Score Aggregation via Spectral Method
نویسندگان
چکیده
The score aggregation problem is to find an aggregate scoring over all candidates given individual scores provided by different agents. This is a fundamental problem with a broad range of applications in social choice and many other areas. The simple and commonly used method is to sum up all scores of each candidate, which is called the sumup method. In this paper, we give good algebraic and geometric explanations for score aggregation, and develop a spectral method for it. If we view the original scores as ‘noise data’, our method can find an ‘optimal’ aggregate scoring by minimizing the ‘noise information’. We also suggest a signalto-noise indicator to evaluate the validity of the aggregation or the consistency of the agents.
منابع مشابه
Spectral MLE: Top-K Rank Aggregation from Pairwise Comparisons
This paper explores the preference-based top-K rank aggregation problem. Suppose that a collection of items is repeatedly compared in pairs, and one wishes to recover a consistent ordering that emphasizes the top-K ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce model that postulates a set of latent preference scores underlying all items, where the odds...
متن کاملThermodynamic Characterization of the Aggregation Phenomena of SafranineT by Spectral Titration and Chemometric Analysis
The dimerization constants of Safranine T have been determined by studying the dependence of its absorption spectra on the temperature in the range 30–70 ◦C at different total concentrations of Safranine T (1.03×10−5, 1.44×10−5 and 1.73×10−5 M). The monomer–dimer equilibrium of Safranine T has been determined by applying MCR-ALS method on the absorpti...
متن کاملThermodynamic Characterization of the Aggregation Phenomena of SafranineT by Spectral Titration and Chemometric Analysis
The dimerization constants of Safranine T have been determined by studying the dependence of its absorption spectra on the temperature in the range 30–70 ◦C at different total concentrations of Safranine T (1.03×10−5, 1.44×10−5 and 1.73×10−5 M). The monomer–dimer equilibrium of Safranine T has been determined by applying MCR-ALS method on the absorpti...
متن کاملState Compression of Markov Processes via Empirical Low-Rank Estimation
Model reduction is a central problem in analyzing complex systems and highdimensional data. We study the state compression of finite-state Markov process from its empirical trajectories. We adopt a low-rank model which is motivated by the state aggregation of controlled systems. A spectral method is proposed for estimating the frequency and transition matrices, estimating the compressed state s...
متن کاملResearch and applications: Patient-level temporal aggregation for text-based asthma status ascertainment
OBJECTIVE To specify the problem of patient-level temporal aggregation from clinical text and introduce several probabilistic methods for addressing that problem. The patient-level perspective differs from the prevailing natural language processing (NLP) practice of evaluating at the term, event, sentence, document, or visit level. METHODS We utilized an existing pediatric asthma cohort with ...
متن کامل