In this job talk, the speaker will begin by introducing statistical learning theory and his scientific contributions to this field. He will then briefly describe his broader research achievements in various other areas including matrix completion (and recommender systems), density estimation, computer vision, time series analysis, etc.
In the main technical part of the talk, the speaker will focus on his recent paper "Fine-grained Analysis of Inductive Matrix Completion" [1], whilst also including one or two results from "Orthogonal inductive Matrix Completion" [2] for context: he will begin by reviewing the basics of nuclear norm-based matrix completion methods, including both the classic Inductive Matrix Completion (IMC) model and his model OMIC (from [2]). The model (OMIC) assumes that the users and items are divided into predetermined families, with the final ratings being an additive combination of group-wise effects and individual effects.
The presentation of this algorithm and its relationship with the classic IMC framework will naturally open much deeper theoretical questions regarding the failings of the state-of-the-art generalization bounds for IMC. He will then present his first main result from [1], which remedies those failings with sample complexity bound of order $\widetilde{O}\left(d^{3/2}\sqrt{r}\right)$ for IMC (here, $d$ denotes the size of the side information and $r$ denotes the ground truth rank), bridging the gap between the state-of-the-arts in IMC and standard matrix completion. After also touching on the proof techniques, it will be natural to move on to his second main contribution in [1]: a data-dependent recalibration of the IMC regulariser which brings the sample complexity down to $\widetilde{O}(rd)$, the same as in the uniform sampling case. Lastly, he will present ongoing work about low-noise IMC, including generalisation bounds involving a multiplicative factor of the subgaussianity constant of the noise, thereby creating a bridge between the approximate recovery and exact recovery settings. He will conclude the talk with a description of his broader research plan for the next few years in both matrix completion and other fields.
[1] Antoine Ledent, Rodrigo Alves, Yunwen Lei and Marius Kloft. "Fine-grained Generalisation Analysis of Inductive Matrix completion. " NeurIPS 2021
[2] Antoine Ledent, Rodrigo Alves and Marius Kloft. "Orthogonal Inductive Matrix Completion". TNNLS 2021.
About the Speaker
Antoine Ledent is a postdoctoral researcher at the department of computer science at TU Kaiserslautern in Marius Kloft's research group. He holds Bachelors' and a Masters' degrees in mathematics from Clare College, University of Cambridge. Previously, he worked on low-dimensional projections of high-dimensional stochastic differential equations at the University of Luxembourg, where he obtained his PhD in 2017. Antoine Ledent's current main research focus is statistical learning theory applied to neural networks, kernel methods, as well as matrix completion problems. He also has a significant interests in applications such as recommender systems and computer vision. He has served as a reviewer/PC member for AiStats, Neural Networks, Transactions of Signal Processing, NeurIPS, ICML, ICLR, ECML and AAAI.
He is a tenure-track faculty candidate for the Artificial Intelligence & Data Science, Machine Learning & Intelligence.
