Modellkomplexität

Modellkomplexität refers to the degree of intricacy or detail within a model, whether it be a mathematical, computational, or conceptual representation of a system or phenomenon. It is a fundamental concept in various fields, including statistics, machine learning, physics, and economics, as it directly influences a model's ability to capture reality, its interpretability, and its computational cost.

A simple model, often called a "parsimonious" model, has few parameters and makes fewer assumptions. Such models are generally easier to understand, faster to train or simulate, and less prone to overfitting, which is when a model learns the training data too well, including its noise, and performs poorly on unseen data. However, overly simple models might fail to capture the essential dynamics or relationships within the system they represent, leading to underfitting.

Conversely, a complex model incorporates a large number of parameters, intricate relationships, or high-dimensional representations. These models have the potential to represent more nuanced and sophisticated patterns in data. They can achieve higher accuracy on complex datasets and are better at capturing subtle interactions. However, increased complexity often comes at the cost of reduced interpretability, longer computation times, and a higher risk of overfitting.

The choice of model complexity is a critical decision in model development, often guided by the principle of Occam's Razor, which suggests preferring simpler explanations when multiple explanations are equally valid. This trade-off between simplicity and accuracy is often visualized in the bias-variance trade-off. Bias represents the error introduced by approximating a real-world problem, which may be complex, by a simpler model. Variance represents the error from sensitivity to small fluctuations in the training set. High complexity models tend to have low bias but high variance, while low complexity models tend to have high bias but low variance. Finding the optimal level of complexity is essential for building effective and reliable models.