Another way of asking this question is “Is a random forest a better model than a decision tree?” And the answer is yes because a random forest is an ensemble method that takes many weak decision trees to make a strong learner. Random forests are more accurate, more robust, and less prone to overfitting.

Whether 50 small decision trees are better than a large one depends on various factors, including the nature of the data, the problem you’re trying to solve, computational resources, and the trade-offs between model complexity and performance.

Here are some reasons why 50 small decision trees might be preferable:

Reduced Overfitting: Small decision trees are less prone to overfitting compared to a single large decision tree. Overfitting occurs when a model learns the training data too well, including noise and outliers, and performs poorly on unseen data. By using multiple small trees, you can reduce the risk of overfitting.
Improved Generalization: Ensemble methods like random forests or boosting, which utilize multiple decision trees, often yield better generalization performance compared to a single large decision tree. Each tree in the ensemble learns different aspects of the data, and their predictions are combined to make a final prediction, leading to better overall performance.
Better Robustness: Small decision trees are generally more robust to noise and outliers in the data. Since they focus on different subsets of features or data points, they may provide a more stable prediction in the presence of noise.
Parallelization: Training multiple small decision trees can be parallelized more easily compared to training a single large decision tree. This can lead to faster training times, especially when dealing with large datasets.

However, there are also scenarios where a large decision tree might be preferable:

Interpretability: A single large decision tree may be easier to interpret and understand compared to an ensemble of smaller trees. If interpretability is crucial, a single decision tree might be preferred.
Resource Efficiency: In some cases, training and deploying a single large decision tree might be more resource-efficient than managing multiple small trees, especially if computational resources are limited.
Specific Problem Characteristics: The characteristics of the problem and the data might favor one approach over the other. For example, if the dataset has a simple underlying structure, a single decision tree might suffice. Conversely, if the data is complex and high-dimensional, an ensemble of trees might perform better.

In conclusion, whether 50 small decision trees are better than a large one depends on the specific context of the problem, including considerations of overfitting, generalization, interpretability, computational resources, and the nature of the data.