision Tree model proved to be highly effective in differentiating champions from non-champions. This implies that a high degree of championship outcome prediction may be made with the features chosen for the model.

3. The Significance of Model Evaluation: By utilizing diverse metrics (precision, recall, F1 score, and the confusion matrix heatmap), we were able to acquire a more profound comprehension of the model's advantages and shortcomings. In other words, the model performs exceptionally well at identifying real champions (high recall), but its precision (accuracy) in identifying champions incorrectly is somewhat compromised. This emphasizes the value of a well-rounded approach to model evaluation that goes beyond simple accuracy.

4.  Decision Tree-Based Visual Insights: The Decision Trees' decision-making process was clearly visible through the visualizations of both the complete and pruned trees. They demonstrated how several characteristics influence the likelihood of a champion, with the clipped trees providing a condensed perspective that highlights the most important deciding factors.

According to the analysis, motorsport is a naturally unpredictable sport, even though previous performance measurements are a good predictor of championship potential. The results of championships can also be influenced by variables not included in the dataset, such as team dynamics, developments in technology, and even pure luck. On the other hand, the model does offer a strong foundation for making informed predictions based on the information at hand.