BIGDATA: F: Reliable Inference with Big Data: Reproducibility, Data Sharing, Heterogeneity

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Over the last decade, 'big data' technologies have allowed the acquisition of vast amount of data (e.g. through smartphones) and their accumulation into large scale databases. Powerful hardware and software systems have been developed to crunch these data and extract statistical models. For instance, the outcome of a certain medical procedure can be modeled in terms of the features of the patient, thus in principle providing a personalized risk score for that procedure. Unfortunately, the increasing complexity of these data and of the algorithms used has made statistical models significantly less transparent. How certain are we of these statistical predictions? What is their limit of validity? How biased is the resulting model?This project focuses on four main challenges that are ubiquitous in big-data, and are crucial to extract reliable insights: reproducibility; data sharing; missing data; data heterogeneity. (1) Reproducibility requires being able to compare two models extracted from different data sets (e.g. after additional data have been accumulated). This is in turn impossible unless we have reliable procedures to quantify uncertainty and confidence in complex high-dimensional models. Recently proposed ideas in this direction are still insufficient to cope with realistic large-scale applications.(2) Data sharing is a key feature of modern data analysis, whereby a single massive data set is being studied by hundreds of independent researchers. Unguarded statistical inference by such a population of researchers unavoidably leads to large numbers of false discoveries. The project builds on false discovery rate-controlling methods to propose safe approaches for decentralized data analysis.(3) Missing data are ubiquitous in big data. While several methods have been developed in the past to deal with missing data, it is unclear to what extent they are applicable to modern scenarios. The project aims at developing principled guidelines based on a rigorous comparison of various approaches, and developing new algorithms based on maximum likelihood.(4) Data heterogeneity. Big data are often produced by the aggregation of multiple data sources. How can we prevent standard statistical procedures to be critically affected by such heterogeneities? The project uses new regularization schemes to fusion information across multiple sources.