Local-Aggregate Modeling for Big-Data via Distributed Optimization: Applications to Neuroimaging

Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging scans. This is an ultra-high-dimensional problem that consists of a matrix of covariates (brain locations by time points) for each subject; few methods currently exist to fit supervised models directly to this tensor data. We propose a novel modeling and algorithmic strategy to apply generalized linear models (GLMs) to this massive tensor data in which one set of variables is associated with locations. Our method begins by fitting GLMs to each location separately, and then builds an ensemble by blending information across locations through regularization with what we term an aggregating penalty. Our so called, Local-Aggregate Model, can be fit in a completely distributed manner over the locations using an Alternating Direction Method of Multipliers (ADMM) strategy, and thus greatly reduces the computational burden. Furthermore, we propose to select the appropriate model through a novel sequence of faster algorithmic solutions that is similar to regularization paths. We will demonstrate both the computational and predictive modeling advantages of our methods via simulations and an EEG classification problem.Comment: 41 pages, 5 figures and 3 table

Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment

Analyzing and Interpreting Neural Networks for NLP: A Report on the First BlackboxNLP Workshop

The EMNLP 2018 workshop BlackboxNLP was dedicated to resources and techniques specifically developed for analyzing and understanding the inner-workings and representations acquired by neural models of language. Approaches included: systematic manipulation of input to neural networks and investigating the impact on their performance, testing whether interpretable knowledge can be decoded from intermediate representations acquired by neural networks, proposing modifications to neural network architectures to make their knowledge state or generated output more explainable, and examining the performance of networks on simplified or formal languages. Here we review a number of representative studies in each category

Decontextualized learning for interpretable hierarchical representations of visual patterns

Apart from discriminative models for classification and object detection tasks, the application of deep convolutional neural networks to basic research utilizing natural imaging data has been somewhat limited; particularly in cases where a set of interpretable features for downstream analysis is needed, a key requirement for many scientific investigations. We present an algorithm and training paradigm designed specifically to address this: decontextualized hierarchical representation learning (DHRL). By combining a generative model chaining procedure with a ladder network architecture and latent space regularization for inference, DHRL address the limitations of small datasets and encourages a disentangled set of hierarchically organized features. In addition to providing a tractable path for analyzing complex hierarchal patterns using variation inference, this approach is generative and can be directly combined with empirical and theoretical approaches. To highlight the extensibility and usefulness of DHRL, we demonstrate this method in application to a question from evolutionary biology