・はじめに統計学の歴史では、頻度主義とベイズ主義という異なる立場の方法が存在し、違いに論争を繰り広げてきました。しかし、近年の統計学者の中には「現代の統計学は…

深層学習の数理：カーネル法, スパース推定との接点 - Download as a PDF or view online for free

大阪公立大学大学院理学研究科FD研修会 「人工知能と数学」2024年2月15日https://www.omu.ac.jp/orp/ocami/activities/fd/list/講演者：鈴木 大慈 氏（東京大学大学院情報理工学系研究科・准教授）講演タイトル：機械学習の数学講演アブストラクト：機械学習は現在，Ch...

Deep learning has shown high performances in various types of tasks from visual recognition to natural language processing, which indicates superior flexibility and adaptivity of deep learning. To...

深層学習の数理 - Download as a PDF or view online for free

Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this...

数学は、二千年以上の長い歴��を有し、現在もなお活発な研究がなされ、急速な発展を続けている分野である。数や図形の深い性質、関数や空間の構造が次々に明らかにされており、約350年間懸案だったフェルマー予想の解決や、約100年間未解決だったポアンカレ予想が解かれる等、最近の数学の進展には目を見張るものがある。また、数学は思考の自由さと汎用性の広さが特徴の分野で、諸科学の共通言語として、理学、工学、...

Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and...

We introduce Particle-SDCA, a gradient-based optimization algorithm for two-layer neural networks in the mean field regime that achieves exponential convergence rate in regularized empirical risk...

We relate the asymptotic behavior of graph neural networks to the graph spectra of underlying graphs and gives principled guidelines for normalizing weights.

Residual Networks (ResNets) have become state-of-the-art models in deep learning and several theoretical studies have been devoted to understanding why ResNet works so well. One attractive...

https://aip.riken.jp/events/event_115479/

While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization has been called into question. This work presents a more nuanced...

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using...

Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and...

We investigate the prior selection problem for predicting an input–output relation by a generalized Bayesian method, α-Bayes prediction. The α-Bayes predictive distribution is given by minimizing t...

Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically. In this paper, we explore theoretical analysis on...

東京大学大学院 情報理工学系研究科 鈴木研究室 准教授 博士（情報理工学） 鈴木 大慈 ルールベースから統計的

IoTの進展によって、あらゆるデータを入手できるようになり、新ビジネス創出の可能性が広がってきた。UCCホールディングスやヤンマー、コニカミノルタなど、先駆者たちの実例から新時代にビジネスを創る方法を学ぶ。

Gradient Langevin dynamics (GLD) and stochastic GLD (SGLD) have attracted considerable attention lately, as a way to provide convergence guarantees in a non-convex setting. However, the known...

Labeling cost is often expensive and is a fundamental limitation of supervised learning. In this paper, we study importance labeling problem, in which we are given many unlabeled data and select a...