TRIPODS@Duke was established in 2019 with a grant from the National Science Foundation to further our understanding of foundational principles in data science and to identify opportunities for innovation. Since then, as many as 25 faculty members – as well as graduate students and postdoctoral fellows – are working across disciplines to develop new tools and methods and to create dialogues in data science throughout North Carolina’s “Research Triangle.”
Project collaborators represent Duke departments including Computer Science, Electrical and Computer Engineering, Mathematics, and Statistical Science, and the team anticipates forging additional partnerships through engagement with the Rhodes Information Initiative at Duke and the regional Statistical and Mathematical Sciences Institute (SAMSI).
Themes
This initiative is part of the NSF’s Harnessing the Data Revolution (HDR) Big Idea activity, and all research and outreach efforts will focus on the three key themes below. Duke scientists have already produced significant scholarship on these topics, as reflected in the lists of recent publications and media coverage.
i. Scalable Algorithms with Uncertainty
In most application areas, it is of paramount importance to obtain an accurate quantification of uncertainty in conducting machine learning and statistical inferences.
This is particularly true for high-dimensional and complex data as the data collection process is inherently prone to uncertainty. Most methodology developed for these data focus on producing point estimates without any characterization of uncertainty. The lack of quantifying uncertainty leads to the risk of over-interpretation and contributes to the replicability crisis in science.
- Estimating Normalizing Constants for Log-Concave Distributions: Algorithms and Lower Bounds
- Efficient Posterior Sampling for High-Dimensional Imbalanced Logistic Regression
- Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets
- Diffusion Based Gaussian Process Regression via Heat Kernel Reconstruction
- Approximating Posteriors with High-Dimensional Nuisance Parameters via Integrated Rotated Gaussian Approximation
- Fast Moment Estimation for Generalized Latent Dirichlet Models
- Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise
- Online Algorithms for Rent-or-Buy with Expert Advice
- Dynamic Set Cover: Improved Algorithms and Lower Bounds
- Multi-Unit Supply-Monotone Auctions with Bayesian Valuation
- Elastic Caching
- Scaling Limit of the Stein Variational Gradient Descent: The Mean Field Regime
ii. Human Machine Interface
Data analytic and artificially intelligent (AI) systems are increasingly directly impacting society and human lives. Two technology based factors are driving this influence. The first factor is the application of data analytics to high-stakes application domains both at the individual level as well as the societal level through applications such as automated bail and parole decisions and the data analytics used to form gerrymandered voting districts, respectively. The second factor is the ubiquity and increased complexity of sensing technologies from social media to wearable devices to 3D imaging and their impact on data analysis from causal inference to medical applications such as clinical trials.
- Machine Learning to Screen for Autism in Children
- New Research Aims to Open the ‘Black Box’ of Computer Vision
- Quantifying Gerrymandering in North Carolina
- Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis
- A New Fully Automated Approach for Aligning and Comparing Shapes
- Duke-Volvo Team Develops First LiDAR System Capable of Long-range Detection and Classification
- This Looks Like That: Deep Learning for Interpretable Image Recognition
- Development and Assessment of Fully Automated and Globally Transitive Geometric Morphometric Methods, With Application to a Biological Comparative Dataset With High Interspecific Variation
- Algorithms to automatically quantify the geometric similarity of anatomical surfaces
- Learning Optimized Risk Scores
iii. Fundamental Limits
The fundamental limits of the algorithms and models proposed in the previous themes.. The types of analysis we consider are lower and upper bounds on conditions with theoretical guarantees, minimax rates for estimators, and approximation theory results for the complexity or expressibility of function classes induced by AI algorithms. Specifically, the challenges we consider include: (a) The fundamental limits of robust optimization with uncertain inputs; (b) Characterizing the statistical and approximation power of deep neural network architectures; and (c) The fundamental limits of causal inference in observational studies.
