Ranking individuals by group comparisons

Huang, Tsung-Hui; Lin, Chih-Jen; Weng, Ruby C.

doi:10.1145/1143844.1143898

Cited by 36 publications

(44 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This idea is generalized to arbitrary combination of predictors [4,5] by extending the definition of F BT (p, x) to F GBT (p, x), , x), we compute p(y|x) for all y ∈ {1, · · · , K} and the label which maximizes the probability is the predicted class. An important problem of this approach is how to compute the maximizer of F GBT (p, x).…”

Section: Numerical Simulationmentioning

confidence: 99%

“…An important problem of this approach is how to compute the maximizer of F GBT (p, x). Some iterative algorithms have been proposed [5,11]. In our experiments, we used the MM algorithm [11].…”

Section: Numerical Simulationmentioning

confidence: 99%

“…This is the MLR and equivalent to (5). The relation between p(y|x; θ) and p(y|x; {η r }) is schematically summarized in figure 8.…”

Section: Consider Maximizing It Undermentioning

confidence: 99%

“…In order to combine soft decisions of binary predictors, the ECOC approach can be used, but Hastie and Tibshirani proposed a different method [3][4][5] which utilizes the Bradley-Terry (BT) model [6]. In this paper, we study the multi-class classification problem from a statistical viewpoint.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Combining binary machines for multi-class: Statistical model and parameter estimation

Ikeda

2010

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract.Combining binary machines for multi-class classification problems is a popular idea, and many related methods have been proposed. When each binary machine reports a hard decision (a binary classifier), one of the most popular methods is to use the error correcting output codes (ECOC), while when each machine reports a soft decision (a binary predictor), another interesting idea is to use the Bradley-Terry (BT) model. In this paper, these methods are reviewed from a statistical viewpoint. As a result, a common framework will be given and natural extensions are derived for both of the ECOC and the BT model approaches. IntroductionSince the proposal of Dietterich and Bakiri [1], the idea of combining binary classifiers for multiclass classifications has become popular.The error correcting output codes (ECOC) approach [1, 2] is a simple method to combine hard decisions of binary classifiers with a predetermined code matrix. In order to combine soft decisions of binary predictors, the ECOC approach can be used, but Hastie and Tibshirani proposed a different method [3][4][5] which utilizes the Bradley-Terry (BT) model [6]. In this paper, we study the multi-class classification problem from a statistical viewpoint. As a result, a unified framework is given and parameter estimation algorithms for these two models are derived.The parameter estimation of the ECOC approach is called the "code matrix" design [7]. Our proposal is to connect it with the multinomial logistic regression (MLR), and to use the elasticnet type sparse estimation method [8] which provides a new method for the code matrix design. The BT model approach is slightly complicated, but it naturally estimates the class probability. The estimated probability is correct if each binary predictor is accurate, otherwise it is not. We propose a method to re-estimate the binary predictors to make the combined statistical model better.

show abstract

Section: Numerical Simulationmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

“…This is the MLR and equivalent to (5). The relation between p(y|x; θ) and p(y|x; {η r }) is schematically summarized in figure 8.…”

Section: Consider Maximizing It Undermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Combining binary machines for multi-class: Statistical model and parameter estimation

Ikeda

2010

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…These properties of paired comparisons have great practical value. In fact, many studies have applied Bradley-Terry models to analyze, for example, psychological data (e.g., Causeur & Husson, 2005;Li & Kim, 2000;Oakes & Slotterback, 2002;Usami, 2009), sports data (e.g., Feddag, 2006;Iwasaki, 2002;Koehler & Ridpath, 1982;Takeuchi & Fujino, 1988), marketing (e.g., Hatzinger & Mazanec, 2007), machine learning (Huang et al, 2006), artificial neural network model (e.g., Menke & Martinez, 2008) and journal citations (Stigler, 1994).…”

Section: Introductionmentioning

confidence: 99%

Individual Differences Multidimensional Bradley-Terry Model Using Reversible Jump Markov Chain Monte Carlo Algorithm

Usami

2010

Behaviormetrika

View full text Add to dashboard Cite

The Bradley-Terry model has been widely and effectively used to rank stimuli from paired comparison data. Existing approaches for paired comparison data analysis, however, have a number of limitations. First, among applied Bradley-Terry models in which multidimensionality is assumed, the effects of individual differences are not considered. Second, in these multidimensional Bradley-Terry models, the number of dimensions is generally evaluated only after analyzing several models with different dimensions separately, thus causing computational inconvenience.In this study, a multidimensional Bradley-Terry model that considers the effects of individual differences is proposed. The proposed model allows estimation of parameters for both scale values of stimuli and individual differences in multidimensional space. A procedure of parameter estimation is presented that uses a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to estimate the optimal number of dimensions as well as associated parameters simultaneously. Simulation studies for examining the utility of the RJMCMC algorithm are performed, and real sports data from sumo are used in a representative example, where the time periods of tournaments are used as parameters for individual differences, in order to verify the validity of the proposed model.

show abstract