Cadre Modeling: Simultaneously Discovering Subpopulations and Predictive Models

We consider the problem in regression analysis of identifying subpopulations that exhibit different patterns of response, where each subpopulation requires a different underlying model. Unlike statistical cohorts, these subpopulations are not known a priori; thus, we refer to them as cadres. When the cadres and their associated models are interpretable, modeling leads to insights about the subpopulations and their associations with the regression target. We introduce a discriminative model that simultaneously learns cadre assignment and target-prediction rules. Sparsity-inducing priors are placed on the model parameters, under which independent feature selection is performed for both the cadre assignment and target-prediction processes. We learn models using adaptive step size stochastic gradient descent, and we assess cadre quality with bootstrapped sample analysis. We present simulated results showing that, when the true clustering rule does not depend on the entire set of features, our method significantly outperforms methods that learn subpopulation-discovery and target-prediction rules separately. In a materials-by-design case study, our model provides state-of-the-art prediction of polymer glass transition temperature. Importantly, the method identifies cadres of polymers that respond differently to structural perturbations, thus providing design insight for targeting or avoiding specific transition temperature ranges. It identifies chemically meaningful cadres, each with interpretable models. Further experimental results show that cadre methods have generalization that is competitive with linear and nonlinear regression models and can identify robust subpopulations.Comment: 8 pages, 6 figure

Should we tweet this? Generative response modeling for predicting reception of public health messaging on Twitter

The way people respond to messaging from public health organizations on social media can provide insight into public perceptions on critical health issues, especially during a global crisis such as COVID-19. It could be valuable for high-impact organizations such as the US Centers for Disease Control and Prevention (CDC) or the World Health Organization (WHO) to understand how these perceptions impact reception of messaging on health policy recommendations. We collect two datasets of public health messages and their responses from Twitter relating to COVID-19 and Vaccines, and introduce a predictive method which can be used to explore the potential reception of such messages. Specifically, we harness a generative model (GPT-2) to directly predict probable future responses and demonstrate how it can be used to optimize expected reception of important health guidance. Finally, we introduce a novel evaluation scheme with extensive statistical testing which allows us to conclude that our models capture the semantics and sentiment found in actual public health responses.Comment: Accepted at ACM WebSci 202

A Mathematics Pipeline to Student Success in Data Analytics through Course-Based Undergraduate Research

This paper reports on Data Analytics Research (DAR), a course-based undergraduate research experience (CURE) in which undergraduate students conduct data analysis research on open real- world problems for industry, university, and community clients. We describe how DAR, offered by the Mathematical Sciences Department at Rensselaer Polytechnic Institute (RPI), is an essential part of an early low-barrier pipeline into data analytics studies and careers for diverse students. Students first take a foundational course, typically Introduction to Data Mathematics, that teaches linear algebra, data analytics, and R programming simultaneously using a project-based learning (PBL) approach. Then in DAR, students work in teams on open applied data analytics research problems provided by the clients. We describe the DAR organization which is inspired in part by agile software development practices. Students meet for coaching sessions with instructors multiple times a week and present to clients frequently. In a fully remote format during the pandemic, the students continued to be highly successful and engaged in COVID-19 research producing significant results as indicated by deployed online applications, refereed papers, and conference presentations. Formal evaluation shows that the pipeline of the single on-ramp course followed by DAR addressing real-world problems with societal benefits is highly effective at developing students\u27 data analytics skills, advancing creative problem solvers who can work both independently and in teams, and attracting students to further studies and careers in data science

Topics in Matrix Sampling Algorithms

We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)"Low-rank Column-based Matrix Approximation". We are given a matrix A and a target rank k. The goal is to select a subset of columns of A and, by using only these columns, compute a rank k approximation to A that is as good as the rank k approximation that would have been obtained by using all the columns; 2) "Coreset Construction in Least-Squares Regression". We are given a matrix A and a vector b. Consider the (over-constrained) least-squares problem of minimizing ||Ax-b||, over all vectors x in D. The domain D represents the constraints on the solution and can be arbitrary. The goal is to select a subset of the rows of A and b and, by using only these rows, find a solution vector that is as good as the solution vector that would have been obtained by using all the rows; 3) "Feature Selection in K-means Clustering". We are given a set of points described with respect to a large number of features. The goal is to select a subset of the features and, by using only this subset, obtain a k-partition of the points that is as good as the partition that would have been obtained by using all the features. We present novel algorithms for all three problems mentioned above. Our results can be viewed as follow-up research to a line of work known as "Matrix Sampling Algorithms". [Frieze, Kanna, Vempala, 1998] presented the first such algorithm for the Low-rank Matrix Approximation problem. Since then, such algorithms have been developed for several other problems, e.g. Graph Sparsification and Linear Equation Solving. Our contributions to this line of research are: (i) improved algorithms for Low-rank Matrix Approximation and Regression (ii) algorithms for a new problem domain (K-means Clustering).Comment: PhD Thesis, 150 page