Post-Pareto Optimality Analysis With Sum of Ranking Differences

2020

PLoS ONE

Sum of Ranking Differences is an innovative statistical method that ranks competing solutions based on a reference point. The latter might arise naturally, or can be aggregated from the data. We provide two case studies to feature both possibilities. Apportionment and districting are two critical issues that emerge in relation to democratic elections. Theoreticians invented clever heuristics to measure malapportionment and the compactness of the shape of the constituencies, yet, there is no unique best method in either cases. Using data from Norway and the US we rank the standard methods both for the apportionment and for the districting problem. In case of apportionment, we find that all the classical methods perform reasonably well, with subtle but significant differences. By a small margin the Leximin method emerges as a winner, but-somewhat unexpectedly-the non-regular Imperiali method ties for first place. In districting, the Lee-Sallee index and a novel parametric method the so-called Moment Invariant performs the best, although the latter is sensitive to the function's chosen parameter.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Apportionment and districting by Sum of Ranking Differences

Sziklai

2020

PLoS ONE

“…Moreover, SRD realizes a multicriteria (multiobjective) optimization, as it ranks and detects the possible groupings of similar solutions of the Pareto front that match the decision maker's preferences. This way, the SRD technique provides a smaller set of optimal solutions …”

Section: Methodsmentioning

confidence: 99%

Comparison of validation variants by sum of ranking differences and ANOVA

Journal of Chemometrics

Kollár-Hunek

2019

The old debate is revived: Definite differences can be observed in suggestions of estimation for prediction performances of models and for validation variants according to the various scientific disciplines. However, the best and/or recommended practice for the same data set cannot be dependent on the field of usage. Fortunately, there is a method comparison algorithm, which can rank and group the validation variants; its combination with variance analysis will reveal whether the differences are significant or merely the play of random errors. Therefore, three case studies have been selected carefully to reveal similarities and differences in validation variants. The case studies illustrate the different significance of these variants well. In special circumstances, any of the influential factors for validation variants can exert significant influence on evaluation by sums of (absolute) ranking differences (SRDs): stratified (contiguous block) or repeated Monte Carlo resampling and how many times the data set is split (5‐7‐10). The optimal validation variant should be determined individually again and again. A random resampling with sevenfold cross‐validations seems to be a good compromise to diminish the bias and variance alike. If the data structure is unknown, a randomization of rows is suggested before SRD analysis. On the other hand, the differences in classifiers, validation schemes, and models proved to be always significant, and even subtle differences can be detected reliably using SRD and analysis of variance (ANOVA).

“…In any modeling task, there are many suboptimal solutions indistinguishable in the statistical sense. SRD as a multicriteria decision making tool is able to distinguish suboptimal solutions . Following our recent comparative studies, the combination of sum of ranking differences (SRD) and analysis of variance (ANOVA) is applied for the evaluations.…”

Section: Introductionmentioning

confidence: 99%

Intercorrelation Limits in Molecular Descriptor Preselection for QSAR/QSPR

Rácz

Bajusz

2019

Molecular Informatics

QSAR/QSPR (quantitative structure‐activity/property relationship) modeling has been a prevalent approach in various, overlapping sub‐fields of computational, medicinal and environmental chemistry for decades. The generation and selection of molecular descriptors is an essential part of this process. In typical QSAR workflows, the starting pool of molecular descriptors is rationalized based on filtering out descriptors which are (i) constant throughout the whole dataset, or (ii) very strongly correlated to another descriptor. While the former is fairly straightforward, the latter involves a level of subjectivity when deciding what exactly is considered to be a strong correlation. Despite that, most QSAR modeling studies do not report on this step. In this study, we examine in detail the effect of various possible descriptor intercorrelation limits on the resulting QSAR models. Statistical comparisons are carried out based on four case studies from contemporary QSAR literature, using a combined methodology based on sum of ranking differences (SRD) and analysis of variance (ANOVA).