ML Algorithms addendum: Passive Aggressive Algorithms

Passive Aggressive Algorithms are a family of online learning algorithms (for both classification and regression) proposed by Crammer at al. The idea is very simple and their performance has been proofed to be superior to many other alternative methods like Online Perceptron and MIRA (see the original paper in the reference section). Classification Let’s suppose to have a dataset: The index t has been chosen to mark the temporal dimension. In this case, in fact, the samples can continue arriving for an indefinite time. Of course, if they are drawn from same data generating distribution, the algorithm will keep learning (probably without large parameter modifications), but if they are drawn from a completely different distribution, the weights will slowly forget the previous one and learn the new distribution. For simplicity, we also assume we’re working with a binary classification based on bipolar labels. Given a weight vector w, the prediction […]