| Talk_id | Date | Speaker | Title |
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31529
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Thursday 1/12
2:30 PM
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Simon Foucart, Texas A&M University
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ZOOM TALK (Passcode: the smallest prime > 100 ): Three uses of semidefinite programming in approximation theory
- Simon Foucart, Texas A&M University
- ZOOM TALK (Passcode: the smallest prime > 100 ): Three uses of semidefinite programming in approximation theory
- 01/12/2023
- 2:30 PM - 3:30 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Mark A Iwen (iwenmark@msu.edu)
In this talk, modern optimization techniques are publicized as fitting computational tools to attack several extremal problems from Approximation Theory which had reached their limitations based on purely analytical approaches. Three such problems are showcased: the first problem---minimal projections---involves minimization over measures and exploits the moment method; the second problem---constrained approximation---involves minimization over polynomials and exploits the sum-of-squares method; and the third problem---optimal recovery from inaccurate observations---is highly relevant in Data Science and exploits the S-procedure. In each of these problems, one ends up having to solve semidefinite programs.
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31530
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Thursday 1/19
2:30 PM
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Madeleine Udell, Stanford University
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ZOOM TALK (Passcode: the smallest prime > 100 ): Low rank approximation for faster optimization
- Madeleine Udell, Stanford University
- ZOOM TALK (Passcode: the smallest prime > 100 ): Low rank approximation for faster optimization
- 01/19/2023
- 2:30 PM - 3:30 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Mark A Iwen ()
Low rank structure is pervasive in real-world datasets. This talk shows how to accelerate the solution of fundamental computational problems, including eigenvalue decomposition, linear system solves, composite convex optimization, and stochastic optimization (including deep learning), by exploiting this low rank structure. We present a simple method based on randomized numerical linear algebra for efficiently computing approximate top eigendecompositions, which can be used to replace large matrices (such as Hessians and constraint matrices) with low rank surrogates that are faster to apply and invert. The resulting solvers for linear systems (NystromPCG), composite convex optimization (NysADMM), and deep learning (SketchySGD) demonstrate strong theoretical and numerical support, outperforming state-of-the-art methods in terms of speed and robustness to hyperparameters.
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31553
|
Thursday 2/2
2:30 PM
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James Murphy, Tufts University
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ZOOM TALK (password the smallest prime > 100) - Towards Intrinsically Low-Dimensional Models in Wasserstein Space: Geometry, Statistics, and Learning
- James Murphy, Tufts University
- ZOOM TALK (password the smallest prime > 100) - Towards Intrinsically Low-Dimensional Models in Wasserstein Space: Geometry, Statistics, and Learning
- 02/02/2023
- 2:30 PM - 3:30 PM
- C304 Wells Hall
- Mark A Iwen ()
We consider the problems of efficient modeling and representation learning for probability distributions in Wasserstein space. We consider a general barycentric coding model in which data are represented as Wasserstein-2 (W2) barycenters of a set of fixed reference measures. Leveraging the Riemannian structure of W2-space, we develop a tractable optimization program to learn the barycentric coordinates when given access to the densities of the underlying measures. We provide a consistent statistical procedure for learning these coordinates when the measures are accessed only by i.i.d. samples. Our consistency results and algorithms exploit entropic regularization of the optimal transport problem, thereby allowing our barycentric modeling approach to scale efficiently. We also consider the problem of learning reference measures given observed data. Our regularized approach to dictionary learning in Wasserstein space addresses core problems of ill-posedness and in practice learns interpretable dictionary elements and coefficients useful for downstream tasks. Applications to image and natural language processing will be shown throughout the talk.
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29395
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Friday 2/24
4:00 PM
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Yuehaw Khoo, U Chicago
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TBA
- Yuehaw Khoo, U Chicago
- TBA
- 02/24/2023
- 4:00 PM - 5:00 PM
- C304 Wells Hall
- Mark A Iwen (iwenmark@msu.edu)
TBA
|
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31533
|
Friday 3/17
4:00 PM
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Terry Haut, Lawerence Livermore National Lab
|
TBA
- Terry Haut, Lawerence Livermore National Lab
- TBA
- 03/17/2023
- 4:00 PM - 5:00 PM
- C304 Wells Hall
- Mark A Iwen ()
TBA
|
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31534
|
Friday 4/21
4:00 PM
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Guosheng Fu, University of Notre Dame
|
High-order variational Lagrangian schemes for compressible fluids
- Guosheng Fu, University of Notre Dame
- High-order variational Lagrangian schemes for compressible fluids
- 04/21/2023
- 4:00 PM - 5:00 PM
- C304 Wells Hall
- Mark A Iwen ()
We present a class of high-order variational Lagrangian schemes for compressible fluids using the tool of energetic variational approach (EnVarA). This is the first time that the EnVarA framework has been applied to non isothermal models where temperature effects are non-negligible. We illustrate the main idea using the classical ideal gas model, and construct variational Lagrangian schemes that are conservative and entropy stable using EnVarA. Efficient implicit time stepping is designed so that the time step size is not restricted by the sound speed and the model is robust in the low Mach number case. Ample numerical examples will be presented to show the good performance of the proposed schemes for problems including strong shocks, low Mach number flows and multimaterial flows. This is a joint work with Prof. Chun Liu from IIT.
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31541
|
Friday 4/28
4:00 PM
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Yulong Xing, Ohio State University
|
TBA
- Yulong Xing, Ohio State University
- TBA
- 04/28/2023
- 4:00 PM - 5:00 PM
- C304 Wells Hall
- Mark A Iwen ()
TBA
|
