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The theoretical foundations of Big Data Science are not fully developed, yet. This study proposes a new scalable framework for Big Data representation, high-throughput analytics (variable selection and noise reduction), and model-free inference. Specifically, we explore the core principles of distribution-free and model-agnostic methods for scientific inference based on Big Data sets. Compressive Big Data analytics (CBDA) iteratively generates random (sub)samples from a big and complex dataset. This subsampling with replacement is conducted on the feature and case levels and results in samples that are not necessarily consistent or congruent across iterations. The approach relies on an ensemble predictor where established model-based or model-free inference techniques are iteratively applied to preprocessed and harmonized samples. Repeating the subsampling and prediction steps many times, yields derived likelihoods, probabilities, or parameter estimates, which can be used to assess the algorithm reliability and accuracy of findings via bootstrapping methods, or to extract important features via controlled variable selection. CBDA provides a scalable algorithm for addressing some of the challenges associated with handling complex, incongruent, incomplete and multi-source data and analytics challenges. Albeit not fully developed yet, a CBDA mathematical framework will enable the study of the ergodic properties and the asymptotics of the specific statistical inference approaches via CBDA. We implemented the high-throughput CBDA method using pure R as well as via the graphical pipeline environment. To validate the technique, we used several simulated datasets as well as a real neuroimaging-genetics of Alzheimer’s disease case-study. The CBDA approach may be customized to provide generic representation of complex multimodal datasets and to provide stable scientific inference for large, incomplete, and multisource datasets.