Past Events

Squishy Mathematical Reasoning in a Robotics Start-up

Industrial Problems Seminar

Michelle Snider (Service Robotics & Technologies)

Abstract

Service Robotics & Technologies (SRT Labs) brings legacy infrastructure, smart sensors, and collaborative robotics into a unified data management ecosystem in order to monitor, analyze and automate systems. Applications range from smart laboratories to smart buildings to smart cities. The smart technology space provides a wealth of interesting projects which may not immediately sound like math problems but whose solutions often greatly benefit from a mathematical perspective. In this talk, I will discuss some different projects where my team applied mathematical approaches to find realistically implementable solutions, interspersed with career lessons learned along the way.

A Varied and Winding Math Career in Industry

Industrial Problems Seminar

Laura Lurati (Edward Jones)

Abstract

In this talk, I'll share my personal career path as an applied mathematician both from the perspective of the various industries I've worked in (aerospace, finance, real estate, and software engineering) and my own transition from an individual contributor to management. I'll give an overview of the types of problems I worked on in each of these fields and the common skills that have helped me throughout my career. Finally, I will share some of my work as a builder of high-performing teams, the rewards of management, and what I look for in candidates when hiring new teammates. As a key message, I hope to share that a career in applied mathematics can take very interesting turns if you are open to new possibilities and continual learning.

Learning in Stochastic Games

Data Science Seminar

Muhammed Omer Sayin (Bilkent University)

Abstract

Reinforcement learning (RL) has been the backbone of many frontier artificial intelligence (AI) applications, such as game playing and autonomous driving, by addressing how intelligent and autonomous systems should engage with an unknown dynamic environment. The progress and interest in AI are now transforming social systems with human decision-makers, such as (consumer/financial) markets and road traffic, into socio-technical systems with AI-powered decision-makers. However, self-interested AI can undermine the social systems designed and regulated for humans. We are delving into the uncharted territory of AI-AI and AI-human interactions. The new grand challenge is to predict and control the implications of AI selfishness in AI-X interactions with systematic guarantees. Hence, there is now a critical need to study self-interested AI dynamics in complex and dynamic environments through the lens of game theory.

In this talk, I will present the recent steps we have taken toward the foundation of how self-interested AI would and should interact with others by bridging the gap between game theory and practice in AI-X interactions. I will specifically focus on stochastic games to model the interactions in complex and dynamic environments since they are commonly used in multi-agent reinforcement learning. I will present new learning dynamics converging almost surely to equilibrium in important classes of stochastic games. The results can also be generalized to the cases where (i) agents do not know the model of the environment, (ii) do not observe opponent actions, (iii) can adopt different learning rates, and (iv) can be selective about which equilibrium they will reach for efficiency. The key idea is to use the power of approximation thanks to the robustness of learning dynamics to perturbations. I will conclude my talk with several remarks on possible future research directions for the framework presented.

IMA Data Science Seminar - Learning in Stochastic Games

Muhammed Omer Sayin (Bilkent University) will give a presentation entitled Learning in Stochastic Games.

Continuous-time probabilistic generative models for dynamic networks

Data Science Seminar

Kevin Xu (Case Western Reserve University)

Abstract

Networks are ubiquitous in science, serving as a natural representation for many complex physical, biological, and social systems. Probabilistic generative models for networks provide plausible mechanisms by which network data are generated to reveal insights about the underlying complex system. Such complex systems are often time-varying, which has led to the development of dynamic network representations to enable modeling, analysis, and prediction of temporal dynamics.

In this talk, I introduce a class of continuous-time probabilistic generative models for dynamic networks that augment statistical models for network structure with multivariate Hawkes processes to model temporal dynamics. The class of models allows an analyst to trade off flexibility and scalability of a model depending on the application setting. I focus on two specific models on opposite ends of the tradeoff: the community Hawkes independent pairs (CHIP) model that scales up to millions of nodes, and the multivariate Community Hawkes (MULCH) model that is flexible enough to replicate a variety of observed structures in real network data, including temporal motifs. I demonstrate how these models can be used for analysis, prediction, and simulation on several real network data sets, including a network of militarized disputes between countries over time.

Working as an Artificial Intelligence Advisor to the US Government

Industrial Problems Seminar

Mitchell Kinney (The MITRE Corporation)

Abstract

Though Artificial Intelligence (AI) has progressed rapidly, many areas of government remain wary of upending legacy systems to capitalize on the technology. MITRE serves as a trusted advisor to government agencies and is a conduit between private industry and government through the management of multiple Federally Funded Research and Development Centers (FFRDCs). As a member of the AI and Autonomy Innovation Center, my role is to help government understand the potential positives and pitfalls of implementing AI technology.

I will discuss my background, my company, my responsibilities and give an overview of a project I worked on to help highlight how machine learning could be used to transfer paper-based systems engineering models into modern software. The prototype we developed uses computer vision techniques to build an internal graph representation of the diagram that can be translated to commercial tools.

Lecture: Adil Ali

Industrial Problems Seminar

Adil Ali (CH Robinson)

Viewing graph solvability and its relevance in 3D Computer Vision

Data Science Seminar

Federica Arrigoni (Politecnico di Milano)

Abstract

“Structure from motion” is a relevant problem in Computer Vision that aims at reconstructing both cameras and the 3D scene starting from multiple images. This talk will explore the theoretical aspects of structure from motion with particular focus on the “viewing graph”: such a graph has a camera for each node and an edge for each available fundamental matrix. In particular, a relevant problem is studying the “solvability” of a viewing graph, namely establishing if it determines a unique configuration of cameras. The talk will be based on the following paper:

Federica Arrigoni, Andrea Fusiello, Elisa Ricci, and Tomas Pajdla. Viewing graph solvability via cycle consistency. ICCV 2021 (Best paper honorable mention)

Applied Math at Boeing

Industrial Problems Seminar

Brittan Farmer (The Boeing Company)

Registration is required to access the Zoom webinar.

Abstract

There are many ways that mathematics is used to support Boeing's lines of business, which include the design, production, and sustainment of commercial and military aircraft. In this talk, I will give a brief overview of Boeing Research and Technology and the Applied Math organization, and describe some of the topics I've worked on at Boeing. I will then focus specifically on the problem of defect detection in metals additive manufacturing, and how mathematics can be used to approach this problem.

Adversarial training and the generalized Wasserstein barycenter problem

Data Science Seminar

Matt Jacobs (Purdue University)

Abstract

Adversarial training is a framework widely used by practitioners to enforce robustness of machine learning models. During the training process, the learner is pitted against an adversary who has the power to alter the input data. As a result, the learner is forced to build a model that is robust to data perturbations. Despite the importance and relative conceptual simplicity of adversarial training, there are many aspects that are still not well-understood (e.g. regularization effects, geometric/analytic interpretations, tradeoff between accuracy and robustness, etc...), particularly in the case of multiclass classification.

In this talk, I will show that in the non-parametric setting, the adversarial training problem is equivalent to a generalized version of the Wasserstein barycenter problem. The connection between these problems allows us to completely characterize the optimal adversarial strategy and to bring in tools from optimal transport to analyze and compute optimal classifiers. This also has implications for the parametric setting, as the value of the generalized barycenter problem gives a universal upper bound on the robustness/accuracy tradeoff inherent to adversarial training.

Joint work with Nicolas Garcia Trillos and Jakwang Kim