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Update BT docstring (#119)
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Artifacts from previous docs format
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pilot7747 authored Aug 12, 2024
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11 changes: 4 additions & 7 deletions crowdkit/aggregation/pairwise/bradley_terry.py
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Expand Up @@ -20,18 +20,15 @@ class BradleyTerry(BasePairwiseAggregator):
according to the Bradley-Terry's probabilistic model,
$P(i > j) = \frac{p_i}{p_i + p_j}$.
Here $\boldsymbol{p}$ is a vector of positive real-valued parameters that the algorithm optimizes. These
Here $\mathbf{p}$ is a vector of positive real-valued parameters that the algorithm optimizes. These
optimization process maximizes the log-likelihood of observed comparisons outcomes by the MM-algorithm:
$L(\boldsymbol{p}) = \sum_{i=1}^n\sum_{j=1}^n[w_{ij}\ln p_i - w_{ij}\ln (p_i + p_j)]$,
$L(\mathbf{p}) = \sum_{i=1}^n\sum_{j=1}^n[w_{ij}\ln p_i - w_{ij}\ln (p_i + p_j)]$,
where $w_{ij}$ denotes the number of comparisons of $i$ and $j$ "won" by $i$.
{% note info %}
The Bradley-Terry model needs the comparisons graph to be **strongly connected**.
{% endnote %}
Note:
The Bradley-Terry model needs the comparisons graph to be **strongly connected**.
David R. Hunter.
MM algorithms for generalized Bradley-Terry models
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