Title: Theoretical advantages of deep neural networks

Abstract:

From statistical points of view, deep neural networks (DNN) are nothing but a (generalized) regression model, but DNNs have solved many problems no other methods have not succeeded in the past. In this talk, I will explain theoretical advantages of DNNs compared to other nonparametric regression models.

Title: Projection onto Minkowski Sums with Application to Constrained Learning

Abstract:

We introduce block descent algorithms for projecting onto Minkowski sums of sets. Projection onto such sets is a crucial step in many statistical learning problems, and may regularize complexity of solutions to an optimization problem or arise in dual formulations of penalty methods. We show that projecting onto the Minkowski sum admits simple, efficient algorithms when complications such as overlapping constraints pose challenges to existing methods. We prove that our algorithm converges linearly when sets are strongly convex or satisfy an error bound condition, and extend the theory and methods to encompass non-convex sets as well. We demonstrate empirical advantages in runtime and accuracy over competitors in applications to ℓ1,p-regularized learning, constrained lasso, and overlapping group lasso.

References:

1. Joong-Ho Won, Jason Xu, Kenneth Lange; Proceedings of the 36th International Conference on Machine Learning, PMLR 97:3642-3651, 2019.

Title: 데이터의 프라이버시를 보존하는 기계학습 (Safe Machine Learning toward Private AI)

Abstract:

기계학습(Machine Learning)은 데이터로부터 이를 도출한 함수를 유추하는 과정으로 최근 다양한 분야에서 흥미로운 응용들이 제시되고 있다. 기계학습이 좋은 성과를 거두려면 데이터의 확보가 필수적인데 개인 프라이버시 문제 혹은 데이터 주권의 문제로 인해 좋은 데이터를 확보하는 것이 쉽지 않은 일이다. 동형암호는 암호화한 데이터상에서 복호화없이 기계학습의 훈련단계(Training)나 예측단계(Inference)를 수행할 수 있도록 하며, 이를 통해 데이터의 프라이버시 문제를 극복하고 Private AI의 시대를 열어가고 있다. 본 강연에서는 이 분야의 최근 결과들로 동형 회귀분석(Homomorphic Logistric Regression), 동형 심층신경망(Homomorphic Deep Neural Network), 동형 의사결정나무(Homomorphic Decision Tree)등의 결과와 이의 신용정보, 의료, 마케팅 등에의 응용을 소개하도록 한다.

Title: Quantum AI, Quantum Machine Learning

Abstract:

Recent development in quantum technology together with advances in quantum algorithms impacts the field of quantum AI and machine learning. Many quantum machine learning algorithms and their applications to AI are being appeared. We present some of these and also our work in the field.

Title: Harmonic Data Analysis for Shape and Centrality

Abstract:

Harmonic data analysis aims to provide topological and combinatorial summaries of data sets by representing them as simplicial complexes. Topological data analysis, which we shall review briefly, initiated a topological approach and introduced shape of data as a new data scientific feature. Recently, the need for simplicial complexes for data analysis arose again due to the emergence of simplicial networks for modeling higher order relations among data points, which requires both topological insight and combinatorial precision. In this talk, we will present methods from topological combinatorics for refining data shape via harmonic cycles and computing network centrality via simplicial effective conductance. Applications to medicine and social networks will be presented. We will also describe recent experiments in machine learning incorporating mathematical data summary.