A log-linear representation of the Bradley-Terry model is presented for multivariate paired comparison data, where judges are asked to compare pairs of objects on more than one attribute. By converting such data to multiple binomial responses, dependencies between the decisions of the judges as well as possible association structures between the attributes can be incorporated in the model, prov...

Log-linear analysis has become a widely used method for the analysis of multivariate frequency tables obtained by crossclassifying sets of nominal, ordinal, or discrete interval level variables. Examples of textbooks discussing categorical data analysis by means of log-linear models are [4], [2], [14], [15], [16], and [27]. We start by introducing the standard hierarchical log-linear modelling ...

In Learning with Label Proportions (LLP), the objective is to learn a supervised classifier when, instead of labels, only label proportions for bags of observations are known. This setting has broad practical relevance, in particular for privacy preserving data processing. We first show that the mean operator, a statistic which aggregates all labels, is minimally sufficient for the minimization...

Two types of cysteine proteases, low-specificity enzymes from the papain family and Asn-specific from the legumain family are generally considered to be the major endopeptidases responsible for the degradation of seed storage proteins during early seedling growth. The action of the corresponding enzymes (CPPh1 and LLP, respectively) from common bean (Phaseolus vulgaris L.) on phaseolin (the com...

• As x gets bigger, so does expx. So raising θsolid with your slider will raise the numerators of p(solid circle) (1) and p(solid triangle) (3). To be precise, each time you increase θsolid by 1, you multiply those numerators by e. (And decreasing θsolid by 1 divides them by e.) • Finally, the four probabilities (1)–(4) always sum to 1 (thanks to their common denominator Z). That’s required bec...