Events

50.047 Mobile Robotics Course – Autonomous Race Car Challenge

In this talk, we will be interested in inverse problems arising in the signal and image processing field. Solving such problems imply in a fist time to formalise the direct problem by understanding the physics behind and in a second time, to solve the associated inverse problem, through a variational formulation, that is, solving an optimization problem. Classical optimization-based approaches consist in, once the optimization problem has been formulated, proposing iterative procedures converging to a solution of the considered inverse problem. More recently, unrolled neural networks have been proposed. They combine optimization and learning, constitute interpretable networks and integrate information about the direct model. We will study and describe such networks for the resolution of two inverse problems: image deconvolution and robust PCA.

In physical experiments, the response of a process or system can be affected by three categories of variables: experimental variables or factors to be investigated, observable variables assumed to be fixed, and lurking variables that are unknown or unmeasurable. The experimental variables are often assumed to be independent of other variables with “constant values”. This talk shows the violation of this assumption in a 3D printing experiment and proposes to infer and control the effects of lurking variables through an effect equivalence approach.

The Laboratory for Air Transportation, Infrastructure, and Connected Environments (LATTICE), situated in the Department of Aerospace Engineering at the University of Michigan, Ann Arbor, is focused on identifying and addressing research problems that contribute towards a safer, more efficient, more resilient, as well as user- and equity-oriented air transportation system and other societal-scale infrastructures. In this presentation, I will cover some ongoing and recently completed projects at LATTICE, spanning methods such as stochastic/robust optimization, bandit (exploration/exploitation) strategies, combinatorial programs (e.g., facility location problems, vehicle routing problems), reinforcement learning, and probabilistic privacy, applied to a variety of settings ranging from air traffic management, UAS traffic management, and space systems/infrastructures. The overarching goal of my presentation is to solicit feedback and spur discussions, potentially leading to new and exciting interdisciplinary and international collaborations.

Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE), Song et al. (2021) demonstrate how the time inhomogeneous drift of the associated reverse-time SDE may be estimated using score-matching. A limitation of this approach is that the forward-time SDE must be run for a sufficiently long time for the final distribution to be approximately Gaussian. In contrast, solving the Schrödinger Bridge problem (SB), i.e. an entropy-regularized optimal transport problem on path spaces, yields diffusions which generate samples from the data distribution in finite time. We present Diffusion SB (DSB), an original approximation of the Iterative Proportional Fitting (IPF) procedure to solve the SB problem, and provide theoretical analysis along with generative modeling experiments. The first DSB iteration recovers the methodology proposed by Song et al. (2021), with the flexibility of using shorter time intervals, as subsequent DSB iterations reduce the discrepancy between the final-time marginal of the forward (resp. backward) SDE with respect to the prior (resp. data) distribution. Beyond generative modeling, DSB offers a widely applicable computational optimal transport tool as the continuous state-space analogue of the popular Sinkhorn algorithm (Cuturi, 2013).

According to a UN report from 2022, time is running out to limit temperature rises to 1.5C by 2050. Around $3.5 trillion climate investment per year is needed to build the net zero economy by 2050. This investment is possible only with significant contribution from the private financial sector. This is specifically the case in emerging markets, where public investments aren’t growing as quickly as needed to meet climate targets. There are a quite a few issues related to data disclosures, transparency and complexities, which needs to be tackled in order to efficiently manage the private sustainable investment need. Data Science and Innovation can help tackle these issues and assist the community is making quick and accurate investment decisions.

Data is now unanimously considered a key firm asset for enabling better operational decisions. However, data-driven decisions can inadvertently expose private data, leaving firms vulnerable to unforeseen danger. How to manage data security risks by protecting data from being inferred from observable decisions thus becomes an important question. In this paper, we focus on data security in supply chains due to their data-intensive nature. Specifically, we examine a data-driven contextual newsvendor problem. To quantify and ensure data security, we adopt the notion of differential privacy, a mathematically rigorous measure of data security that limits an attacker’s inference accuracy. Employing convolution smoothing and noise injection, we propose several differentially private algorithms that provably guarantee both data security and asymptotic optimality with (near) optimal rates. In the non-asymptotic regime, we further identify three drivers of the cost of data security; namely, dataset size, context, and number of products. This finding suggests that gathering more data, collecting detailed context, and pooling data from multiple products can lower data security cost. Lastly, we examine the impact of a newsvendor’s private algorithms on supply chain partners. We discover additional distortion to the demand signaling process and lower profit share for an upstream supplier.

Assessing license applications submitted by Financial Institutions can be a long and manual process with stringent requirements to be met to ensure Singapore remains a secure and stable financial hub. How might we enable a smooth and comprehensive process for Financial Institutions to transact with Monetary Authority of Singapore so that applications can be processed more efficiently? With the launch of eLicensing application, the application process has now become more streamlined with automated processes and built-in validations for forms.

It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos, to maximize the information processing power. Investigating the same hypothesis on the ‘artificial’ brains, i.e. the modern computer vision models, we find that they exhibits the same pattern, i.e. highest test accuracy or lowest test loss at the edge of chaos. A theoretical investigation demonstrates that, the best performance is attributed to the maximal metastable states/periodic cycle length near the edge of chaos, where each metastable state can represent an information point. Applied on a very simple network equivalent of the SK spin glass model and Fashion MNIST dataset, we illustrate a simple and principled training method that can achieve both high accuracy and prevent fitting noisy labels automatically.

Vincent Leon (University of Illinois at Urbana-Champaign) – Limited-Trust in Diffusion of Competing Alternatives Over Social Networks & Apurv Shukla (Texas A&M University) – Differentially Private Online Resource Allocation