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Maxwell Institute Colloquium
Join us for a Maxwell Institute Colloquium on Thursday, December 1st, 2022 at 40 George Square, Lecture Theatre A.
Stéphane Mallat will present Multiscale Models of Deep Neural Networks from 14:00-15:30, with refreshments available from 13:30.
Stéphane Mallat was Professor at NYU in computer science, until 1994, then at Ecole Polytechnique in Paris and Department Chair. From 2001 to 2007 he was co-founder and CEO of a semiconductor start-up company. Since 2017, he holds the “Data Sciences” chair at the Collège de France. He is a member of the French Academy of sciences, of the Academy of Technologies, and a foreign member of the US National Academy of Engineering. Stéphane Mallat’s research interests include machine learning, signal processing and harmonic analysis. He developed the multiresolution wavelet theory and algorithms at the origin of the compression standard JPEG-2000, and sparse signal representations in dictionaries through matching pursuits. He currently works on mathematical models of deep neural networks for data analysis and physics.
Deep Neural Networks
Deep neural networks have spectacular applications but remain mostly a mathematical mystery. An outstanding issue is to understand how they circumvent the curse of dimensionality to generate or classify data. Inspired by the renormalization group in physics, we show that a key element is that data distributions can be factorized and renormalized into simpler conditional probabilities across scales. They often have local dependencies and can thus can be estimated with limited databases. This is first applied to generate turbulence and cosmological fields as well as structured images. We then derive classification architectures reaching the state of the art on complex image data bases such as ImageNet.
All are welcome!
Professor Thaleia Zariphopoulou is a Greek-American mathematician specializing in mathematical finance. She is the Presidential Chair in Mathematics and the Neuhaus Centennial Professor of Finance at the University of Texas at Austin. Zariphopoulou earned a B.S. in electrical engineering from the National Technical University of Athens in 1984. She then went to Brown University for graduate studies in applied mathematics and earned her master’s degree in 1985 and her Ph.D. degree in 1989 under the supervision of Wendell Fleming. She was an assistant professor at Worcester Polytechnic Institute and an associate professor at the University of Wisconsin-Madison, before she moved to the University of Texas at Austin in 1999. Thaleia was the first holder of the statutory Oxford-Man Chair in Quantitative Finance, Mathematical Institute, University of Oxford from 2009-2012. She became a fellow of the Society for Industrial and Applied Mathematics in 2012. Zariphopoulou was an invited speaker at the 2014 International Congress of Mathematicians in Seoul.
Human-machine interaction models and stochastic optimization
This talk will offer an introduction to human-machine interaction (HMI) models in asset allocation (e.g. robo-advising) and a discussion on the related modeling and mathematical challenges. Modeling difficulties stem from the limited ability to quantify the human’s risk preferences and describe their evolution, but also from the fact that the stochastic environment, in which the machine optimizes, adapts to real time incoming information that is exogeneous to the human. Furthermore, the human’s risk preferences/goals and the machine’s actions may evolve at different scales. This dynamic interaction creates an adaptive cooperative game with both asymmetric and incomplete information exchange between the two parties. As a result, challenging questions arise on, among others, how frequently the human and the machine should communicate, how much information can the machine accurately detect, infer and predict, how should the human’s (over)reaction to exogeneous events and realized performance be processed and tamed by the machine, and how the performance of the machine could be compared with the one of a human advisor. Such HMI models give rise to new, non-standard optimization problems that combine adaptive stochastic control, time-inconsistency, stochastic differential games, optimal stopping, multi-scale analysis, and learning.
The Maxwell Institute runs four series of Distinguished Lecture.
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