Prior work on perceptual effectiveness has decomposed visualizations into smaller common units (e.g., channels such as angle, position, and length) to establish rankings. While useful, these decompositions lack the computational structure to predict performance for new visualization $\times$ task combinations, requiring new experiments for each. We propose an alternative unit of analysis: operationalizing quantitative visualization interpretation as sequences of composable visual decoding operators. Using probability density function (PDF) and cumulative distribution function (CDF) charts, we examine how chart-specific tasks can be decomposed into reusable, chart-agnostic perceptual operations and characterize their error profiles through hierarchical Bayesian modeling. We then test generalizability by composing learned operators to predict performance on a structurally different task: Moritz et al.'s [35] scatterplot mean-estimation experiment, where the chart type, chart dimensions, and analytic goal all differ from the learning conditions. With a pre-registered analysis plan, we compose operators under six candidate strategies and evaluate each against empirical data with no parameters fit to the response data. One strategy captures both bias and variance of observed responses; five alternatives fail in distinguishable ways. We argue that this decoding-operator-oriented approach to empirical visualization research and theory-building lays the groundwork for generative models that can predict a distribution of likely interpretations under different viewing conditions, new chart types, and new tasks. Free copy of this paper and supplemental materials: https://osf.io/prtfq; experiment interface: https://gleaming-dolphin-799fda.netlify.app/vis-decode-slider.

翻译：先前的感知有效性研究将可视化分解为更小的通用单元（如角度、位置和长度等通道）以建立排序。虽然这些分解方法有用，但缺乏预测新可视化×任务组合性能的计算结构，每次都需要进行新的实验。我们提出一种替代分析单元：将定量可视化解释操作化为可组合的视觉解码算子序列。利用概率密度函数（PDF）和累积分布函数（CDF）图表，我们研究图表特定任务如何分解为可重用的、与图表无关的感知操作，并通过层次贝叶斯建模刻画其误差特征。随后，通过组合学习到的算子预测结构不同的任务（Moritz等人[35]的散点图均值估计实验）的性能来检验泛化能力——该实验的图表类型、图表维度及分析目标均与学习条件不同。在预注册分析方案下，我们基于六种候选策略组合算子，并在未对响应数据拟合任何参数的情况下，将各策略与实证数据进行比较。其中一种策略同时捕获了观测响应的偏差和方差；其余五种策略则以可区分的方式失败。我们认为，这种以解码算子为导向的实证可视化研究与理论构建方法，为生成模型奠定了坚实基础，使其能够预测不同观看条件、新图表类型及新任务下可能解释的分布。本文及补充材料免费获取地址：https://osf.io/prtfq；实验界面：https://gleaming-dolphin-799fda.netlify.app/vis-decode-slider。