Speaker
Description
In this presentation, I will begin by introducing shuffled regression and the entropic optimal transport (EOT) as one possible tool for solving shuffled regression. A common approach for this optimization is to use a first-order optimizer, which requires the gradient of the OT distance. For faster convergence, one might also resort to a second-order optimizer, which additionally requires the Hessian. I will present the analytical derivatives of EOT, provide a brief overview of numerical condition numbers, and explain how to compute a crucial linear system robustly. Through analytical derivation and spectral analysis, we identify the numerical instability caused by the singularity and ill-posedness of a key linear system, prove the asymptotic limits of its condition number when both sample size $N$ goes to infinity and regularization strength $\varepsilon$ goes to 0, and improve the efficiency and robustness of computation. Finally, I would like to discuss future work as well as extensions.