Analysis of social communities with iceberg and stability-based concept lattices

International audienceIn this paper, we presents a research work based on formal concept analysis and interest measures associated with formal concepts. This work focuses on the ability of concept lattices to discover and represent special groups of individuals, called social communities. Concept lattices are very useful for the task of knowledge discovery in databases, but they are hard to analyze when their size become too large. We rely on concept stability and support measures to reduce the size of large concept lattices. We propose an example from real medical use cases and we discuss the meaning and the interest of concept stability for extracting and explaining social communities within a healthcare network

From metaphor to computation:Constructing the potential landscape for multivariate psychological formal models

For psychological formal models, the stability of different phases is an important property for understanding individual differences and change processes. Many researchers use landscapes as a metaphor to illustrate the concept of stability, but so far there is no method to quantify the stability of a system’s phases. We here propose a method to construct the potential landscape for multivariate psychological models. This method is based on the generalized potential function defined by Wang et al. (2008) and Monte Carlo simulation. Based on potential landscapes we define three different types of stability for psychological phases: absolute stability, relative stability, and geometric stability. The panic disorder model by Robinaugh et al. (2019) is used as an example, to demonstrate how the method can be used to quantify the stability of states and phases, illustrate the influence of model parameters, and guide model modifications. An R package, simlandr, was developed to provide an implementation of the method

Shapley and Banzhaf Vectors of a Formal Concept

We propose the usage of two power indices from cooperative game theory and public choice theory for ranking attributes of closed sets, namely intents of formal concepts (or closed itemsets). The introduced indices are related to extensional concept stability and based on counting generators, especially those that contain a selected attribute. The introduction of such indices is motivated by the so-called interpretable machine learning, which supposes that we do not only have the class membership decision of a trained model for a particular object, but also a set of attributes (in the form of JSM-hypotheses or other patterns) along with individual importance of their single attributes (or more complex constituent elements). We characterise computation of Shapley and Banzhaf values of a formal concept in terms of minimal generators and their order filters, provide the reader with their properties important for computation purposes, and show experimental results

Black box tests for algorithmic stability

Algorithmic stability is a concept from learning theory that expresses the degree to which changes to the input data (e.g., removal of a single data point) may affect the outputs of a regression algorithm. Knowing an algorithm's stability properties is often useful for many downstream applications -- for example, stability is known to lead to desirable generalization properties and predictive inference guarantees. However, many modern algorithms currently used in practice are too complex for a theoretical analysis of their stability properties, and thus we can only attempt to establish these properties through an empirical exploration of the algorithm's behavior on various data sets. In this work, we lay out a formal statistical framework for this kind of "black box testing" without any assumptions on the algorithm or the data distribution, and establish fundamental bounds on the ability of any black box test to identify algorithmic stability.Comment: 26 pages. Updates to Section 2.1.1 and Sections B.1 & B.

Veto players

Veto players are political actors whose consent is necessary to adopt a new policy. Put otherwise, they\ud have veto power which allows them to prevent a change to the status quo. The concept is crucial to the\ud influential veto player theory developed by George Tsebelis. Building on earlier work in formal\ud modeling and social choice, Tsebelis developed veto player theory to compare political systems in\ud terms of their ability for policy change. A political system with a high number of veto players or with\ud large ideological differences among veto players has high policy stability. High policy stability in turn\ud can lead to government or regime instability as it becomes harder to adapt policy to changing\ud circumstances. Furthermore, high policy stability increases bureaucratic and judicial independence as\ud acts by these branches cannot be easily overruled by new or more specific legislation. Finally, high\ud policy stability limits the effect of agenda-setting power. The following summarizes the main points of\ud veto player theory, discusses some criticisms of it, and briefly compares veto player theory to\ud Immergut’s concept of veto points