Decision Trees

Overview

A decision tree is a supervised learning algorithm often used for classification tasks, though it can also be adapted for regression. At its core, the decision tree algorithm works by creating a flowchart-like structure where data is split at various points, or “nodes,” based on feature values. These splits are strategically chosen to maximize the predictive accuracy of the model, ultimately guiding the data to its final classification at the “leaves” or endpoints of the tree. Through this method, decision trees can make predictions by tracing each observation through the tree structure, where each split is a decision rule directing it down one branch or another.

A key component of training a decision tree involves choosing the optimal splitting points at each node. This is achieved using concepts like Gini impurity and entropy, two measures that quantify the “purity” of a split. The Gini impurity metric, which ranges from 0 to 1, assesses the probability of incorrectly classifying a randomly chosen element if it were assigned a label based on the observed distribution at that node. Lower values indicate a more “pure” split where observations largely belong to one class. Alternatively, entropy, rooted in information theory, measures the disorder or randomness at a given split. When entropy is low, data at the split is more homogeneous, and as entropy rises, the data becomes more mixed.

Both Gini impurity and entropy are used to calculate information gain, which determines the effectiveness of a feature in improving classification accuracy. Information gain represents the reduction in impurity or disorder achieved after a split. During model training, the algorithm iteratively chooses the feature and threshold that yield the highest information gain, incrementally building a tree that optimally separates data by class. Thus, information gain acts as the guiding principle for selecting each split, allowing the decision tree to structure itself in a way that maximizes classification accuracy while minimizing misclassification risk.

Code

Results and Conclusions

The decision tree classifier produced a high accuracy in distinguishing between the presence or absence of snow, with accuracy values near 98%. This suggests that the selected features are strong predictors for this classification task. Visualizations include a confusion matrix that shows a clear breakdown of true positive, false positive, true negative, and false negative predictions, providing a granular view of the model’s predictive performance. For the Gini-based decision tree, we observe a similar structure in classification accuracy, reinforcing the decision tree model’s robustness across both splitting criteria.

The confusion matrix offers critical insights into the classifier’s performance by showing a high rate of correctly classified instances and minimal misclassifications. Specifically, the model effectively distinguishes between conditions where snow is present and absent, affirming that our chosen features provide meaningful distinctions for the classifier. This accuracy aligns with the model’s feature importance rankings, where TAVG_Avg (temperature average) appears as the primary predictive factor, influencing both presence and absence conditions.

Feature Importance

These results highlight temperature as a primary indicator of snow presence, with soil moisture and precipitation levels reinforcing the environmental conditions suitable for snowfall. The model’s structure and importance rankings suggest that deep soil moisture is much more important than initially thought. Soil moisture at 8ft ends up being a predictor of snowfall, rather than a strictly reactionary value. It's possible that snow seeps into the ground more quickly than thought and sticks around longer.

Ultimately, these findings not only corroborate the expected meteorological relationships but also illustrate how soil and precipitation factors can enhance predictive accuracy when assessing snow events. This framework provides a strong basis for further exploration, such as incorporating additional seasonal factors or examining regional variability in snow predictions.