Mean Average Precision (MAP) is a metric used to evaluate the performance of information retrieval systems, such as search engines and recommendation systems. It calculates the average precision across multiple queries, providing a single score that summarizes how well the system ranks relevant documents. MAP takes into account both the precision of the results—how many relevant items are returned—and the order in which they appear. Higher MAP scores indicate better performance, as they reflect a system's ability to retrieve relevant items early in the list of results.
To understand MAP, let's break down its components. First, for each query, you calculate the precision at each position in the result list where a relevant item appears. For example, if you returned ten documents for a query and three of them are relevant, you would compute precision at all the points where those relevant documents appear. The average of these precision scores for a given query is known as the Average Precision (AP). Then, MAP is simply the mean of the Average Precisions calculated for all queries considered. If you evaluate on five queries with their corresponding APs of 0.8, 0.6, 0.9, 0.7, and 0.5, the MAP would be (0.8 + 0.6 + 0.9 + 0.7 + 0.5) / 5 = 0.7.
MAP is particularly useful in scenarios where ranking order is important, such as search queries or recommendation systems. For example, in an e-commerce website, if a user searches for "wireless headphones," the system might return a list of products. If the first few results are highly relevant and popular items, while less relevant items are farther down the list, the MAP score will help quantify the effectiveness of the retrieval algorithm. It can be employed for tuning the model parameters or comparing different retrieval approaches by providing a clear metric that reflects user satisfaction based on the ranking quality.