Instance-dependent cost-sensitive learning addresses classification problems where each observation has a different misclassification cost. In this paper, we propose cost-sensitive parametric models to minimize the expectation of losses. A loss function incorporating the misclassification costs is defined, which serves as the objective function for obtaining cost-sensitive parameter estimators. The consistency and asymptotic normality of these estimators are established under general conditions, theoretically demonstrating their good performance. Additionally, we derive bounds for the bias introduced when regularizing the optimization problem, which is generally necessary in practice. To conclude, the effectiveness of the proposed estimators is evaluated through an extensive novel simulation study and the analysis of five real data sets, further demonstrating their proficiency in practical settings.

A new strategy for probabilistic graphical modeling is developed that draws parallels to community detection analysis. The method jointly estimates an undirected graph and homogeneous communities of nodes. The structure of the communities is taken into account when estimating the graph and at the same time, the structure of the graph is accounted for when estimating communities of nodes. The procedure uses a joint group graphical lasso approach with community detection-based grouping, such that some groups of edges co-occur in the estimated graph. The grouping structure is unknown and is estimated based on community detection algorithms. Theoretical derivations regarding graph convergence and sparsistency, as well as accuracy of community recovery are included, while the method's empirical performance is illustrated in an fMRI context, as well as with simulated examples.

Past research has shown that both social and local features are informative for customer churn, however some studies have found that combining both kinds of data into a single model is ineffective. People who churn based on their neighbors' behavior are a distinct subset of customers from those who churn for personal reasons. However, for an effective retention campaign, it is desired to identify both groups of likely churners, attempt to explain the factors that lead to churn in both cases, and still determine the customers most likely to churn so they can be contacted. The goal of this research is to evaluate different techniques for combining features and models based on customer attributes and customer social networks to identify the best approaches to deal with this problem.