Past Events

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

Overparametrization in machine learning: insights from linear models

Data Science Seminar

Andrea Montanari (Stanford University)

Abstract

Deep learning models are often trained in a regime that is forbidden by classical statistical learning theory. The model complexity can be larger than the sample size and the train error does not concentrate around the test error. In fact, the model complexity can be so large that the network interpolates noisy training data. Despite this, it behaves well on fresh test data, a phenomenon that has been dubbed `benign overfitting.'

I will review recent progress towards a precise quantitative understanding of this phenomenon in linear models and kernel regression. In particular, I will present a recent characterization of ridge regression in Hilbert spaces which provides a unified understanding on several earlier results.

[Based on joint work with Chen Cheng]

Meta-Analysis of Randomized Experiments: Applications to Heavy-Tailed Response Data

Industrial Problems Seminar

Dominique Perrault-Joncas (Amazon)

Abstract

A central obstacle in the objective assessment of treatment effect (TE) estimators in randomized control trials (RCTs) is the lack of ground truth (or validation set) to test their performance. In this paper, we propose a novel cross-validation-like methodology to address this challenge. The key insight of our procedure is that the noisy (but unbiased) difference-of-means estimate can be used as a ground truth “label" on a portion of the RCT, to test the performance of an estimator trained on the other portion. We combine this insight with an aggregation scheme, which borrows statistical strength across a large collection of RCTs, to present an end-to-end methodology for judging an estimator’s ability to recover the underlying treatment effect as well as produce an optimal treatment "roll out" policy. We evaluate our methodology across 699 RCTs implemented in the Amazon supply chain. In this heavy-tailed setting, our methodology suggests that procedures that aggressively downweight or truncate large values, while introducing bias, lower the variance enough to ensure that the treatment effect is more accurately estimated.

Lecture: Yuxin Chen

Data Science Seminar

Yuxin Chen (University of Pennsylvania)

Registration is required to access the Zoom webinar.

Title: Taming Nonconvexity in Tensor Completion: Fast Convergence and Uncertainty Quantification

Abstract: Recent years have witnessed a flurry of activity in solving statistical estimation and learning problems via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple first-order optimization methods have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently.

This talk explores the effectiveness of nonconvex optimization for noisy tensor completion --- the problem of reconstructing a low-CP-rank tensor from highly incomplete and randomly corrupted observations of its entries. While randomly initialized gradient descent suffers from a high-volatility issue in the sample-starved regime, we propose a two-stage nonconvex algorithm that is guaranteed to succeed, enabling linear convergence, minimal sample complexity and minimax statistical accuracy all at once. In addition, we characterize the distribution of this nonconvex estimator down to fine scales, which in turn allows one to construct entrywise confidence intervals for both the unseen tensor entries and the unknown tensor factors. Our findings reflect the important role of statistical models in enabling efficient and guaranteed nonconvex statistical learning.

Lecture: Roy Lederman

Data Science Seminar

Roy Lederman (Yale University)

Registration is required to access the Zoom webinar.

The Geometry of Molecular Conformations in Cryo-EM

Cryo-Electron Microscopy (cryo-EM) is an imaging technology that is revolutionizing structural biology. Cryo-electron microscopes produce many very noisy two-dimensional projection images of individual frozen molecules; unlike related methods, such as computed tomography (CT), the viewing direction of each particle image is unknown. The unknown directions and extreme noise make the determination of the structure of molecules challenging. While other methods for structure determination, such as x-ray crystallography and NMR, measure ensembles of molecules, cryo-electron microscopes produce images of individual particles. Therefore, cryo-EM could potentially be used to study mixtures of conformations of molecules. We will discuss a range of recent methods for analyzing the geometry of molecular conformations using cryo-EM data and some new issues that arise.

Math & Money: Career Paths in Financial Services

Industrial Problems Seminar

Margaret Holen (Princeton University)

Registration is required to access the Zoom webinar.

Abstract

We face financial choices every day. From buying a morning coffee, to an online shopping errand in the afternoon, we are asked “Cash, Credit or Debit?” and “Pay Now or Later?” We occasionally face bigger decisions, like whether to take out a car loan, or to open a retirement account, or to take out a life insurance policy.

The finance industry offers mathematicians a rich array of career opportunities. Many of those include working with new technologies, complex data sets, and novel algorithms. Whether or not you enter the industry, we all play roles as consumers and as citizens influencing regulations.
This talk will share an overview of the finance sector, core mathematical ideas important in it, and my career path through it. My goal is to inspire you make the most of your backgrounds to shape your financial futures and the future of this industry.