Dianne Cook

Przemyslaw Biecek, Hubert Baniecki, Mateusz Krzyzinski et al.

The usual goal of supervised learning is to find the best model, the one that optimizes a particular performance measure. However, what if the explanation provided by this model is completely different from another model and different again from another model despite all having similarly good fit statistics? Is it possible that the equally effective models put the spotlight on different relationships in the data? Inspired by Anscombe's quartet, this paper introduces a Rashomon Quartet, i.e. a set of four models built on a synthetic dataset which have practically identical predictive performance. However, the visual exploration reveals distinct explanations of the relations in the data. This illustrative example aims to encourage the use of methods for model visualization to compare predictive models beyond their performance.

Nicholas Spyrison, Dianne Cook, Przemyslaw Biecek

The increased predictive power of machine learning models comes at the cost of increased complexity and loss of interpretability, particularly in comparison to parametric statistical models. This trade-off has led to the emergence of eXplainable AI (XAI) which provides methods, such as local explanations (LEs) and local variable attributions (LVAs), to shed light on how a model use predictors to arrive at a prediction. These provide a point estimate of the linear variable importance in the vicinity of a single observation. However, LVAs tend not to effectively handle association between predictors. To understand how the interaction between predictors affects the variable importance estimate, we can convert LVAs into linear projections and use the radial tour. This is also useful for learning how a model has made a mistake, or the effect of outliers, or the clustering of observations. The approach is illustrated with examples from categorical (penguin species, chocolate types) and quantitative (soccer/football salaries, house prices) response models. The methods are implemented in the R package cheem, available on CRAN.

Weihao Li, Emily Dodwell, Dianne Cook

This paper proposes a spatiotemporal clustering algorithm and its implementation in the R package spotoroo. This work is motivated by the catastrophic bushfires in Australia throughout the summer of 2019-2020 and made possible by the availability of satellite hotspot data. The algorithm is inspired by two existing spatiotemporal clustering algorithms but makes enhancements to cluster points spatially in conjunction with their movement across consecutive time periods. It also allows for the adjustment of key parameters, if required, for different locations and satellite data sources. Bushfire data from Victoria, Australia, is used to illustrate the algorithm and its use within the package.

Natalia da Silva, Dianne Cook, Eun-Kyung Lee

This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where depth is constrained to be less than the number of classes -- a limitation that proves too rigid for complex classification problems. Our extensions improve performance in multi-class settings with unequal variance-covariance structures and nonlinear class separations by allowing more splits and more flexible class groupings in the projection pursuit computation. Proposing algorithmic improvements is straightforward; demonstrating their actual utility is not. We therefore develop two visual diagnostic approaches to verify that the enhancements perform as intended. Using high-dimensional visualization techniques, we examine model fits on benchmark datasets to assess whether the algorithm behaves as theorized. An interactive web application enables users to explore the behavior of both the original and enhanced classifiers under controlled scenarios. The enhancements are implemented in the R package PPtreeExt.

Natalia da Silva, Dianne Cook, Eun-Kyung Lee

This paper presents a new ensemble learning method for classification problems called projection pursuit random forest (PPF). PPF uses the PPtree algorithm introduced in Lee et al. (2013). In PPF, trees are constructed by splitting on linear combinations of randomly chosen variables. Projection pursuit is used to choose a projection of the variables that best separates the classes. Utilizing linear combinations of variables to separate classes takes the correlation between variables into account which allows PPF to outperform a traditional random forest when separations between groups occurs in combinations of variables. The method presented here can be used in multi-class problems and is implemented into an R (R Core Team, 2018) package, PPforest, which is available on CRAN, with development versions at https://github.com/natydasilva/PPforest.

Harriet Mason, Dianne Cook, Sarah Goodwin et al.

Better representation of the uncertainty in a data visualisation is a focus of recent research activity. A problem with the current literature is that there is a lack of clarity about the definition of uncertainty and what it means to represent it in a plot. This confusion results in a significant amount of conflicting results in the literature, especially in experiments that assess the effectiveness of different uncertainty representations. In this review, we summarise the current literature, provide workable definitions, and illustrate these definitions with examples. In doing so, we ask what it really takes to achieve transparency in statistical graphics. It is hoped that it will be useful for guiding new graphics methodology and experimental research.

Weihao Li, Dianne Cook, Emi Tanaka et al.

Plotting the residuals is a recommended procedure to diagnose deviations from linear model assumptions, such as non-linearity, heteroscedasticity, and non-normality. The presence of structure in residual plots can be tested using the lineup protocol to do visual inference. There are a variety of conventional residual tests, but the lineup protocol, used as a statistical test, performs better for diagnostic purposes because it is less sensitive and applies more broadly to different types of departures. However, the lineup protocol relies on human judgment which limits its scalability. This work presents a solution by providing a computer vision model to automate the assessment of residual plots. It is trained to predict a distance measure that quantifies the disparity between the residual distribution of a fitted classical normal linear regression model and the reference distribution, based on Kullback-Leibler divergence. From extensive simulation studies, the computer vision model exhibits lower sensitivity than conventional tests but higher sensitivity than human visual tests. It is slightly less effective on non-linearity patterns. Several examples from classical papers and contemporary data illustrate the new procedures, highlighting its usefulness in automating the diagnostic process and supplementing existing methods.

Ursula Laa, Dianne Cook, German Valencia

Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for visualising data with concavities, or non-linear structure. It is associated with conditional distributions in statistics, and also linked brushing between plots in interactive data visualisation. This short technical note describes a simple approach for slicing in the orthogonal space of projections obtained when running a tour, thus presenting the viewer with an interpolated sequence of sliced projections. The method has been implemented in R as an extension to the tourr package, and can be used to explore for concave and non-linear structures in multivariate distributions.

Natalia da Silva, Dianne Cook, Eun-Kyung Lee

This paper describes structuring data and constructing plots to explore forest classification models interactively. A forest classifier is an example of an ensemble, produced by bagging multiple trees. The process of bagging and combining results from multiple trees, produces numerous diagnostics which, with interactive graphics, can provide a lot of insight into class structure in high dimensions. Various aspects are explored in this paper, to assess model complexity, individual model contributions, variable importance and dimension reduction, and uncertainty in prediction associated with individual observations. The ideas are applied to the random forest algorithm, and to the projection pursuit forest, but could be more broadly applied to other bagged ensembles. Interactive graphics are built in R, using the ggplot2, plotly, and shiny packages.