The off-switch game is a game theoretic model of a highly intelligent robot interacting with a human. In the original paper by Hadfield-Menell et al. (2016b), the analysis is not fully game-theoretic as the human is modelled as an irrational player, and the robot's best action is only calculated under unrealistic normality and soft-max assumptions. In this paper, we make the analysis fully game theoretic, by modelling the human as a rational player with a random utility function. As a consequence, we are able to easily calculate the robot's best action for arbitrary belief and irrationality assumptions.
Background: The t-distributed Stochastic Neighbour Embedding (t-SNE) algorithm has emerged as one of the leading methods for visualising High Dimensional (HD) data in a wide variety of fields, especially for revealing cluster structure in HD single cell transcriptomics data. However, t-SNE often fails to correctly represent hierarchical relationships between clusters and creates spurious patterns in the embedding. In this work we generalized t-SNE using shape-aware graph distances to mitigate some of the limitations of the t-SNE. Although many methods have been recently proposed to circumvent the shortcomings of t-SNE, notably Uniform manifold approximation (UMAP) and Potential of heat diffusion for affinity-based transition embedding (PHATE), we see a clear advantage of the proposed graph based method. Results: The superior performance of the proposed method is first demonstrated on simulated data, where a significant improvement compared to t-SNE, UMAP and PHATE, based on quantitative validation indices, is observed when visualizing imbalanced, nonlinear, continuous and hierarchically structured data. Thereafter the ability of the proposed method compared to the competing methods to create faithfully low dimensional embeddings is shown on two real-world data sets, the single cell transcriptomics data and the MNIST image data. In addition, the only hyper-parameter of the method can be automatically chosen in a data-driven way, which is consistently optimal across all test cases in this study. Conclusions: In this work we show that the proposed shape-aware stochastic neighbor embedding method creates low dimensional visualisations that robustly and accurately reveal key structures of high dimensional data.
Background The t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm has emerged as one of the leading methods for visualising high-dimensional (HD) data in a wide variety of fields, especially for revealing cluster structure in HD single-cell transcriptomics data. However, t-SNE often fails to correctly represent hierarchical relationships between clusters and creates spurious patterns in the embedding. In this work we generalised t-SNE using shape-aware graph distances to mitigate some of the limitations of the t-SNE. Although many methods have been recently proposed to circumvent the shortcomings of t-SNE, notably Uniform manifold approximation (UMAP) and Potential of heat diffusion for affinity-based transition embedding (PHATE), we see a clear advantage of the proposed graph-based method. Results The superior performance of the proposed method is first demonstrated on simulated data, where a significant improvement compared to t-SNE, UMAP and PHATE, based on quantitative validation indices, is observed when visualising imbalanced, nonlinear, continuous and hierarchically structured data. Thereafter the ability of the proposed method compared to the competing methods to create faithfully low-dimensional embeddings is shown on two real-world data sets, the single-cell transcriptomics data and the MNIST image data. In addition, the only hyper-parameter of the method can be automatically chosen in a data-driven way, which is consistently optimal across all test cases in this study. Conclusions In this work we show that the proposed shape-aware stochastic neighbor embedding method creates low-dimensional visualisations that robustly and accurately reveal key structures of high-dimensional data.
In this paper, we provide a detailed review of previous classifications of $$2\times 2$$ 2 × 2 games and suggest a mathematically simple way to classify the symmetric $$2\times 2$$ 2 × 2 games based on a decomposition of the payoff matrix into a cooperative and a zero-sum part. We argue that differences in the interaction between the parts is what makes games interesting in different ways. Our claim is supported by evolutionary computer experiments and findings in previous literature. In addition, we provide a method for using a stereographic projection to create a compact 2-d representation of the game space.
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