When fitting a model, what is a significant trade-off in using higher complexity models?

Choosing a higher complexity model typically introduces an increase in variance. This is a fundamental concept in statistical modeling known as the bias-variance trade-off.

Higher complexity models, such as those with more parameters or intricate structures, have greater flexibility to capture the nuances in the training data. While this allows them to fit the training set very well, it also risks overfitting. Overfitting occurs when a model is so finely tuned to the training data that it loses its generalizability to new, unseen data. This means while the model may perform exceptionally well on the training set, it might perform poorly on a test set due to the high variance stemming from its sensitivity to fluctuations or noise in the training data.

In contrast, simpler models tend to have higher bias. They make strong assumptions about the form of the data and may underfit, missing out on important patterns. The relationship between complexity, bias, and variance is thus crucial for model selection and highlights the importance of balancing these elements to achieve good predictive performance.

In this context, increased variance is the correct identification of the trade-off associated with using higher complexity models.