DOGSPOT @ UCSD

The DOGSPOT Seminar is a weekly meeting of graduate students who are working with advisor Alex Cloninger. The format of the seminar is a mix of working research talks and guest talks, to the latter of which any member of the UCSD Mathematics Department is invited.

In Winter 2024, the seminar is organized by Sawyer Robertson. We are meeting Fridays 11am-12pm in AP&M 5829.

Spring 2024 Schedule

• 4/5: Organizing Meeting

• 4/12: Alex Cloninger - Part paper, part something he wants to work on

• *4/18 @ 11:30AM - Keaton Hamm MINDS Seminar Talk

• 4/19: Speaker TBD

• 4/26: Speaker TBD

• 5/3: Sawyer Robertson - Research update

• *5/9: Xiuyuan Cheng - Virtual MINDS Seminar Talk

• 5/10: Nick Karris - TBD Substitute organizer

• 5/17: Dhruv Kohli - TBD 

• 5/24: Varun Khurana - Practice Defense Talk

• 5/31: Yiming Zhang - TBD

• 6/7: Speaker TBD

*Separate seminar, special talks

Winter 2024 Schedule

• 1/12: Organizing meeting

• 1/19: Sawyer Robertson Clustering on Graphs via Ricci Curvature

  • Ollivier-Ricci Curvature, Clustering, and 1-Wasserstein distance

  • https://arxiv.org/abs/2307.10155

• 1/26: Talk Cancelled due to travel

• 2/2: Varun Khurana - A Neural Network 2-Sample Test

• 2/9: Caroline Moosmueller via Zoom - Iterative slicing-and-matching schemes for measure transport

  • Transporting and estimating probability measures are fundamental tasks in various generative modeling methods like normalizing flows. An equally crucial aspect is having a suitable metric to gauge model performance and guide algorithm design, particularly for scalability. The focus of this talk lies on an iterative slicing-and-matching scheme for effective measure transport, initially introduced to transfer color statistics of images. We establish connections with a gradient descent scheme using the sliced-Wasserstein distance as loss function, which offers computationally efficient closed-form solutions, especially beneficial in high-dimensional scenarios. We will also discuss a convergence proof of this iterative scheme, justifying its use in data science applications. This talk is based on joint work with Shiying Li.

• 2/16: Nick Karris - Time Series on the Wasserstein Manifold

  • Describe an Euler-like scheme for projecting forward the evolution of measures on Wasserstein space, and hopefully talk a bit about the curvature of the Wasserstein manifold

• 2/23: Working/Social lunch

• 3/1: Dhruv Kohli - Analysis of Doubly Stochastic Scaling of Heat Kernel on Manifolds with Boundary

  • We’ll examine the results in [1] that describe the doubly stochastic scaling factors of the heat kernel on closed manifolds. Subsequently, we’ll utilize the asymptotic expansion of the heat kernel on manifolds with boundaries, as presented in [2], to characterize the scaling factors in this scenario.

  • [1] Landa, B., & Cheng, X. (2023). Robust inference of manifold density and geometry by doubly stochastic scaling. SIAM Journal on Mathematics of Data Science, 5(3), 589-614.

  • [2] Vaughn, R., Berry, T., & Antil, H. (2019). Diffusion maps for embedded manifolds with boundary with applications to pdes. arXiv preprint arXiv:1912.01391.

• 3/8: Yiming Zhang - Domain Adaptation and Optimal Transport - **LOCATED IN AP&M 2402** due to grad open house