Submission of Evidence on Online Violence Against Women to the UN Special Rapporteur on Violence Against Women, its Causes and Consequences, Dr Dubravka Šimonović

Figure S1. B3GALNT2 levels determined by W.B. and ROC curve. a–c Relative mRNA expression of B3GALNT2 in HCC tumor tissues and normal liver tissues obtained from GSE76427, GSE36376, and TCGA-LIHC datasets. d Western blot analysis of B3GALNT2 levels in 24 pairs of HCC tissues. T HCC tumor tissue, N adjacent non-tumor tissue. e ROC curve analysis of the sensitivity and specificity for the predictive value of TNM model, B3GALNT2 expression, and the combination model. (TIFF 546 kb

Robust Orthogonal Complement Principal Component Analysis

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust orthogonal complement principal component analysis (ROC-PCA) is proposed. The framework combines the popular sparsity-enforcing and low rank regularization techniques to deal with row-wise outliers as well as element-wise outliers. A non-asymptotic oracle inequality guarantees the accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle the computational challenges, an efficient algorithm is developed on the basis of Stiefel manifold optimization and iterative thresholding. Furthermore, a batch variant is proposed to significantly reduce the cost in ultra high dimensions. The paper also points out a pitfall of a common practice of SVD reduction in robust PCA. Experiments show the effectiveness and efficiency of ROC-PCA in both synthetic and real data

Analytic Models of the ROC Curve: Applications to Credit Rating Model Validation

In this paper, the authors use the concept of the population ROC curve to build analytic models of ROC curves. Information about the population properties can be used to gain greater accuracy of estimation relative to the non-parametric methods currently in vogue. If used properly this is particularly helpful in some situations where the number of sick loans is rather small; a situation frequently met in periods of benign macro-economic background.validation; credit analysis; rating model; ROC; Basel II

Colour image processing and texture analysis on images of porterhouse steak meat

This paper outlines two colour image processing and texture analysis techniques applied to meat images and assessment of error due to the use of JPEG compression at image capture. JPEG error analysis was performed by capturing TIFF and JPEG images, then calculating the RMS difference and applying a calibration between block boundary features and subjective visual JPEG scores. Both scores indicated high JPEG quality. Correction of JPEG blocking error was trialled and found to produce minimal improvement in the RMS difference. The texture analysis methods used were singular value decomposition over pixel blocks and complex cell analysis. The block singular values were classified as meat or non- meat by Fisher linear discriminant analysis with the colour image processing result used as ‘truth.’ Using receiver operator characteristic (ROC) analysis, an area under the ROC curve of 0.996 was obtained, demonstrating good correspondence between the colour image processing and the singular values. The complex cell analysis indicated a ‘texture angle’ expected from human inspection

Measuring the Discriminative Power of Rating Systems

Assessing the discriminative power of rating systems is an important question to banks and to regulators. In this article we analyze the Cumulative Accuracy Profile (CAP) and the Receiver Operating Characteristic (ROC) which are both commonly used in practice. We give a test-theoretic interpretation for the concavity of the CAP and the ROC curve and demonstrate how this observation can be used for more efficiently exploiting the informational contents of accounting ratios. Furthermore, we show that two popular summary statistics of these concepts, namely the Accuracy Ratio and the area under the ROC curve, contain the same information and we analyse the statistical properties of these measures. We show in detail how to identify accounting ratios with high discriminative power, how to calculate confidence intervals for the area below the ROC curve, and how to test if two rating models validated on the same data set are different. All concepts are illustrated by applications to real data. --Validation,Rating Models,Credit Analysis

Accommodating Covariates in ROC Analysis

Classification accuracy is the ability of a marker or diagnostic test to discriminate between two groups of individuals, cases and controls, and is commonly summarized using the receiver operating characteristic (ROC) curve. In studies of classification accuracy, there are often covariates that should be incorporated into the ROC analysis. We describe three different ways of using covariate informa- tion. For factors that affect marker observations among controls, we present a method for covariate adjustment. For factors that affect discrimination (ie the ROC curve), we describe methods for mod- elling the ROC curve as a function of covariates. Finally, for factors that contribute to discrimination, we propose combining the marker and covariate information, and ask how much discriminatory accu- racy improves with the addition of the marker to the covariates (incremental value). These methods follow naturally when representing the ROC curve as a summary of the distribution of case marker observations, standardized with respect to the control distribution