What type of error is reduced when using a greater number of nearest neighbors in k-nearest neighbors?

In the context of k-nearest neighbors (k-NN) algorithms, using a greater number of nearest neighbors tends to reduce variance. Variance refers to the sensitivity of the model to fluctuations in the training data. By increasing the number of neighbors, the model averages the output over a larger portion of the training dataset, which stabilizes the predictions and leads to less variability in the model's output. Essentially, this averaging effect helps in smoothing out the noise present in the data, resulting in a more generalizable model that is less likely to overfit to the specificities of the training data.

Irreducible error, on the other hand, is associated with the inherent noise within the data itself and cannot be reduced by modifying the model or its parameters. Similarly, bias refers to systematic errors introduced by approximating a real-world problem with a simplistic model. Increasing the number of neighbors can slightly reduce bias because it can lead to a more complex decision boundary, but that change is less significant than the effect on variance.

Thus, choosing to increase the number of nearest neighbors primarily targets the reduction of variance in predictions, making the k-NN model more robust to fluctuations in the data.