For the K-nearest neighbors classifier, what happens as K increases?

As K increases in the K-nearest neighbors (KNN) classifier, the model becomes less flexible. This decrease in flexibility is primarily due to the larger neighborhood being considered when making predictions. When K is small, the model closely follows the training data, which can lead to high variance as it may react strongly to noise in the data.

However, as K rises, the influence of outliers is reduced because they have less impact when averaged with more neighbors. Consequently, this leads to a more generalized model that is robust but may oversimplify the underlying patterns in more complex datasets. Hence, while the variance decreases due to the model being less sensitive to fluctuations in the training set, the increase in K also impacts bias. Specifically, the squared bias tends to decrease as well, since the model starts making predictions based on a wider range of observations, effectively smoothing out the decision boundary.

In summary, an increase in K results in reduced flexibility, thereby decreasing both variance and squared bias as the KNN classifier averages over a larger set of neighbors, leading to a more stable yet less sensitive prediction.