A Review on Quantification Learning <s> Probabilistic Adjusted Count <s> Quantification is the name given to a novel machine learning task which deals with correctly estimating the number of elements of one class in a set of examples. The output of a quantifier is a real value, since training instances are the same as a classification problem, a natural approach is to train a classifier and to derive a quantifier from it. Some previous works have shown that just classifying the instances and counting the examples belonging to the class of interest classify count typically yields bad quantifiers, especially when the class distribution may vary between training and test. Hence, adjusted versions of classify count have been developed by using modified thresholds. However, previous works have explicitly discarded (without a deep analysis) any possible approach based on the probability estimations of the classifier. In this paper, we present a method based on averaging the probability estimations of a classifier with a very simple scaling that does perform reasonably well, showing that probability estimators for quantification capture a richer view of the problem than methods based on a threshold. <s> BIB001 </s> A Review on Quantification Learning <s> Probabilistic Adjusted Count <s> The increasing availability of participatory web and social media presents enormous opportunities to study human relations and collective behaviors. Many applications involving decision making want to obtain certain generalized properties about the population in a network, such as the proportion of actors given a category, instead of the category of individuals. While data mining and machine learning researchers have developed many methods for link-based classification or relational learning, most are optimized to classify individual nodes in a network. In order to accurately estimate the prevalence of one class in a network, some quantification method has to be used. In this work, two kinds of approaches are presented: quantification based on classification or quantification based on link analysis. Extensive experiments are conducted on several representative network data, with interesting findings reported concerning efficacy and robustness of different quantification methods, providing insights to further quantify the ebb and flow of online collective behaviors at macro-level. <s> BIB002 </s> A Review on Quantification Learning <s> Probabilistic Adjusted Count <s> How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year’s portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fixed. From this observation we can conclude that the standard default rate forecast based on last year’s conditional default rates will always be located between last year’s portfolio-wide default rate and the ML forecast for next year. As an application example, cost quantification is then discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem. <s> BIB003 </s> A Review on Quantification Learning <s> Probabilistic Adjusted Count <s> Sentiment classification has become a ubiquitous enabling technology in the Twittersphere, since classifying tweets according to the sentiment they convey towards a given entity (be it a product, a person, a political party, or a policy) has many applications in political science, social science, market research, and many others. In this paper, we contend that most previous studies dealing with tweet sentiment classification (TSC) use a suboptimal approach. The reason is that the final goal of most such studies is not estimating the class label (e.g., Positive, Negative, or Neutral) of individual tweets, but estimating the relative frequency (a.k.a. “prevalence”) of the different classes in the dataset. The latter task is called quantification, and recent research has convincingly shown that it should be tackled as a task of its own, using learning algorithms and evaluation measures different from those used for classification. In this paper, we show (by carrying out experiments using two learners, seven quantification-specific algorithms, and 11 TSC datasets) that using quantification-specific algorithms produces substantially better class frequency estimates than a state-of-the-art classification-oriented algorithm routinely used in TSC. We thus argue that researchers interested in tweet sentiment prevalence should switch to quantification-specific (instead of classification-specific) learning algorithms and evaluation measures. <s> BIB004
The expected behavior of PCC should be similar to that of CC. PCC will underestimate or overestimate the actual prevalence when the distribution of the classes changes between the training and the testing phase, see BIB003 (Corollary 6, p. 157) . Then, the authors introduce an improved version of PCC, denoted as Scaled Probability Average (SPA). Here we called it Probabilistic Adjusted Count (PAC) to establish a parallelism with AC. The estimation obtained by PCC using 74:18 P. González et al. Equation (35) is adjusted applying the following formula: in which TP pa (TP probability average) and FP pa (FP probability average) are estimated using the training data and are respectively defined as the averaged probability of the positive examples, and the averaged probability of the negative examples, with D + and D − being the set of examples in the training data belonging, respectively, to the positive and to the negative class. The expression defined in Equation (36) is a probabilistic version of Formans correction formula (Equation (32)). The experimental performance of PCC/PAC is not as conclusive as that of CC/AC. PAC outperforms PCC in the experiments reported in BIB001 and BIB002 but underperforms PCC in the experimental study presented by BIB004 .