Frontiers in Computing + Mathematical Sciences Symposium

Frontiers in Computing and Mathematical Sciences

Monday, January 10, 2022
Talks will be hosted in Zoom. Please contact Sydney Garstang for the Zoom link.

This Symposium features talks on recent advances in computing and mathematical sciences from talented faculty candidates!

Program

Viewable at http://cms.caltech.edu/frontiers

• 8:55am: Introduction
  Adam Wierman, Computing and Mathematical Sciences, Caltech
  
  
• 9:00am: Tractable Probabilistic Reasoning for Trustworthy AI
  YooJung Choi, UCLA
  
  Automated decision-making systems are increasingly being deployed in areas with personal and societal impacts: from financial services to healthcare and criminal justice. This led to growing interest and need for trustworthy AI and ML systems--that is, models that are robust, explainable, fair, and so on. It is important to note that these guarantees only hold with respect to a certain model of the world, with inherent uncertainties. In this talk, I will present how probabilistic modeling and inference, by incorporating a distribution, offer a principled way to handle different kinds of uncertainties when reasoning about decision-making system behaviors. For example, labels in training data may be biased; I will show that probabilistic circuits, a class of tractable probabilistic models (TPMs), can be effective in enforcing and auditing fairness properties by explicitly modeling a latent unbiased label. Another common source of uncertainty is missing values at prediction time, which also leads to fairness and robustness queries that account for this to be computationally hard inference tasks. I will also demonstrate how TPMs can again tractably answer these more complex queries. Finally, I will conclude with my future work towards a framework to flexibly reason about and enforce trustworthy AI/ML system behaviors.
  
  
• 10:15am: Bridging Safety and Learning in Human-Robot Interaction
  Andrea Bajcsy, UC Berkeley
  
  From autonomous cars in cities to mobile manipulators at home, robots must interact with people. What makes this hard is that human behavior—especially when interacting with other agents—is vastly complex, varying between individuals, environments, and over time. Thus, robots rely on data and machine learning throughout the design process and during deployment to build and refine models of humans. However, by blindly trusting their data-driven human models, today's robots confidently plan unsafe behaviors around people, resulting in anything from miscoordination to dangerous collisions.
  
  My research aims to ensure safety in human-robot interaction, particularly when robots learn from and about people. In this talk, I will discuss how treating robot learning algorithms as dynamical systems driven by human data enables safe human-robot interaction. I will first introduce a Bayesian monitor which infers online if the robot's learned human model can evolve to well-explain observed human data. I will then discuss how control-theoretic tools enable us to formally quantify what the robot could learn online from human data and how quickly it could learn it. Coupling these ideas with robot motion planning algorithms, I will demonstrate how robots can safely and automatically adapt their behavior based on how trustworthy their learned human models are. I will end this talk by taking a step back and raising the question: "What is the ‘right' notion of safety when robots interact with people?" and discussing opportunities for how rethinking our notions of safety can capture more subtle aspects of human-robot interaction.
  
  
• 11:30am: Learning to Generate Data by Estimating Gradients of the Data Distribution
  Yang Song, Stanford
  
  Generating data with complex patterns, such as images, audio, and molecular structures, requires fitting very flexible statistical models to the data distribution. Even in the age of deep neural networks, building such models is difficult because they typically require an intractable normalization procedure to represent a probability distribution. To address this challenge, I propose to model the vector field of gradients of the data distribution (known as the score function), which does not require normalization and therefore can take full advantage of the flexibility of deep neural networks. I will show how to (1) estimate the score function from data with principled statistical methods, (2) generate new data using stochastic differential equations and numerical techniques, and even (3) evaluate probabilities as in a traditional statistical model. The resulting method, called score-based generative modeling, achieves record-breaking performance in applications including image synthesis, image compression, text-to-speech generation, time series prediction, and point cloud generation, challenging the long-time dominance of generative adversarial networks (GANs) on many of these tasks. Furthermore, unlike GANs, score-based generative models are suitable for Bayesian reasoning tasks such as solving ill-posed inverse problems, and I have demonstrated their superior performance on examples like sparse-view computed tomography and accelerated magnetic resonance imaging. Finally, I will discuss how score-based generative modeling opens up new opportunities for solving data generation problems in various disciplines of science and engineering.
  
