SIAM Student Chapter Seminar: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
VisualWikitext
No edit summary
 
(12 intermediate revisions by 3 users not shown)
Line 1: Line 1:
__NOTOC__
__NOTOC__


*'''When:''' Fridays at 1 PM unless noted otherwise
*'''When:''' Fridays at 1:30 PM unless noted otherwise
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Organizers:''' Yahui Qu, Peiyi Chen and Zaidan Wu
*'''Organizers:''' Yahui Qu, Peiyi Chen and Zaidan Wu
Line 18: Line 18:
|Title
|Title
|-
|-
|
|03/07
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|}
 
 
== Fall 2024 ==
 
{| class="wikitable"
|+
!Date
!Location
!Speaker
!Title
|-
|10 AM 10/4
|Birge 346
|Federica Ferrarese (University of Ferrara, Italy)
|Control plasma instabilities via an external magnetic field: deterministic and uncertain approaches
|-
|11 AM 10/18
|9th floor
|Martin Guerra (UW-Madison)
|Swarm-Based Gradient Descent Meets Simulated Annealing
|-
|12:30 PM 10/31
|VV 901
|Chuanqi Zhang (University of Technology Sydney)
|Faster isomorphism testing of p-groups of Frattini class-2
|-
|11/8
|9th floor
|9th floor
|Borong Zhang (UW-Madison)
|Ang Li
|Solving the Inverse Scattering Problem: Leveraging Symmetries for Machine Learning
|Applying for postdocs and different industry jobs ... at the
same time
|-
|-
|11/15
|04/04
|9th floor
|9th floor
(zoom)
|Borong Zhang
|Yantao Wu (Johns Hopkins University)
|Stochastic Multigrid Minimization for Ptychographic Phase Retrieval
|Conditional Regression on Nonlinear Variable Model
|-
|
|
|
|
|-
|-
|
|04/11
|
|903
|
|Ian McPherson
|
|Convergence Rates for Riemannian Proximal Bundle Methods
|-
|-
|
|04/25
|
|903
|
|Weidong Ma
|
|A topic in kernel based independence testing
|}
|}


==Abstracts==
==Abstracts==
'''October 4th, Federica Ferrarese (University of Ferrara, Italy)''': The study of the problem of plasma confinement in huge devices, such as for example Tokamaks and Stellarators, has attracted a lot of attention in recent years. Strong magnetic fields in these systems can lead to instabilities, resulting in vortex formation. Due to the extremely high temperatures in plasma fusion, physical materials cannot be used for confinement, necessitating the use of external magnetic fields to control plasma density. This approach involves studying the evolution of plasma, made up of numerous particles, using the Vlasov-Poisson equations. In the first part of the talk, the case without uncertainty is explored. Particle dynamics are simulated using the Particle-in-Cell (PIC) method, known for its ability to capture kinetic effects and self-consistent interactions. The goal is to derive an instantaneous feedback control that forces the plasma density to achieve a desired distribution. Various numerical experiments are presented to validate the results. In the second part, uncertainty is introduced into the system, leading to the development of a different control strategy. This method is designed to steer the plasma towards a desired configuration even in the presence of uncertainty. The presentation concludes with a comparison of the two control strategies, supported by various numerical experiments.


'''October 18th, Martin Guerra (UW-Madison)''': In generic non-convex optimization, one needs to be able to pull samples out of local optimal points to achieve global optimization. Two common strategies are deployed: adding stochasticity to samples such as Brownian motion, as is done in simulated annealing (SA), and employing a swarm of samples to explore the whole landscape, as is done in Swarm-Based Gradient Descent (SBGD). The two strategies have severe drawbacks but complement each other on their strengths. SA fails in the accuracy sense, i.e., finding the exact optimal point, but succeeds in always being able to get close, while SBGD fails in the probability sense, i.e., it has non-trivial probability to fail, but if succeeds, can find the exact optimal point. We propose to combine the strength of the two and develop a swarm-based stochastic gradient method with samples automatically adjusting their annealing. Using mean-field analysis and long-time behavior PDE tools, we can prove the method to succeed in both the accuracy sense and the probability sense. Numerical examples verify these theoretical findings.
'''March 7th, Ang Li (UW-Madison)''': I will share my experience with postdoc and industry job applications. This talk might be helpful for those who haven’t decided between academia and industry or are considering different paths within industry since I made my own decision quite late.
 
