SIAM Student Chapter Seminar: Difference between revisions

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*'''When:''' Every Other Wednesday at 2:15 pm (except as otherwise indicated)
*'''When:''' Most Friday at 11:30 pm (see e-mail)
*'''Where:''' 901 Van Vleck Hall
*'''Where:''' 901 Van Vleck Hall
*'''Organizers:''' [http://www.math.wisc.edu/~ke/ Ke Chen]  
*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]  
*'''To join the SIAM Chapter mailing list:''' email [join-siam-chapter@lists.wisc.edu] website.
*'''To join the SIAM Chapter mailing list:''' email [join-siam-chapter@lists.wisc.edu] website.


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== Fall 2018 ==
== Fall 2019 ==


{| cellpadding="8"
{| cellpadding="8"
Line 18: Line 18:
!align="left" | title
!align="left" | title
|-
|-
| Sept. 12
| Sept. 27
|[http://www.math.wisc.edu/~ke/ Ke Chen] (Math)
|[http://www.math.wisc.edu/~xshen/ Xiao Shen] (Math)
|''[[#Sep 12: Ke Chen (Math)|Inverse Problem in Optical Tomography]]''
|''[[#Sep 27: Xiao Shen (Math)|The corner growth model]]''
|-
|-
| Spet. 26 
| Oct. 4    
|[http://www.math.wisc.edu/~kehlert/ Kurt Ehlert] (Math)
|
|''[[#Sept 26: Kurt Ehlert (Math)|  How to bet when gambling]]''
|
|-
| Oct. 10    
|[http://TBD Zachary Hansen] (Atmospheric and Oceanic Sciences)
|''[[#Oct 10: Zachary Hansen (Atmospheric and Oceanic Sciences)|  Land-Ocean contrast in lightning  ]]''
|-
| Oct. 24 
|[http://TBD Xuezhou Zhang] (Computer Science)
|''[[#Oct 24: Xuezhou Zhang (Computer Science)|  An Optimal Control Approach to Sequential Machine Teaching  ]]''
|-
| Nov. 7
|[http://TBD Cancelled]
|''[[#Nov 7: Cancelled|  ]]''
|-
| Nov. 21
|[http://TBD Cancelled due to Thanksgiving]
|''[[#Nov 21: Cancelled| ]]''
|-
|-
| Nov. 28
|[http://TBD Xiaowu Dai] (Statistics)
|''[[#Nov 28: Xiaowu Dai (Statistics)| Toward the Theoretical Understanding of Large-batch Training in Stochastic Gradient Descent  ]]''
|-
|
|}
|}




== Abstract ==
== Abstract ==


=== Sep 12: Ke Chen (Math) ===
=== Sep 27: Xiao Shen (Math) ===
Inverse Problem in Optical Tomography
The corner growth model
 
I will briefly talk about my researches on the inverse problems of radiative transfer equations, which is usually used as a model to describe the transport of neutrons or other particles in a certain media. Such inverse problems considers the following question: given the knowledge of multiple data collected at the boundary of the domain of interest, is it possible to reconstruct the optical property of the interior of media? In this talk, I will show you that stability of this problem is deteriorating as the Knudsen number is getter smaller. The talk will be introductory and anyone graduate is welcome to join us.
 
=== Sept 26: Kurt Ehlert (Math) ===
How to bet when gambling
 
When gambling, typically casinos have an edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.
 
=== Oct 10: Zachary Hansen (Atmospheric and Oceanic Sciences) ===
Land-Ocean contrast in lightning
 
Land surfaces have orders of magnitude more lightning flashes than ocean surfaces. One explanation for this difference is that land surfaces may generate greater convective available potential energy (CAPE), which fuels stronger thunderstorms. Using a high resolution cloud-resolving atmospheric model, we test whether an island can produce stronger thunderstorms just by having a land-like surface. We find that the island alters the distribution of rainfall but does not produce stronger storms. An equilibrium state known as boundary layer quasi-equilibrium follows, and is explored in more detail.
 
=== Oct 24: Xuezhou Zhang (Computer Science) ===
An Optimal Control Approach to Sequential Machine Teaching
 
Given a sequential learning algorithm and a target model, sequential machine teaching aims to find the shortest training sequence to drive the learning algorithm to the target model. We present the first principled way to find such shortest training sequences. Our key insight is to formulate sequential machine teaching as a time-optimal control problem. This allows us to solve sequential teaching by leveraging key theoretical and computational tools developed over the past 60 years in the optimal control community. Specifically, we study the Pontryagin Maximum Principle, which yields a necessary condition for opti- mality of a training sequence. We present analytic, structural, and numerical implica- tions of this approach on a case study with a least-squares loss function and gradient de- scent learner. We compute optimal train- ing sequences for this problem, and although the sequences seem circuitous, we find that they can vastly outperform the best available heuristics for generating training sequences.
 
=== Nov 7: Cancelled ===
 
=== Nov 21: Cancelled ===
 
=== Nov 28: Xiaowu Dai (Statistics) ===
Toward the Theoretical Understanding of Large-batch Training in Stochastic Gradient Descent
 
Stochastic gradient descent (SGD) is almost ubiquitously used for training nonconvex optimization tasks including deep neural networks. Recently, a hypothesis that "large batch SGD tends to converge to sharp minimizers of training function" has received increasing attention. We develop some new theory to give a justification of this hypothesis. In particular, we provide new properties of SGD in both finite-time and asymptotic regimes, with the tools from empirical processes and Partial Differential Equations. A connection between the stochasticity in SGD and the idea of smoothing splines in nonparametric statistics is also built. We include numerical experiments to corroborate these theoretical findings.


Imagine there is an arbitrary amount of donuts attached to the integer points of Z^2. The goal is to pick an optimal up-right path which allows you to eat as much donuts as possible along the way. We will look at some basic combinatorial observations, and how specific probability distribution would help us to study this model.


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Revision as of 18:32, 20 September 2019



  • When: Most Friday at 11:30 pm (see e-mail)
  • Where: 901 Van Vleck Hall
  • Organizers: Xiao Shen
  • To join the SIAM Chapter mailing list: email [join-siam-chapter@lists.wisc.edu] website.



Fall 2019

date speaker title
Sept. 27 Xiao Shen (Math) The corner growth model
Oct. 4


Abstract

Sep 27: Xiao Shen (Math)

The corner growth model

Imagine there is an arbitrary amount of donuts attached to the integer points of Z^2. The goal is to pick an optimal up-right path which allows you to eat as much donuts as possible along the way. We will look at some basic combinatorial observations, and how specific probability distribution would help us to study this model.


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