Data-Inspire A Tripods Institute

This institute is premised on our belief that advances in data science principles are needed to impact the emerging paradigm of intelligent machines and their convergence with human society. This foundational understanding is needed to further improve the performance and better explain the operation of such machines so they can accomplish diverse, real-world tasks and interact effectively with people. To realize these advances, a new integration of mathematical, inferential, and algorithmic expertise is required. Thus, DATA-INSPIRE brings together mathematicians, statisticians, computer scientists to catalyze a new foundational data-science community focused on the development of intelligent, interactive machines.

On Going:

A set of activities are designed to catalyze an Institute, making it more than the sum of its parts, and build capacity toward a full Phase II TRIPODS Institute. This effort will build on the experience and the facilities of DIMACS, one of the original NSF Science and Technology Centers, with extensive experience in multi-disciplinary research projects, workshops, and innovative education. Briefly, these activities are:

• 3 research groups (with members from CS, Math, Stat) focus on research topics and meet regularly. The groups meet together several times a semester for cross-fertilization.
• Our seminar series brings all project participants together, and features both internal and external speakers, including speakers from existing TRIPODS Institutes.
• Education and training of PhD students and a postdocs take place through co-advising by faculty across the participating disciplines. They engage in all the research groups and are housed together at DIMACS in order to facilitate collaboration and Institute-building.
• Undergraduates will be mentored as part of the DIMACS REU site.
• Technical workshops with tutorial components connect faculty and students outside the locals, industry/government partners, and other TRIPODS Institutes, and advance a research agenda in the focus topics.
• Boot camps for advanced undergraduates and graduate students will expose them to the main themes of the Institute (Boot Camp Summer 2020, Boot Camp Winter 2021).
• Special topics graduate courses co-taught among Math, CS, and Stat aim to bring the disciplines together and aid in curriculum development.

Slides About DATA-INSPIRE:

The TRIPODs PI meeting originally planned for March 12th and 13th has been canceled. However, we have made the presentation materials available below:
• DATA-Inspire Poster
• Multi-Object Rearrangement Poster
• Colors in Context Inference challenges in Bayesian cognitive science Presentation

• Pranjal Awasthi – Computer Science
• Kostas Bekris – co-PI and Research Director; Computer Science
• Fioralba Cakoni – Mathematics
• Rong Chen – Statistics
• Lazaros Gallos – DIMACS
• Ying Hung – Statistics
• Jason M. Klusowski – Statistics
• Konstantin Mischaikow – co-PI; Mathematics
• Fred S. Roberts – PI; Mathematics
• Matthew Stone – co-PI and Education Program Lead; Computer Science
• Jingjin Yu – Computer Science
• Cun-Hui Zhang – co-PI and Head of Postdoc Mentoring Team; Statistics
• Wujun Zhang – Mathematics
• Kathy Haynie – STEM Education

Human and Machine Inference

Integration of Models and Data for Inference about Humans and Machines

This research direction aims to bridge the verification and explainability gap inherent in data-driven approaches. By investigating statistical, mathematical, and computational tools, researchers capture realistic prior knowledge about physical and social processes. This approach alleviates the burden of large training datasets, underwrites performance guarantees, and constrains inference in real time for more reliable intelligent behavior.

Research Highlights:

• Bayesian Methods for Inverse Scattering: Utilizing Gaussian Process (GP) models as surrogates for computationally intensive mathematical models (like PDEs). This allows for efficient prediction and uncertainty quantification in engineering applications such as non-destructive testing.
• Statistical Properties of Decision Trees: Proving the consistency of Classification and Regression Trees (CART) even when variables grow sub-exponentially. This research provides finite sample performance guarantees for variable ranking and screening in nonparametric models.
• Human Communication Models: Developing data-driven, latent-variable models to quantify human reasoning and communicative strategies. These models are leveraged in reinforcement learning for dialogue planning, allowing interactive systems to provide targeted, context-sensitive feedback.

Data-informed Dynamical Systems

Dealing with Dynamics through a Data-informed Dynamical Systems Theory

Focused on addressing significant nonlinearities, oscillations, and complex feedback loops, this area employs dynamical systems theory, real algebraic geometry, and topology. The goal is to develop algorithms that satisfy mathematical constraints during machine operation, providing rigorous guarantees for safety, efficiency, and robustness in intelligent machines.

Research Highlights:

• Combinatorial Framework via TDA: Using Topological Data Analysis (TDA) to extract reliable information from sparse data, such as robot trajectories. This framework identifies dynamic behaviors like periodic orbits and bistability without the need for predetermined models.
• Morse Graphs for Robot Controllers: Developing a topological framework to analyze the global dynamics of robot controllers. By building combinatorial representations (Morse graphs), researchers can identify attractors, regions of attraction (RoAs), and physical limitations of robotic systems.
• Rigorous Probabilistic Analysis: Modeling data through special Gaussian processes (Brownian motion) to provide precise probabilities that a given topological characterization of dynamics is accurate.

Combinatorics of Intelligent, Interactive Systems

The Role of Data and Combinatorics in Scaling Intelligent, Interactive Systems

This direction explores how intelligent systems can coordinate across many machines and complex environments under strict timelines. Researchers investigate statistical assumptions of problem instances and mathematical characterizations of solution spaces to overcome combinatorial challenges, such as NP-hard problems in object manipulation and path planning.

Research Highlights:

• Optimal Task Planning for Rearrangement: Addressing hard combinatorial challenges (like the Feedback Vertex Set) in object rearrangement. Researchers developed a "Depth-First Dynamic Programming" (DFDP) algorithm that is highly scalable and optimal for tabletop and in-shelf tasks.
• Retrieving Objects via Persistent Homology: Utilizing Persistent Homology (PH) to automatically identify clusters of blocking objects in cluttered, confined spaces. This enables robots to use non-prehensile (pushing) actions more effectively than conventional pick-and-place methods.
• Multi-Robot Path Planning: Researching sub-1.5 time-optimal path planning on grids and minimizing running buffers for tabletop rearrangement to improve efficiency in industrial and logistics applications.

Kostas Bekris – This email address is being protected from spambots. You need JavaScript enabled to view it.
Fred Roberts – This email address is being protected from spambots. You need JavaScript enabled to view it.
Lazaros Gallos – This email address is being protected from spambots. You need JavaScript enabled to view it.