Research map / Learning theory and algorithms / Sample complexity
Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the Thurstone/BTL parametric MLE instead of SST-class estimators when data are non-parametric | parametric MLE · simulations with high SNR and independent bands matrices | normalized squared Frobenius error | Hurt |
| Soft singular value thresholding of the observation matrix (sharpened analysis) | SVT estimator over full SST class · synthetic SST class, single comparison per pair | normalized squared Frobenius error | Helped |
| Minimum feedback arc set ordering used as first step over the full SST class | FAS-based estimator · full SST class (counterexample) | estimation performance | Hurt |
| Partial observations: observing each pair with probability p and using SVT with rescaled matrix | SVT estimator · Erdos-Renyi partial observations | normalized squared error bound | Helped |
| Restrict to high-SNR subclass (entries bounded away from 1/2) for the two-stage FAS+isotonic estimator | two-stage estimator · high-SNR SST subclass | minimax rate | No clear effect |
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