- The Geometry of Community Detection via the MMSE Matrix
- The All-or-Nothing Phenomenon in Sparse Linear Regression
- All-or-Nothing Phenomena: From Single-Letter to High Dimensions
- Gibbs Posterior Convergence and the Thermodynamic Formalism
- How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms
People
Principal Investigators
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Sayan Mukherjee, PI Professor of Statistical Science, Mathematics and Computer Science |
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Robert Calderbank, Co-PI |
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Cynthia Rudin, Co-PI Professor of Computer Science Prediction Analysis Lab |
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Jianfeng Lu, Co-PI Associate Professor of Mathematics and Chemistry |
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Rong Ge, Co-PI Assistant Professor of Computer Science |
Senior Personnel
Visiting Research Scholars
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Nicolas Fraiman I am an assistant professor in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill, where I am a member of the probability group. |
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Student and Postdoctoral Research
| Youngsoo Baek My research is in analyzing medical image data to improve clinical diagnoses. In particular, I am interested in drawing ideas from machine learning methods to address computational burden and likelihood intractability that pose challenges to applying classical statistical models. |
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Alina Barnett My research is in designing inherently interpretable models for computer vision. By providing interpretable algorithms, I enable scientists to validate their models and ensure that their models are making predictions based on meaningful representations rather than on confounding information. |
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| Jordan Bryan I work with cancer genomics data, with a particular eye towards using tensor models for datasets with several experimental modalities. More recently, I have been spending time thinking about statistical inference problems using ideas from optimal transport. |
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| Michele Caprio My research is focused on imprecise probabilities. I am also interested in more foundational topics, like extended probabilities, and in the theoretical properties of neural networks. |
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Abraham Frandsen |
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Henry Kirveslahti I work on applied topology, Bayesian statistics and their applications to imaging and biology. I am particularly interested in highly dissimilar data and soft tissue. |
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Anilesh Kollagunta Krishnaswamy I am primarily interested in questions regarding the design of fair and robust algorithms for machine learning, using ideas from optimization and game theory |
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Holden Lee I am primarily interested in questions regarding the design of fair and robust algorithms for machine learning, using ideas from optimization and game theory |
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Zining Ma (Past Participant) In my research, we propose a method to generate a specific form of 3D shapes representation that could be applied in statistical analysis. We use Euler Characteristic curves to create the representation of shapes and utilize scaling function bases from diffusion wavelet to generate the representation. We discuss the details of our method and in the last we apply our method on a shape classification problem to test the performance of the representation. |
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| Ezinne Nwankwo (Past Participant) My primary research interests lie in improving the trustworthiness and reliability of machine learning models and applying machine learning to address societal challenges. Currently, my research focuses on using causal inference methods to identify and mitigate algorithmic bias/discrimination. |
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| Xiang Wang I am interested in the theory of deep learning, especially the optimization of neural networks. |
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| Lihan Wang (Past Participant) I am currently interested in the analytic behavior and numerical performance of Markov Chain Monte Carlo sampling algorithms that arise from stochastic processes. |
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Data Science Pathways in Education
The educational goal of TRIPODS@Duke is to develop and implement a Data Science Pathway that targets the entire “data to knowledge to action” pipeline to prepare undergraduates, graduate students, and postdoc trainees in cutting-edge data science research, being able to wrangle and analyze data in a responsible and ethical manner, and being able to work effectively in interdisciplinary teams.
Undergraduate
View our interactive Data Science interdisciplinary course map.
Departmental Pathways
- Computer Science
- Degree Programs
- Interdepartmental Majors (also detailed below)
- Electrical & Computer Engineering
- Degree Programs
- Concentration in Machine Learning (open only to ECE majors, Complete five courses—Earn a notation on your Duke transcript)
- Minor in Machine Learning and AI (open to both Pratt and Trinity undergraduates)
- Mathematics
- Statistical Science
- Degree Programs
- Interdepartmental Majors (IDMs) (also detailed below)
Interdepartmental Majors (IDMs) combine two academic disciplines in Trinity College, drawing 7 courses from each to create a major.
- Data Science - Computer Science and Statistics
- Data Science - Computer Science and Math
Research Opportunities
- Data+
- Duke Opportunities in Mathematics (DOmath)
- Code+
- Program for Research for Undergraduates (PRUV)
Activities
Reading Groups
Theoretical Aspects of Deep Learning
Thursdays @ 11am via Zoom
Contact Jianfeng Lu to join: jianfeng@math.duke.edu
The reading group meets and discusses recent works in mathematical and theoretical analysis of deep learning models and algorithms.
Diversity, Equity, and Inclusion
Our work cannot be complete unless all are given the genuine opportunity to succeed regardless of race, ethnicity, religion, national origin, gender identity, sexual orientation, or disability. We are well aware that past and current injustices have prevented far too many people from living up to their potential. We are committed to maintaining a culture that is welcoming and nurturing to all. We expect that everyone conducts themselves in a manner that is consistent with these values and free from any form of discrimination or harassment.
*This material is based upon work supported by the National Science Foundation under Grant Number 1934964. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
