Interpretable modeling, representation, and learning with transport transforms

Data or patterns (e.g., signals and images) emanating from physical sensors and biomedical systems often live in high dimensional spaces and exhibit complicated non-linear structures. The known and unknown non-linearities present in high dimensional data post challenges in modeling and hence constructing effective learning algorithms for downstream tasks. Though many ‘black-box’ models and algorithms exist and perform very well in various applications in terms of accuracy, there are issues like high computational cost and difficulty in interpreting the results. 

In this talk, I will show situations where simple models are as accurate as more complicated models while having the advantage of being more interpretable and computationally efficient. The modeling combines a template-deformation-based assumption which naturally describes morphological variations within data and a representation of data in an embedding space via certain invertible non-linear transforms motivated by the optimal transport theory. I describe situations when data geometry is simplified (convexified) in the embedding space, where the computational complexity can be reduced significantly. Such modeling also gives rise to simple machine learning algorithms with the ability incorporate meaningful invariances, with few or no hyperparameters, and which are robust to out-of-distribution samples (generalizability). I will show applications in various image and signal classification problems.