We introduce Union of Intersections (UoI), a flexible, modular, and scalable framework for enhanced model selection and estimation.

The increasing size and complexity of scientific data could dramatically enhance discovery and prediction for basic scientific applications. Realizing this potential, however, requires novel statistical analysis methods that are both interpretable and predictive. We introduce Union of Intersections (UoI), a flexible, modular, and scalable framework for enhanced model selection and estimation. Methods based on UoI perform model selection and model estimation through intersection and union operations, respectively. We show that UoI-based methods achieve low-variance and nearly unbiased estimation of a small number of interpretable features, while maintaining high-quality prediction accuracy.

Localization of unknown faults in industrial systems is a difficult task for data-driven diagnosis methods. The classification performance of many machine learning methods relies on the quality of training data. Unknown faults, for example faults not represented in training data, can be detected using, for example, anomaly classifiers. However, mapping these unknown faults to an actual location in the real system is a non-trivial problem. In model-based diagnosis, physical-based models are used to create residuals that isolate faults by mapping model equations to faulty system components. Developing sufficiently accurate physical-based models can be a time-consuming process. Hybrid modeling methods combining physical-based methods and machine learning is one solution to design data-driven residuals for fault isolation. In this work, a set of neural network-based residuals are designed by incorporating physical insights about the system behavior in the residual model structure. The residuals are trained using only fault-free data and a simulation case study shows that they can be used to perform fault isolation and localization of unknown faults in the system.

Memory management is now a really important topic in Machine Learning. Because of memory constraints, it is becoming quite common to train Deep Learning models using cloud tools such as Kaggle and Google Colab thanks to their free NVIDIA Graphical Processing Unit (GPU) support. Nonetheless, memory can still be a huge constraint in the cloud when working with large amounts of data. In my last article, I explained how to speed up Machine Learning workflow execution. This article aims instead to explain to you how to efficiently reduce memory usage when implementing Deep Learning models.

The increasing size and complexity of scientific data could dramatically enhance discovery and prediction for basic scientific applications, e.g., neuroscience, genetics, systems biology, etc. Realizing this potential, however, requires novel statistical analysis methods that are both interpretable and predictive. We introduce the Union of Intersections (UoI) method, a flexible, modular, and scalable framework for enhanced model selection and estimation. The method performs model selection and model estimation through intersection and union operations, respectively. We show that UoI can satisfy the bi-criteria of low-variance and nearly unbiased estimation of a small number of interpretable features, while maintaining high-quality prediction accuracy. We perform extensive numerical investigation to evaluate a UoI algorithm ($UoI_{Lasso}$) on synthetic and real data. In doing so, we demonstrate the extraction of interpretable functional networks from human electrophysiology recordings as well as the accurate prediction of phenotypes from genotype-phenotype data with reduced features. We also show (with the $UoI_{L1Logistic}$ and $UoI_{CUR}$ variants of the basic framework) improved prediction parsimony for classification and matrix factorization on several benchmark biomedical data sets. These results suggest that methods based on UoI framework could improve interpretation and prediction in data-driven discovery across scientific fields.