Evaluating Search Engines by Modeling the Relationship Between Relevance and Clicks

by Ben Carterette and Rosie Jones

This paper tells us about a method to evaluating two ranking reseults based on clicks of users. We know the ranking affects exposures of the links, i.e. the higher rank one item has, the more attension human beings pay to. Therefore it is more reasonable to use a discounted relavance called discounted cumulative gain (DCG)

\mathrm{DCG}_l = \mathrm{rel}_1 + \sum_{i = 2}^l \frac{\mathrm{rel}_i}{\log_2 i}.

That is, the rank 1 item has no discount while rank i item has a discount ratio of 1/\log_2 i.

So if we want to compare two ranking results, we have to calculate the relevance score given by given the query. This is not always known. People might have been asked to score the documents with discrete values (on a scale of 5, e.g.) but not all documents will be marked. We model this scale with a multinomial distribution and simulated the scoring procedure and compare the two DCG values. If for 95% cases, one is higher than the other, we might assert it is better.

The author proposed quite a simple model to model \Pr(X_i \mid q, c, ). It is an ordinal logistic regression model with linear and quadratic features. So when we trained the model, we can simulate the DCG and compare two rankings.