SIAM Student Chapter Seminar: Difference between revisions

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|Title
|Title
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|-
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|03/07
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|9th floor
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|Ang Li
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|Applying for postdocs and different industry jobs ... at the
same time
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|-
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|04/04
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|9th floor
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|Borong Zhang
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|Stochastic Multigrid Minimization for Ptychographic Phase Retrieval
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|-
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|04/11
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|903
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|Ian McPherson
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|Convergence Rates for Riemannian Proximal Bundle Methods
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|04/25
|903
|Weidong Ma
|A topic in kernel based independence testing
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==Abstracts==
==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==
==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

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