Shapley values as a generic approach to interpretable feature selection

The Shapley value is one of the most popular frameworks for explaining black-box machine learning models, originating from cooperative game theory. Shapley values compute the average of all the marginal contributions of each feature. Consequently, they provide a ranking of features based on their average contribution to the model’s output, which is frequently used for feature selection in practical work. Despite the significant amount of literature analyzing the performance of such feature selection, two major points are missing: a detailed analysis of the performance of Shapley-values-based feature selection relative to other, more traditional feature selection techniques across various datasets and domains, and a discussion about the validity of using Shapley values for feature selection in the first place. This thesis aims to compare the performance of Shapley-values-based feature selection with other well-established methods across various domains, including the state-of-the-art minimal-redundancy-maximal-relevance algorithm. Furthermore, it will explore the implications of the Shapley value axioms on feature selection. In this thesis work, Shapley-values-based feature selection is compared to other methods using multiple datasets for both binary and multiclass text classification to gauge the method’s capabilities with high dimensional text data, and low and high dimensional numerical datasets. The Shapley-values-based method emerged as one of the top performers according to the used evaluation metrics, i.e. F1-score, precision and recall. However, it did not consistently outperform domain-specific methods. The Shapley-values-based method turned out to be a fast ”wrapper-like” feature selection technique that, unlike fast filter methods, considers feature interactions in its feature ranking. Yet, it does not guarantee an optimal feature subset, nor is it able to handle redundancy by itself due to the limitations of Shapley values definition. Some more sophisticated algorithms based on Shapley values, such as Interaction Shapley Values, are capable of mitigating the mentioned disadvantages, but they are neither as fast nor as memory-efficient

Complexity Theory, Adaptation, and Administrative Law

Recently, commentators have applied insights from complexity theory to legal analysis generally and to administrative law in particular. This Article focuses on one of the central problems that complexity. theory addresses, the importance and mechanisms of adaptation within complex systems. In Part I, the Article uses three features of complex adaptive systems-emergence from self-assembly, nonlinearity, and sensitivity to initial conditions-and explores the extent to which they may add value as a matter of positive analysis to the understanding of change within legal systems. In Part H, the Article focuses on three normative claims in public law scholarship that depend explicitly or implicitly on notions of adaptation: that states offer advantages over the federal government because experimentation can make them more adaptive, that federal agencies should themselves become more experimentalist using the tool of adaptive management, and that administrative agencies shou Id adopt collaborative mechanisms in policymaking. Using two analytic tools found in the complexity literature, the genetic algorithm and evolutionary game theory, the Article tests the extent to which these three normative claims are borne out

Defusing Ideological Defenses in Biology

Ideological language is widespread in theoretical biology. Evolutionary game theory has been defended as a worldview and a leap of faith, and sexual selection theory has been criticized for what it posits as basic to biological nature. Views such as these encourage the impression of ideological rifts in the field. I advocate an alternative interpretation, whereby many disagreements between different camps of biologists merely reflect methodological differences. This interpretation provides a more accurate and more optimistic account of the state of play in the field of biology. It also helps account for biologists' tendency to embrace ideological positions

Exploring cooperative game mechanisms of scientific coauthorship networks

Scientific coauthorship, generated by collaborations and competitions among researchers, reflects effective organizations of human resources. Researchers, their expected benefits through collaborations, and their cooperative costs constitute the elements of a game. Hence we propose a cooperative game model to explore the evolution mechanisms of scientific coauthorship networks. The model generates geometric hypergraphs, where the costs are modelled by space distances, and the benefits are expressed by node reputations, i. e. geometric zones that depend on node position in space and time. Modelled cooperative strategies conditioned on positive benefit-minus-cost reflect the spatial reciprocity principle in collaborations, and generate high clustering and degree assortativity, two typical features of coauthorship networks. Modelled reputations generate the generalized Poisson parts and fat tails appeared in specific distributions of empirical data, e. g. paper team size distribution. The combined effect of modelled costs and reputations reproduces the transitions emerged in degree distribution, in the correlation between degree and local clustering coefficient, etc. The model provides an example of how individual strategies induce network complexity, as well as an application of game theory to social affiliation networks

Evidence of coevolution in multi-objective evolutionary algorithms

This paper demonstrates that simple yet important characteristics of coevolution can occur in evolutionary algorithms when only a few conditions are met. We find that interaction-based fitness measurements such as fitness (linear) ranking allow for a form of coevolutionary dynamics that is observed when 1) changes are made in what solutions are able to interact during the ranking process and 2) evolution takes place in a multi-objective environment. This research contributes to the study of simulated evolution in a at least two ways. First, it establishes a broader relationship between coevolution and multi-objective optimization than has been previously considered in the literature. Second, it demonstrates that the preconditions for coevolutionary behavior are weaker than previously thought. In particular, our model indicates that direct cooperation or competition between species is not required for coevolution to take place. Moreover, our experiments provide evidence that environmental perturbations can drive coevolutionary processes; a conclusion that mirrors arguments put forth in dual phase evolution theory. In the discussion, we briefly consider how our results may shed light onto this and other recent theories of evolution

How to Play 3x3-Games A Strategy Method Experiment

We report an experiment that uses the strategy method (Selten 1967) to elicit subjects' general strategy for playing any 2-person 3x3-game with integer payoffs between 0 and 99. Each two subjects' strategies play 500000 games in each of the 5 tournaments. For games with pure strategy equilibria (ca. 80%), the frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, in which there is equilibrium play in 98% of all games with only one pure equilibrium. In games with more than one pure equilibrium, a tendency towards the selection of the one with the maximum joint payoff is observed. For games without pure equilibria, subjects’ strategies do not search for mixed equilibria. The strategy programs are based on much simpler strategic concepts combined in various ways. The simplest one is MAP, maximal average payoff, the strategy which maximizes the sum of the three payoffs obtainable against the possible choices of the other player. BR-MAP, the best reply to MAP, and BR-BR-MAP, the best reply to BR-MAP, are also important ingredients of the strategy programs. Together these three form a hierarchy to which we refer to as the best-reply cascade.2-person games, experimental economics