Spearman's rank correlation coefficient

In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter \rho (rho) or as r_s, is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not). If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other. Intuitively, the Spearman correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relativ

Feature-based no-reference video quality assessment using Extra Trees

Arash Amini, Hatef Otroshi Shahreza

With the emergence of social networks and improvements in the internet speed, the video data has become an ever-increasing portion of the global internet traffic. Besides the content, the quality of a video sequence is an important issue at the user end which is often affected by various factors such as compression. Therefore, monitoring the quality is crucial for the video content and service providers. A simple monitoring approach is to compare the raw video content (uncompressed) with the received data at the receiver. In most practical scenarios, however, the reference video sequence is not available. Consequently, it is desirable to have a general reference-less method for assessing the perceived quality of any given video sequence. In this paper, a no-reference video quality assessment technique based on video features is proposed. In particular, a long list of video features (21 sets of features, each consisting of 1 to 216 features) is considered and all possible combinations (2(21) - 1) for training an Extra Trees regressor is examined. This choice of the regressor is wisely selected and is observed to perform better than other common regressors. The results reveal that the top 20 performing feature subsets all outperformthe existing featurebased assessment methods in terms of the Pearson linear correlation coefficient (PLCC) or the Spearman rank order correlation coefficient (SROCC). Specially, the best performing regressor achieves PLCC = 0.786 on the test data over the KonVid-1k dataset. It is believed that the results of the comprehensive comparison could be potentially useful for other feature-based video-related problems. The source codes of the implementations are publicly available.

WILEY2022

Evaluating the Explainers: Black-Box Explainable Machine Learning for Student Success Prediction in MOOCs

Natasa Krco, Mirko Marras, Vinitra Swamy

Neural networks are ubiquitous in applied machine learning for education. Their pervasive success in predictive performance comes alongside a severe weakness, the lack of explainability of their decisions, especially relevant in human-centric fields. We implement five state-of-the-art methodologies for explaining black-box machine learning models (LIME, PermutationSHAP, KernelSHAP, DiCE, CEM) and examine the strengths of each approach on the downstream task of student performance prediction for five massive open online courses. Our experiments demonstrate that the families of explainers do not agree with each other on feature importance for the same Bidirectional LSTM models with the same representative set of students. We use Principal Component Analysis, Jensen-Shannon distance, and Spearman's rank-order correlation to quantitatively cross-examine explanations across methods and courses. Furthermore, we validate explainer performance across curriculum-based prerequisite relationships. Our results come to the concerning conclusion that the choice of explainer is an important decision and is in fact paramount to the interpretation of the predictive results, even more so than the course the model is trained on. Source code and models are released at http://github.com/epfl-ml4ed/evaluating-explainers.

2022

Inﬂuence of a wastewater treatment plant on mercury contamination and sediment characteristics in Vidy Bay (Lake Geneva, Switzerland)

Yosef Akhtman, Neil Graham, Serge Stoll

Previous direct observations of the sediment surface in Vidy Bay, Lake Geneva (Switzerland), revealed a range of sediment characteristics in terms of colour, texture and morphology. Dives with the MIR submersibles during the éLEMO project permitted the exploration of a large portion of Vidy Bay. It is the most contaminated part of Lake Geneva, due to inputs of treated and untreated waters from a large wastewater treatment plant (WWTP). To evaluate the influence of WWTP effluent on mercury contamination and sediment characteristics, 14 sediment cores were retrieved in the vicinity of the wastewater treatment plant effluent. Total mercury concentrations in sediments ranged between 0.32 and 10.1 mg/kg. Inorganic mercury and monomethylmercury concentrations in overlying and pore waters were also measured. The total partition coefficients of mercury (logKd) ranged from 3.6 to 5.8. The monomethylmercury concentration in pore waters of surface sediments was a large proportion of the total mercury concentration (44 ± 25 %). A Spearman test showed a negative correlation between the distance to the wastewater treatment plant outlet and the concentrations of total mercury in sediments and pore waters. Visual observations from the submersible allowed recognising six different types of sediment. The areal distribution of these different sediment types clearly showed the influence of the wastewater treatment plant outlet on the sediment surface patterns. However, no relationship with mercury concentrations could be established.

Springer Verlag2014