'''April 4th, Borong Zhang (UW-Madison)''': In this talk, we introduce a novel stochastic multigrid minimization method designed for ptychographic phase retrieval. By reformulating the inverse problem as the iterative minimization of a quadratic surrogate that majorizes the original objective function, our approach unifies a range of iterative algorithms, including first-order methods and the well-known Ptychographic Iterative Engine (PIE). By efficiently solving the surrogate problem using a multigrid method, our method delivers significant improvements in both convergence speed and reconstruction quality compared to conventional PIE techniques.
 
'''April 11th, Ian McPherson (Johns-Hopkins):''' Nonsmooth convex optimization is a classically studied regime with a plethora of different optimization algorithms being developed in order to solve them. Of these methods, proximal bundle methods have been created and used within the Euclidean setting for decades - attempting to mimic the dynamics of the proximal point method. While practitioners have enjoyed very robust convergence results with respect to choice of parameters, it was not until the late 2020s that we have had theoretical results giving non-asymptotic guarantees - recovering optimal convergence rates. Within the past few years, the first Riemannian Proximal Bundle Methods have been proposed, again lacking non-asymptotic guarantees. Within this talk, we discuss how we are able to both generalize proposed methods and lift the non-asymptotic rates to the Riemannian setting. Moreover, we will do so without access to exponential maps or parallel transports. In addition, to our knowledge these are the first theoretical guarantees for non-smooth geodesically convex optimization in the Riemannian setting, without access to either exponential maps and parallel transports. The work presented is joint work with Mateo Diaz and Benjamin Grimmer.


'''October 31st, Chuanqi Zhang''' (University of Technology Sydney): The finite group isomorphism problem asks to decide whether two finite groups of order N are isomorphic. Improving the classical $N^{O(\log N)}$-time algorithm for group isomorphism is a long-standing open problem. It is generally regarded that p-groups of class 2 and exponent p form a bottleneck case for group isomorphism in general. The recent breakthrough by Sun (STOC '23) presents an $N^{O((\log N)^{5/6})}$-time algorithm for this group class. Our work sharpens the key technical ingredients in Sun's algorithm and further improves Sun's result by presenting an $N^{\tilde O((\log N)^{1/2})}$-time algorithm for this group class. Besides, we also extend the result to the more general p-groups of Frattini class-2, which includes non-abelian 2-groups. In this talk, I will present the problem background and our main algorithm in detail, and introduce some connections with other research topics. For example, one intriguing connection is with the maximal and non-commutative ranks of matrix spaces, which have recently received considerable attention in algebraic complexity and computational invariant theory. Results from the theory of Tensor Isomorphism complexity class (Grochow--Qiao, SIAM J. Comput. '23) are utilized to simplify the algorithm and achieve the extension to p-groups of Frattini class-2.  
'''April 25th, Weidong Ma (Univeristy of Pennsylvania)''': Testing the independence of random vectors is a fundamental problem across many scientific disciplines. In this talk, I will first introduce several widely used methods for independence testing, including distance covariance (DC), the Hilbert-Schmidt Independence Criterion (HSIC), and their applications. Most of these methods lack tractable asymptotic distributions under the null hypothesis (i.e., independence), making their use rely on computationally intensive procedures such as permutation tests or bootstrap methods.


'''November 8th, Borong Zhang''' (UW-Madison): The inverse scattering problem—reconstructing the properties of an unknown medium by probing it with waves and measuring the medium's response at the boundary—is fundamental in physics and engineering. This talk will focus on how leveraging the symmetries inherent in this problem can significantly enhance machine learning methods for its solution. By incorporating these symmetries into both deterministic neural network architectures and probabilistic frameworks like diffusion models, we achieve more accurate and computationally efficient reconstructions. This symmetry-driven approach reduces the complexity of the models and improves their performance, illustrating how physical principles can inform and strengthen machine learning techniques. Applications demonstrating these benefits will be briefly discussed.  
To address this, I will present our recent work aimed at reducing the computational cost of independence testing.  We propose a modified HSIC test, termed HSICskb, which incorporates a bandwidth adjustment where one kernel’s bandwidth shrinks to zero as the sample size grows. We establish a Gaussian approximation result for our test statistic, which allows us to compute the p-value efficiently.


