Counterfactual causal inference faces significant challenges when extended to multi-category, multi-valued treatments, where complex cross-effects between heterogeneous interventions are difficult to model. Existing methodologies remain constrained to binary or single-type treatments and suffer from restrictive assumptions, limited scalability, and inadequate evaluation frameworks for complex intervention scenarios. We present XTNet, a novel network architecture for multi-category, multi-valued treatment effect estimation. Our approach introduces a cross-effect estimation module with dynamic masking mechanisms to capture treatment interactions without restrictive structural assumptions. The architecture employs a decomposition strategy separating basic effects from cross-treatment interactions, enabling efficient modeling of combinatorial treatment spaces. We also propose MCMV-AUCC, a suitable evaluation metric that accounts for treatment costs and interaction effects. Extensive experiments on synthetic and real-world datasets demonstrate that XTNet consistently outperforms state-of-the-art baselines in both ranking accuracy and effect estimation quality. The results of the real-world A/B test further confirm its effectiveness.

Cluster analysis methods are used to identify homogeneous subgroups in a data set. In biomedical applications, one frequently applies cluster analysis in order to identify biologically interesting subgroups. In particular, one may wish to identify subgroups that are associated with a particular outcome of interest. Conventional clustering methods generally do not identify such subgroups, particularly when there are a large number of high-variance features in the data set. Conventional methods may identify clusters associated with these high-variance features when one wishes to obtain secondary clusters that are more interesting biologically or more strongly associated with a particular outcome of interest. A modification of sparse clustering can be used to identify such secondary clusters or clusters associated with an outcome of interest. This method correctly identifies such clusters of interest in several simulation scenarios. The method is also applied to a large prospective cohort study of temporomandibular disorders and a leukemia microarray data set.

We study the complexity of a combinatorial variant of the Shift Bribery problem in elections. In the standard Shift Bribery problem, we are given an election where each voter has a preference order over the set of candidates and where an outside agent, the briber, can pay each voter to rank the briber's favorite candidate a given number of positions higher. The goal is to ensure the victory of the briber's preferred candidate. The combinatorial variant of the problem, introduced in this paper, models settings where it is possible to affect the position of the preferred candidate in multiple votes, either positively or negatively, with a single bribery action. This variant of the problem is particularly interesting in the context of large-scale campaign management problems (which, from the technical side, are modeled as bribery problems). We show that, in general, the combinatorial variant of the problem is highly intractable; specifically, NP-hard, hard in the parameterized sense, and hard to approximate. Nevertheless, we provide parameterized algorithms and approximation algorithms for natural restricted cases.