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1. How Data Analysts Use a Visualization Grammar in Practice

   https://doi.org/10.1145/3544548.3580837  

   Pu, Xiaoying; Kay, Matthew (April 2023, CHI '23: Proceedings of the 2023 CHI Conference on Human Factors in Computing Systems)

   Visualization grammars, often based on the Grammar of Graphics (GoG), have much potential for augmenting data analysis in a programming environment. However, we do not know how analysts conceptualize grammar abstractions, or how a visualization grammar works with data analysis in practice. Therefore, we qualitatively analyzed how experienced analysts (N = 6) from TidyTuesday, a social data project, wrangled and visualized data using GoG-based ggplot2 without given tasks in R Markdown. Though participants’ analysis and customization needs could mismatch with GoG component design, their analysis processes aligned with the goal of GoG to expedite visualization iteration. We also found a feedback loop and tight coupling between visualization and data transformation code, explaining both participants’ productivity and their errors. From these results, we discuss how future visualization grammars can become more practical for analysts and how visualization grammar and analysis tools can better integrate within a programming (i.e., computational notebook) environment. 

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2. Statistical summaries of unlabelled evolutionary trees

   https://doi.org/10.1093/biomet/asad025  

   Samyak, Rajanala; Palacios, Julia A (April 2023, Biometrika)

   Summary Rooted and ranked phylogenetic trees are mathematical objects that are useful in modelling hierarchical data and evolutionary relationships with applications to many fields such as evolutionary biology and genetic epidemiology. Bayesian phylogenetic inference usually explores the posterior distribution of trees via Markov chain Monte Carlo methods. However, assessing uncertainty and summarizing distributions remains challenging for these types of structures. While labelled phylogenetic trees have been extensively studied, relatively less literature exists for unlabelled trees that are increasingly useful, for example when one seeks to summarize samples of trees obtained with different methods, or from different samples and environments, and wishes to assess the stability and generalizability of these summaries. In our paper, we exploit recently proposed distance metrics of unlabelled ranked binary trees and unlabelled ranked genealogies, or trees equipped with branch lengths, to define the Fréchet mean, variance and interquartile sets as summaries of these tree distributions. We provide an efficient combinatorial optimization algorithm for computing the Fréchet mean of a sample or of distributions on unlabelled ranked tree shapes and unlabelled ranked genealogies. We show the applicability of our summary statistics for studying popular tree distributions and for comparing the SARS-CoV-2 evolutionary trees across different locations during the COVID-19 epidemic in 2020. Our current implementations are publicly available at https://github.com/RSamyak/fmatrix. 

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3. A Probabilistic Grammar of Graphics

   https://doi.org/10.1145/3313831.3376466  

   Pu, Xiaoying; Kay, Matthew (April 2020, CHI '20: Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems)

   Visualizations depicting probabilities and uncertainty are used everywhere from medical risk communication to machine learning, yet these probabilistic visualizations are difficult to specify, prone to error, and their designs are cumbersome to explore. We propose a Probabilistic Grammar of Graphics (PGoG), an extension to Wilkinson's original framework. Inspired by the success of probabilistic programming languages, PGoG makes probability expressions, such as P(A|B), a first-class citizen in the language. PGoG abstractions also reflect the distinction between probability and frequency framing, a concept from the uncertainty communication literature. It is expressive, encompassing product plots, density plots, icon arrays, and dotplots, among other visualizations. Its coherent syntax ensures correctness (that the proportions of visual elements and their spatial placement reflect the underlying probability distribution) and reduces edit distance between probabilistic visualization specifications, potentially supporting more design exploration. We provide a proof-of-concept implementation of PGoG in R. 

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4. Diagnostics for conditional density models and Bayesian inference algorithms

   Zhao, David; Dalmasso, Niccolo; Izbicki, Rafael; Lee, Ann B. (January 2021, Proceedings of Machine Learning Research)

   There has been growing interest in the AI community for precise uncertainty quantification. Conditional density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, it is challenging to assess conditional density estimates and gain insight into modes of failure. While existing diagnostic tools can determine whether an approximated conditional density is compatible overall with a data sample, they lack a principled framework for identifying, locating, and interpreting the nature of statistically significant discrepancies over the entire feature space. In this paper, we present rigorous and easy-to-interpret diagnostics such as (i) the “Local Coverage Test” (LCT), which distinguishes an arbitrarily misspecified model from the true conditional density of the sample, and (ii) “Amortized Local P-P plots” (ALP) which can quickly provide interpretable graphical summaries of distributional differences at any location x in the feature space. Our validation procedures scale to high dimensions and can potentially adapt to any type of data at hand. We demonstrate the effectiveness of LCT and ALP through a simulated experiment and applications to prediction and parameter inference for image data. 

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5. Spatial adaptation by Bayesian unsupervised trees.

   Liu, Linxi; Ma, Li (December 2024, Proceedings of Machine Learning Research)

   Agrawal, Shipra; Roth, Aaron (Ed.)

   Tree-based methods are popular nonparametric tools for capturing spatial heterogeneity and making predictions in multivariate problems. In unsupervised learning, trees and their ensembles have also been applied to a wide range of statistical inference tasks, such as multi-resolution sketching of distributional variations, localization of high-density regions, and design of efficient data compression schemes. In this paper, we study the spatial adaptation property of Bayesian tree-based methods in the unsupervised setting, with a focus on the density estimation problem. We characterize spatial heterogeneity of the underlying density function by using anisotropic Besov spaces, region-wise anisotropic Besov spaces, and two novel function classes as their extensions. For two types of commonly used prior distributions on trees under the context of unsupervised learning—the optional P{ó}lya tree (Wong and Ma, 2010) and the Dirichlet prior (Lu et al., 2013)—we calculate posterior concentration rates when the density function exhibits different types of heterogeneity. In specific, we show that the posterior concentration rate for trees is near minimax over the anisotropic Besov space. The rate is adaptive in the sense that to achieve such a rate we do not need any prior knowledge of the parameters of the Besov space. 

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