Communication theoretic inference on heterogeneous data

Statistical learning has attracted considerable recent research interest due to the wide-ranging demands of big data analytics. The recent introduction of communication theory and information coupling theory into this area suggests a new perspective on statistical learning and inference for data analytics. This paper investigates inference of one data variable from heterogeneous data variables, a problem that plays an increasingly important role in the emerging applications of big data analytics. To generalize the existing conceptual approach, information coupling filtering under hidden data structure or unknown knowledge of interactions among data variables is developed. A least-mean-squares (LMS) filtering approach for non-stationary data similar to an equalizer is suggested, while the training data gives the depth of the filter analogously to model selection in learning theory. The information combining in diversity communication is extended to fuse more data variables for even greater precision of inference. Extending from multiuser detection, an algorithm based on Multiple Signal Classification (MUSIC) is demonstrated to identify useful data variables for inference, as a novel solution to knowledge discovery. A series of examples illustrate the effectiveness of this framework, suggesting that statistical communication theory and statistical signal processing can substantially contribute to statistical learning theory.