  
• 1:30pm: A New Toolbox for Scheduling Theory
  Ziv Scully, Carnegie Mellon
  
  Queueing-induced delays due to resource contention are ubiquitous in many domains, including computer systems, service systems, supply chains, and transportation. One of the main tools system designers have to reduce delay is scheduling. However, scheduling is complicated; designing policies and evaluating their performance impact are difficult tasks. The role of queueing theory, and in particular scheduling theory, is to provide a rigorous mathematical basis for understanding scheduling, including evaluating policy performance and guiding policy design.
  
  Unfortunately, the scope of today's queueing and scheduling theory fails to address many practical concerns of today's computer systems. For example, scheduling theory seldom explicitly models nontrivial preemption limitations, instead assuming that preemption is either always or never possible. As another example, there is very little theory for scheduling in multiserver queues.
  
  We present two new, broadly applicable tools that greatly expand the reach of scheduling theory, applying each to solve multiple open problems.
  
  The first tool, called "SOAP", is a new unifying theory of single-server scheduling, specifically the M/G/1 queueing model. SOAP characterizes the delay distribution of a broad space of policies, most of which have never been analyzed before. Among the newly analyzed policies are the Gittins index policy, which minimizes mean delay in low-information settings, and many policies with nontrivial preemption limitations.
  
  The second tool, called "KIWI", is a new queueing identity that complements Little's law. KIWI enables a new method of analyzing complex queueing systems, most notably the M/G/k multiserver queue, by relating them to simpler systems, such as the M/G/1. This results in the first delay bounds for the M/G/k under scheduling policies like SRPT (shortest remaining processing time) and the Gittins index policy.
  
  
• 2:45pm: Two Topics in Monte Carlo for Scientific Computing
  Michael Lindsey, NYU
  
  In the first part of the talk, I consider the problem of sampling from a probability distribution with known density, which arises almost ubiquitously in the mathematical sciences. The most generic and widely-used method for this task is Markov chain Monte Carlo (MCMC), though this method typically suffers from extremely long autocorrelation times when the target density has many modes that are separated by regions of low probability. I will present an ensemble MCMC approach with interacting walkers designed to overcome this obstacle.
  In the second part of the talk, I consider the problem of computing the ground-state energy and wavefunction of a quantum many-body system, i.e., the lowest eigenpair of an exponentially high-dimensional Hermitian operator. I present a new optimization approach within the framework of variational Monte Carlo (VMC), in which the problem is solved by stochastic optimization over a parametric class of wavefunctions. Of particular interest are recently introduced neural-network-based parametrizations for which our approach yields state-of-the-art results. I will also discuss a new optimization approach for simultaneously computing the lowest several eigenpairs while avoiding intractable wavefunction orthogonality constraints.
  
  
• 4:00pm: Transport and beyond: efficient optimization over probability distributions
  Jason Altschuler, MIT
  
  The core of classical optimization focuses on the setting where decision variables are vectors in R^d. However, modern applications throughout machine learning, applied mathematics, and engineering demand high-dimensional optimization problems where decision variables are probability distributions. Can such optimization problems be solved efficiently? This talk presents two vignettes in this direction.
  
  The first vignette concerns entropic optimal transport and related problems including Min-Mean-Cycle and Matrix Preconditioning. We present approximation algorithms that are faster in both theory and practice, yielding near-linear runtimes in general, and even faster runtimes in commonly arising geometric settings. The second vignette concerns Wasserstein barycenters and more generally, multimarginal optimal transport problems. Despite considerable attention, even in dimension as low as 2, it remained unknown whether Wasserstein barycenters can be computed in polynomial time. We uncover the subtle dependence of the answer on the dimension: yes in fixed dimension and no in general. Taken together, these two vignettes illustrate the growing interface of optimization, probability, and efficient algorithms.