2022-02-09

Interpolating between Optimal Transport and MMD using Sinkhorn Divergences

Reading notes on Interpolating between Optimal Transport and MMD using Sinkhorn Divergences

The purpose of this paper is to show that the Sinkhorn divergences are convex, smooth, positive definite loss functions that metrize the convergence in law.

Countless methods in machine learning and image processing reley on comparisons betwen probability distributions. But simple dissimilarities such as the Total Variation norm or the Kullback-Leibler relative entropy do not take into account the distance d on the feature space $\chi$ . As a result, they do not metrize the convergence in law and are unstable with respect to deformations of the distributions’ support. Optimal Transport distances (sometimes refeered as Earth Mover’s Distance) and Maximum Mean Discrepancies are continuous with respect to convergence in law and metrize its topology when feature space $\chi$ is compact.

2022-01-21

Life

英国留学-疫情下的期末考试

大噶好，sao年回来啦，上周五刚结束期末考试，迫不及待地想写点东西，上篇的总结中，给自己立了几个flag，我也打算通过一系列的文章来记录我这一年的英国留学之路，希望能给后来者一些借鉴。由于期末考刚结束，趁热打铁，所以这篇文章就讲讲英国疫情下的考试吧。

2021-12-19

Algorithm

Caeser's cipher and Diffie-Hallman key exchange

In my IoT class, one of my coursework is to implement a Diffie-Hallman key exchange algorithm which is used to exchange data without leaking safty information in the network communications. In my experiment, some communications take place between a client and a server, the transmitted data have been encrypted and decrypt with Caeser’s cipher when sent to the server from client after the connection is built. So my task is just to add Diffie-Hallman key exchange to secure a message delivery. In this article, I’ll introduce two algorithms, Caeser’s cipher or shift cipher^[1] and Diffie-Hallman key exchange.