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Ranking individuals by group comparison

Ranking individuals by group comparison. New exponentiel model Two methods for calculations Regularized least square Maximum likelihood. Ranking individuals by group comparison. Bradley-Terry model k individuals, m competitions I+ and I- opposing teams p vector of individual strengths.

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Ranking individuals by group comparison

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  1. Ranking individuals by group comparison • New exponentiel model • Two methods for calculations • Regularized least square • Maximum likelihood

  2. Ranking individuals by group comparison • Bradley-Terry model • k individuals, m competitions • I+ and I- opposing teams • p vector of individual strengths

  3. Ranking individuals by group comparison • Estimated by minimizing log likelihood • Iterative approach • May only find local minimum, not global

  4. Ranking individuals by group comparison • Definitions: • v vector of individual strengths • T is theoretical team performance • Y is actual team performance

  5. Ranking individuals by group comparison

  6. Ranking individuals by group comparison • New exponential model can be derived • The old model

  7. Ranking individuals by group comparison • New exponential model can be derived • The old model

  8. Regularized least square

  9. Regularized least square

  10. Regularized least square

  11. Regularized least square

  12. Maximum Likelihood

  13. Maximum Likelihood

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