'''November 15th, Yantao Wu''' (Johns Hopkins): We consider the problem of estimating the intrinsic structure of composite functions of the type $\mathbb{E} [Y|X] = f(\Pi_\gamma X) $ where $\Pi_\gamma:\mathbb{R}^d\to\mathbb{R}^1$ is the closest point projection operator onto some unknown smooth curve $\gamma: [0, L]\to \mathbb{R}^d$ and  $f: \mathbb{R}^1\to \mathbb{R}^1$ is some unknown  {\it link} function. This model is the generalization of the single-index model where $\mathbb{E}[Y|X]=f(\langle v, X\rangle)$ for some unknown {\it index} vector $v\in\mathbb{S}^{d-1}$. On the other hand, this model is a particular case of function composition model where $\mathbb{E}[Y|X] = f(g(x))$ for some unknown multivariate function $g:\mathbb{R}^d\to\mathbb{R}$. In this paper, we propose an algorithm based on conditional regression and show that under some assumptions restricting the complexity of curve $\gamma$, our algorithm can achieve the one-dimensional optimal minimax rate, plus a curve approximation error bounded by $\mathcal{O}(\sigma_\zeta^2)$. We also perform numerical tests to verify that our algorithm is robust, in the sense that even without some assumptions, the mean squared error can still achieve $\mathcal{O}(\sigma_\zeta^2)$.  
To assess statistical efficiency, we also conduct a local power analysis of the standard bootstrap-based HSIC test—an independently interesting contribution—and compare it with our HSICskb test. Finally, I will demonstrate the application of our method to real data, exploring the relationship between age and personal traits.


==Past Semesters==
==Past Semesters==

Latest revision as of 04:41, 21 April 2025


Spring 2025

Date Location Speaker Title
03/07 9th floor Ang Li Applying for postdocs and different industry jobs ... at the

same time

04/04 9th floor Borong Zhang Stochastic Multigrid Minimization for Ptychographic Phase Retrieval
04/11 903 Ian McPherson Convergence Rates for Riemannian Proximal Bundle Methods
04/25 903 Weidong Ma A topic in kernel based independence testing


Abstracts

March 7th, Ang Li (UW-Madison): I will share my experience with postdoc and industry job applications. This talk might be helpful for those who haven’t decided between academia and industry or are considering different paths within industry since I made my own decision quite late.

April 4th, Borong Zhang (UW-Madison): In this talk, we introduce a novel stochastic multigrid minimization method designed for ptychographic phase retrieval. By reformulating the inverse problem as the iterative minimization of a quadratic surrogate that majorizes the original objective function, our approach unifies a range of iterative algorithms, including first-order methods and the well-known Ptychographic Iterative Engine (PIE). By efficiently solving the surrogate problem using a multigrid method, our method delivers significant improvements in both convergence speed and reconstruction quality compared to conventional PIE techniques.

April 11th, Ian McPherson (Johns-Hopkins): Nonsmooth convex optimization is a classically studied regime with a plethora of different optimization algorithms being developed in order to solve them. Of these methods, proximal bundle methods have been created and used within the Euclidean setting for decades - attempting to mimic the dynamics of the proximal point method. While practitioners have enjoyed very robust convergence results with respect to choice of parameters, it was not until the late 2020s that we have had theoretical results giving non-asymptotic guarantees - recovering optimal convergence rates. Within the past few years, the first Riemannian Proximal Bundle Methods have been proposed, again lacking non-asymptotic guarantees. Within this talk, we discuss how we are able to both generalize proposed methods and lift the non-asymptotic rates to the Riemannian setting. Moreover, we will do so without access to exponential maps or parallel transports. In addition, to our knowledge these are the first theoretical guarantees for non-smooth geodesically convex optimization in the Riemannian setting, without access to either exponential maps and parallel transports. The work presented is joint work with Mateo Diaz and Benjamin Grimmer.

April 25th, Weidong Ma (Univeristy of Pennsylvania): Testing the independence of random vectors is a fundamental problem across many scientific disciplines. In this talk, I will first introduce several widely used methods for independence testing, including distance covariance (DC), the Hilbert-Schmidt Independence Criterion (HSIC), and their applications. Most of these methods lack tractable asymptotic distributions under the null hypothesis (i.e., independence), making their use rely on computationally intensive procedures such as permutation tests or bootstrap methods.

To address this, I will present our recent work aimed at reducing the computational cost of independence testing. We propose a modified HSIC test, termed HSICskb, which incorporates a bandwidth adjustment where one kernel’s bandwidth shrinks to zero as the sample size grows. We establish a Gaussian approximation result for our test statistic, which allows us to compute the p-value efficiently.

To assess statistical efficiency, we also conduct a local power analysis of the standard bootstrap-based HSIC test—an independently interesting contribution—and compare it with our HSICskb test. Finally, I will demonstrate the application of our method to real data, exploring the relationship between age and personal traits.

Past Semesters

Retrieved from "https://wiki.math.wisc.edu/index.php?title=SIAM_Student_Chapter_Seminar&oldid=28458"