Ranking

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Revision as of 20:47, 15 April 2024 by David (talk | contribs) (Created page with "Some notes on ranking techniques ==Basics== [https://medium.com/@mayurbhangale/pointwise-pairwise-and-listwise-learning-to-rank-baf0ad76203e Pointwise, Pairwise and Listwise Learning to Rank] ===Point-wise ranking=== In point-wise ranking, you have some scores for you document <math>y_i</math> so you can train your model <math>f</math> to predict such scores in a ==Metrics== ===Cumulative Gain=== Suppose you have a list of results <math>x_1,..., x_n</math> with rel...")
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Some notes on ranking techniques

Basics

Pointwise, Pairwise and Listwise Learning to Rank

Point-wise ranking

In point-wise ranking, you have some scores for you document \(\displaystyle y_i\) so you can train your model \(\displaystyle f\) to predict such scores in a


Metrics

Cumulative Gain

Suppose you have a list of results \(\displaystyle x_1,..., x_n\) with relevency \(\displaystyle r_1,...,r_n\).
Then the cumulative gain at position \(\displaystyle p\) is the sum of the relevency of the first \(\displaystyle p\) results: \(\displaystyle \begin{equation} CG_p = \sum_{i=1}^{p} r_i \end{equation} \)

The discounted cumulative gain (DCG) takes the position into account, discounting lower-ranked results: \(\displaystyle \begin{equation} DCG_p = \sum_{i=1}^{p} \frac{r_i}{\log_2 (i+1)} \end{equation} \)

The normalized discounted cumulative gain (NDCG) is 1-normalized by dividing over the best possible ranking: \(\displaystyle \begin{equation} NCDG_p = \frac{DCG_g(\mathbf{r})}{\max_{\mathbf{r}DCG_p(\mathbf{r})}} \end{equation} \)