Elbert Woodard works in a single warehouse that houses holiday ornaments. He's keen on using historical data from this warehouse to predict how many holiday widgets he should have in stock for December. In his predictive model, he strives to find the lowest mean square error and he achieves this by increasing the model complexity. As he adds more terms to his model, what happens to the bias?

Question

Elbert Woodard works in a single warehouse that houses holiday ornaments. He's keen on using historical data from this warehouse to predict how many holiday widgets he should have in stock for December. In his predictive model, he strives to find the lowest mean square error and he achieves this by increasing the model complexity. As he adds more terms to his model, what happens to the bias?

BlackTom AI · Accepted Answer

When considering how bias behaves as model complexity increases, the central idea is that a more flexible model can capture more of the underlying structure of the training data, reducing systematic error in the fit.
Option 1: 'Bias goes up - worse predictions in sample' This is incorrect because increasing model complexity typically reduces bias, not increases it. A more complex model can approximate the true function more closely, thereby lowering the bias component of error.
Option 2: 'Bias goes down - better predictions in sample' This statement aligns with the bias-variance tradeoff: adding terms and increasing flexibility generally lowers bias, and in the training (in-sample) context, predictions tend to look better as the model can fit the observed data more closely. The caveat is that variance may rise, but the question specifically asks about bias.
Option 3: 'Hard to tell - data dependent' While in theory the exact amount of bias can depend on how well the model class matches the true data-generating process, in the common learning-theory view, increasing complexity reduces bias as a general trend, making this option less accurate for the typical expectation in this scenario.

FA25_QTM_110_1 Quiz #11: Prediction, Machine Learning, and the Bias-Variance Tradeoff

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