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Theoretical analysis shows that all the strict optimal joint actions are stable critical points of the model of LA-OCA in cooperative repeated games with an arbitrary finite number of players and actions. Simulation results show that LA-OCA obtains the pure optimal joint strategy with a success rate of 100% in all of the three cooperative tasks and outperforms the other algorithms in terms of learning speed.Multiverse analysis is an approach to data analysis in which all "reasonable" analytic decisions are evaluated in parallel and interpreted collectively, in order to foster robustness and transparency. However, specifying a multiverse is demanding because analysts must manage myriad variants from a cross-product of analytic decisions, and the results require nuanced interpretation. We contribute Baba an integrated domain-specific language (DSL) and visual analysis system for authoring and reviewing multiverse analyses. With the Boba DSL, analysts write the shared portion of analysis code only once, alongside local variations defining alternative decisions, from which the compiler generates a multiplex of scripts representing all possible analysis paths. The Boba Visualizer provides linked views of model results and the multiverse decision space to enable rapid, systematic assessment of consequential decisions and robustness, including sampling uncertainty and model fit. We demonstrate Boba's utility through two data analysis case studies, and reflect on challenges and design opportunities for multiverse analysis software.A Bayesian view of data interpretation suggests that a visualization user should update their existing beliefs about a parameter's value in accordance with the amount of information about the parameter value captured by the new observations. Extending recent work applying Bayesian models to understand and evaluate belief updating from visualizations, we show how the predictions of Bayesian inference can be used to guide more rational belief updating. We design a Bayesian inference-assisted uncertainty analogy that numerically relates uncertainty in observed data to the user's subjective uncertainty, and a posterior visualization that prescribes how a user should update their beliefs given their prior beliefs and the observed data. In a pre-registered experiment on 4,800 people, we find that when a newly observed data sample is relatively small (N=158), both techniques reliably improve people's Bayesian updating on average compared to the current best practice of visualizing uncertainty in the observed data. For large data samples (N=5208), where people's updated beliefs tend to deviate more strongly from the prescriptions of a Bayesian model, we find evidence that the effectiveness of the two forms of Bayesian assistance may depend on people's proclivity toward trusting the source of the data. We discuss how our results provide insight into individual processes of belief updating and subjective uncertainty, and how understanding these aspects of interpretation paves the way for more sophisticated interactive visualizations for analysis and communication.Graph mining plays a pivotal role across a number of disciplines, and a variety of algorithms have been developed to answer who/what type questions. For example, what items shall we recommend to a given user on an e-commerce platform? The answers to such questions are typically returned in the form of a ranked list, and graph-based ranking methods are widely used in industrial information retrieval settings. However, these ranking algorithms have a variety of sensitivities, and even small changes in rank can lead to vast reductions in product sales and page hits. As such, there is a need for tools and methods that can help model developers and analysts explore the sensitivities of graph ranking algorithms with respect to perturbations within the graph structure. In this paper, we present a visual analytics framework for explaining and exploring the sensitivity of any graph-based ranking algorithm by performing perturbation-based what-if analysis. We demonstrate our framework through three case studies inspecting the sensitivity of two classic graph-based ranking algorithms (PageRank and HITS) as applied to rankings in political news media and social networks.Using causal relations to guide decision making has become an essential analytical task across various domains, from marketing and medicine to education and social science. While powerful statistical models have been developed for inferring causal relations from data, domain practitioners still lack effective visual interface for interpreting the causal relations and applying them in their decision-making process. Through interview studies with domain experts, we characterize their current decision-making workflows, challenges, and needs. Wortmannin in vitro Through an iterative design process, we developed a visualization tool that allows analysts to explore, validate, and apply causal relations in real-world decision-making scenarios. The tool provides an uncertainty-aware causal graph visualization for presenting a large set of causal relations inferred from high-dimensional data. On top of the causal graph, it supports a set of intuitive user controls for performing what-if analyses and making action plans. We report on two case studies in marketing and student advising to demonstrate that users can effectively explore causal relations and design action plans for reaching their goals.An important approach for scientific inquiry across many disciplines involves using observational time series data to understand the relationships between key variables to gain mechanistic insights into the underlying rules that govern the given system. In real systems, such as those found in ecology, the relationships between time series variables are generally not static; instead, these relationships are dynamical and change in a nonlinear or state-dependent manner. To further understand such systems, we investigate integrating methods that appropriately characterize these dynamics (i.e., methods that measure interactions as they change with time-varying system states) with visualization techniques that can help analyze the behavior of the system. Here, we focus on empirical dynamic modeling (EDM) as a state-of-the-art method that specifically identifies causal variables and measures changing state-dependent relationships between time series variables. Instead of using approaches centered on parametric equations, EDM is an equation-free approach that studies systems based on their dynamic attractors.

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