## Gabriel Peyré (CNRS and Ecole Normale Supérieure) 2021/11/10 14:00–15:00

### Scaling Optimal Transport for High dimensional Learning [スライド]

Optimal transport (OT) has recently gained lot of interest in machine learning. It is a natural tool to compare in a geometrically faithful way probability distributions. It finds applications in both supervised learning (using geometric loss functions) and unsupervised learning (to perform generative model fitting). OT is however plagued by the curse of dimensionality, since it might require a number of samples which grows exponentially with the dimension. In this talk, I will explain how to leverage entropic regularization methods to define computationally efficient loss functions, approximating OT with a better sample complexity. More information and references can be found on the website of our book “Computational Optimal Transport” https://optimaltransport.github.io/

## Samory Kpotufe (Columbia University) 2021/11/11 13:00–14:00

### Some Recent Insights on Transfer and Multitask Learning [スライド]

A common situation in Machine Learning is one where training data is not fully representative of a target population due to bias in the sampling mechanism or due to prohibitive target sampling costs. In such situations, we aim to ‘transfer’ relevant information from the training data (a.k.a. source data) to the target application. How much information is in the source data about the target application? Would some amount of target data improve transfer? These are all practical questions that depend crucially on ‘how far’ the source domain is from the target. However, how to properly measure ‘distance’ between source and target domains remains largely unclear.

In this talk we will argue that much of the traditional notions of ‘distance’ (e.g. KL-divergence, extensions of TV such as D_A discrepancy, density-ratios, Wasserstein distance) can yield an over-pessimistic picture of transferability. Instead, we show that some new notions of ‘relative dimension’ between source and target (which we simply term ‘transfer-exponents’) capture a continuum from easy to hard transfer. Transfer-exponents uncover a rich set of situations where transfer is possible even at fast rates; they encode relative benefits of source and target samples, and have interesting implications for related problems such as ‘multi-task or multi-source learning’.

In particular, in the case of transfer from multiple sources, we will discuss (if time permits) a strange phenomena: no procedure can achieve a rate better than that of having a single data source, even in seemingly mild situations where multiple sources are informative about the target.

The talk is based on earlier work with Guillaume Martinet, and ongoing work with Steve Hanneke.

## 西浦 博（京大）2021/11/11 11:00-12:00

### COVID-19の疫学モデル

新型コロナウイルス感染症の疫学動態の把握において、世界中で数理モデルが利用される機会が爆発的に増加した。予防接種が人口内に入るまでの間は非特異的対策として人口全体の接触やハイリスクな接触を避ける対策が実施されてきたが、その設計のためにリアルタイム分析が頻用されるようになった。その過程においては様々な予測分析やリスクの濃淡に関する異質性の分析が実施されている。本講演では，その目的や技術的問題点、今後の課題などについて整理してご紹介する。