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Table of Contents
1. Abstract
2. Introduction
3. Problem Setting
4. Binary Classification Algorithms
5. Analysis
6. Theorem 2: Loss Bound for PA Algorithm (Separable Case)
7. Theorem 3: Loss Bound for PA Algorithm (Normalized Instances)
8. Theorem 4: Mistake Bound for PA-I Algorithm
Summary
The document discusses Online Passive-Aggressive Algorithms for margin-based online learning in various prediction tasks including binary and multiclass categorization, regression, uniclass prediction, and sequence prediction. The algorithms are based on constrained optimization problems with a focus on worst-case loss bounds. The PA algorithm is presented along with two variations, PA-I and PA-II, that adjust the aggressiveness of the updates. The analysis includes loss bounds for the PA algorithm in separable and normalized instance cases, as well as a mistake bound for the PA-I algorithm.