A data value metric for quantifying information content and utility

Data-driven innovation is propelled by recent scientific advances, rapid technological progress, substantial reductions of manufacturing costs, and significant demands for effective decision support systems. This has led to efforts to collect massive amounts of heterogeneous and multisource data, however, not all data is of equal quality or equally informative. Previous methods to capture and quantify the utility of data include value of information (VoI), quality of information (QoI), and mutual information (MI). This manuscript introduces a new measure to quantify whether larger volumes of increasingly more complex data enhance, degrade, or alter their information content and utility with respect to specific tasks. We present a new information-theoretic measure, called Data Value Metric (DVM), that quantifies the useful information content (energy) of large and heterogeneous datasets. The DVM formulation is based on a regularized model balancing data analytical value (utility) and model complexity. DVM can be used to determine if appending, expanding, or augmenting a dataset may be beneficial in specific application domains. Subject to the choices of data analytic, inferential, or forecasting techniques employed to interrogate the data, DVM quantifies the information boost, or degradation, associated with increasing the data size or expanding the richness of its features. DVM is defined as a mixture of a fidelity and a regularization terms. The fidelity captures the usefulness of the sample data specifically in the context of the inferential task. The regularization term represents the computational complexity of the corresponding inferential method. Inspired by the concept of information bottleneck in deep learning, the fidelity term depends on the performance of the corresponding supervised or unsupervised model. We tested the DVM method for several alternative supervised and unsupervised regression, classification, clustering, and dimensionality reduction tasks. Both real and simulated datasets with weak and strong signal information are used in the experimental validation. Our findings suggest that DVM captures effectively the balance between analytical-value and algorithmic-complexity. Changes in the DVM expose the tradeoffs between algorithmic complexity and data analytical value in terms of the sample-size and the feature-richness of a dataset. DVM values may be used to determine the size and characteristics of the data to optimize the relative utility of various supervised or unsupervised algorithms.