The complexity of a probabilistic model refers to the number of parameters or variables that the model uses to represent the data. A more complex model may be able to capture more intricate patterns in the data, but it may also require more computation to fit and make predictions.
There is often a trade-off between computational complexity and the richness of a probabilistic model. On one hand, a more complex model may be able to capture more subtle patterns in the data and may therefore have improved performance. On the other hand, a more complex model may require more computational resources to fit and make predictions, which can be a burden if the model is being used in a resource-constrained setting.
To balance these trade-offs, it is important to choose a model that is rich enough to capture the patterns in the data but not so complex that it becomes computationally infeasible to use. One way to do this is to use model selection methods, such as cross-validation, to identify the optimal level of complexity for a given dataset. Another approach is to use regularization techniques, which can help to prevent overfitting by penalizing overly complex models.