### TBA by Adrien Saumard

- Series
- Stochastics Seminar
- Time
- Thursday, April 6, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Adrien Saumard – ENSAI and CREST – adrien.saumard@ensai.fr

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- Series
- Stochastics Seminar
- Time
- Thursday, April 6, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Adrien Saumard – ENSAI and CREST – adrien.saumard@ensai.fr

- Series
- Stochastics Seminar
- Time
- Thursday, March 30, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Philippe Rigollet – Massachusetts Institute of Technology

- Series
- Stochastics Seminar
- Time
- Thursday, March 2, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Wasiur R. KhudaBukhsh – University of Nottingham – wasiur.khudabukhsh@nottingham.ac.uk

- Series
- Stochastics Seminar
- Time
- Thursday, November 17, 2022 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Ming Yuan – Columbia University

Independent component analysis is a useful and general data analysis tool. It has found great successes in many applications. But in recent years, it has been observed that many popular approaches to ICA do not scale well with the number of components. This debacle has inspired a growing number of new proposals. But it remains unclear what the exact role of the number of components is on the information theoretical limits and computational complexity for ICA. Here I will describe our recent work to specifically address these questions and introduce a refined method of moments that is both computationally tractable and statistically optimal.

- Series
- Stochastics Seminar
- Time
- Thursday, November 10, 2022 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Ionel Popescu – University of Bucharest and Simion Stoilow Institute of Mathematics – ioionel@gmail.com

Zoom link to the seminar: https://gatech.zoom.us/j/91330848866

I will show how to construct a numerical scheme for solutions to linear Dirichlet-Poisson boundary problems which does not suffer of the curse of dimensionality. In fact we show that as the dimension increases, the complexity of this scheme increases only (low degree) polynomially with the dimension. The key is a subtle use of walk on spheres combined with a concentration inequality. As a byproduct we show that this result has a simple consequence in terms of neural networks for the approximation of the solution. This is joint work with Iulian Cimpean, Arghir Zarnescu, Lucian Beznea and Oana Lupascu.

- Series
- Stochastics Seminar
- Time
- Thursday, November 3, 2022 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Daesung Kim – Georgia Tech

We consider a random walk on the $d\ge 3$ dimensional discrete torus starting from vertices chosen independently and uniformly at random. In this talk, we discuss the fluctuation behavior of the size of the range of the random walk trajectories at a time proportional to the size of the torus. The proof relies on a refined analysis of tail estimates for hitting time. We also discuss related results and open problems. This is based on joint work with Partha Dey.

- Series
- Stochastics Seminar
- Time
- Thursday, October 27, 2022 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Matthew Junge – Baruch College, CUNY – Matthew.Junge@baruch.cuny.edu

In the late 20th century, statistical physicists introduced a chemical reaction model called ballistic annihilation. In it, particles are placed randomly throughout the real line and then proceed to move at independently sampled velocities. Collisions result in mutual annihilation. Many results were inferred by physicists, but it wasn’t until recently that mathematicians joined in. I will describe my trajectory through this model. Expect tantalizing open questions.

- Series
- Stochastics Seminar
- Time
- Thursday, October 20, 2022 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Anru Zhang – Duke University – anru.zhang@duke.edu

The analysis of tensor data, i.e., arrays with multiple directions, has become an active research topic in the era of big data. Datasets in the form of tensors arise from a wide range of scientific applications. Tensor methods also provide unique perspectives to many high-dimensional problems, where the observations are not necessarily tensors. Problems in high-dimensional tensors generally possess distinct characteristics that pose great challenges to the data science community.

In this talk, we discuss several recent advances in statistical tensor learning and their applications in computational imaging, social network, and generative model. We also illustrate how we develop statistically optimal methods and computationally efficient algorithms that interact with the modern theories of computation, high-dimensional statistics, and non-convex optimization.

- Series
- Stochastics Seminar
- Time
- Friday, October 14, 2022 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Dmitrii M. Ostrovskii – University of Southern California

In the problem of online portfolio selection as formulated by Cover (1991), the trader repeatedly distributes her capital over $ d $ assets in each of $ T > 1 $ rounds, with the goal of maximizing the total return. Cover proposed an algorithm called Universal Portfolios, that performs nearly as well as the best (in hindsight) static assignment of a portfolio, with

an $ O(d\log(T)) $ regret in terms of the logarithmic return. Without imposing any restrictions on the market, this guarantee is known to be worst-case optimal, and no other algorithm attaining it has been discovered so far. Unfortunately, Cover's algorithm crucially relies on computing the expectation over certain log-concave density in R^d, so in a practical implementation this expectation has to be approximated via sampling, which is computationally challenging. In particular, the fastest known implementation, proposed by Kalai and Vempala in 2002, runs in $ O( d^4 (T+d)^{14} ) $ per round, which rules out any practical application scenario. Proposing a practical algorithm with a near-optimal regret is a long-standing open problem. We propose an algorithm for online portfolio selection with a near-optimal regret guarantee of $ O( d \log(T+d) ) $ and the runtime of only $ O( d^2 (T+d) ) $ per round. In a nutshell, our algorithm is a variant of the follow-the-regularized-leader scheme, with a time-dependent regularizer given by the volumetric barrier for the sum of observed losses. Thus, our result gives a fresh perspective on the concept of volumetric barrier, initially proposed in the context of cutting-plane methods and interior-point methods, correspondingly by Vaidya (1989) and Nesterov and Nemirovski (1994). Our side contribution, of independent interest, is deriving the volumetrically regularized portfolio as a variational approximation of the universal portfolio: namely, we show that it minimizes Gibbs's free energy functional, with accuracy of order $ O( d \log(T+d) ) $. This is a joint work with Remi Jezequel and Pierre Gaillard.

- Series
- Stochastics Seminar
- Time
- Thursday, October 6, 2022 - 15:30 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/86578123009
- Speaker
- Dan Mikulincer – MIT – Danmiku@gmail.com

**Please Note:** Recording: https://us02web.zoom.us/rec/share/cIdTfvS0tjar04MWv9ltWrVxAcmsUSFvDznprSBT285wc0VzURfB3X8jR0CpWIWQ.Sz557oNX3k5L1cpN

We revisit the notion of noise stability in the hypercube and show how one can replace the usual heat semigroup with more general stochastic processes. We will then introduce a re-normalized Brownian motion, embedding the discrete hypercube into the Wiener space, and analyze the noise stability along its paths. Our approach leads to a new quantitative form of the 'Majority is Stablest' theorem from Boolean analysis and to progress on the 'most informative bit' conjecture of Kumar and Courtade.

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