A Partition-Based Framework for Building and Validating Regression Models

Abstract

Regression models play a key role in many application domains for analyzing or predicting a quantitative dependent variable based on one or more independent variables. Automated approaches for building regression models are typically limited with respect to incorporating domain knowledge in the process of selecting input variables (also known as feature subset selection). Other limitations include the identification of local structures, transformations, and interactions between variables. The contribution of this paper is a framework for building regression models addressing these limitations. The framework combines a qualitative analysis of relationship structures by visualization and a quantification of relevance for ranking any number of features and pairs of features which may be categorical or continuous. A central aspect is the local approximation of the conditional target distribution by partitioning 1D and 2D feature domains into disjoint regions. This enables a visual investigation of local patterns and largely avoids structural assumptions for the quantitative ranking. We describe how the framework supports different tasks in model building (e.g., validation and comparison), and we present an interactive workflow for feature subset selection. A real-world case study illustrates the step-wise identification of a five-dimensional model for natural gas consumption. We also report feedback from domain experts after two months of deployment in the energy sector, indicating a significant effort reduction for building and improving regression models.

Supporting theoretically-grounded model building in the social sciences through interactive visualisation

“…The authors observed that a visualization-powered approach not only speeds up model building process but also increases the trust and confidence in the results. Mühlbacher and Piringer [13] discuss how the process of building regression models can benefit from integrating domain knowledge. Berger et al [14] introduce an interactive approach to inspect the parameter space in comparison to multiple target values.…”

Leveraging Spatial Abstraction in Traffic Analysis and Forecasting with Visual Analytics

“…A classifier may be built for assigning new objects to previously obtained clusters [3] [26]. Visual analytics techniques also support derivation of linear trend models from multivariate data [32], regression models [51], and time series models [13] [34]. Other works focus on supporting assessment of existing models, including classification [49], engineering simulation [47] [48], and spatio-temporal models [21][46] [55].…”

On Computationally-Enhanced Visual Analysis of Heterogeneous Data and Its Application in Biomedical Informatics

“…[51], [52], [53], [54], [55], [56] Groups & Classification [57] [58], [59] [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74] [75], [76], [77], [78], [79], [80] Dependence & Prediction [81], [82], [46] [83], [84], [85], [86], [87], [88], [89] [90], [91], [92] being analyzed. The results are then presented to the user through different visual encodings that are often accompanied by interaction.…”

“…Mühlbacher and Piringer [85] (see Figure 6) discuss how the process of building regression models can benefit from integrating domain knowledge. In the framework called Vismon, visualization has helped analysts to make predictions and investigate the uncertainties that are existent in relations within simulation parameters [86] (see Figure 5).…”