Ranking: Difference between revisions
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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NCDG_p = \frac{DCG_g(\mathbf{r})}{\max_{\mathbf{r}DCG_p(\mathbf{r}) | NCDG_p = \frac{DCG_g(\mathbf{r})}{\max_{\mathbf{r}}DCG_p(\mathbf{r})} | ||
\end{equation} | \end{equation} | ||
</math> | </math> | ||
Revision as of 20:47, 15 April 2024
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: \(\displaystyle \begin{equation} NCDG_p = \frac{DCG_g(\mathbf{r})}{\max_{\mathbf{r}}DCG_p(\mathbf{r})} \end{equation} \)