Related papers: Lecture notes on rough paths and applications to m…

The kernel of a pair of linear systems is studied in the framework of commutative ring theory with applications to behavioral perspective of linear systems

Path signatures provide a rich representation of sequential data, with strong theoretical guarantees and good performance in a variety of machine-learning tasks. While signatures have progressed from fixed feature extractors to trainable…

Many applications from camera arrays to sensor networks require efficient compression and processing of correlated data, which in general is collected in a distributed fashion. While information-theoretic foundations of distributed…

We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random…

Learning curves are a concept from social sciences that has been adopted in the context of machine learning to assess the performance of a learning algorithm with respect to a certain resource, e.g., the number of training examples or the…

Robust machine learning formulations have emerged to address the prevalent vulnerability of deep neural networks to adversarial examples. Our work draws the connection between optimal robust learning and the privacy-utility tradeoff…

We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability…

Despite Graph neural networks' significant performance gain over many classic techniques in various graph-related downstream tasks, their successes are restricted in shallow models due to over-smoothness and the difficulties of…

Since about 100 years ago, to learn the intrinsic structure of data, many representation learning approaches have been proposed, including both linear ones and nonlinear ones, supervised ones and unsupervised ones. Particularly, deep…

We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…

This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students…

In recent years, pre-trained graph neural networks (GNNs) have been developed as general models which can be effectively fine-tuned for various potential downstream tasks in materials science, and have shown significant improvements in…

Brief lecture notes for a course about random matrices given at the University of Cambridge.

The development of IT and WWW provides different teaching strategies, which are chosen by teachers. Students can acquire knowledge through different learning models. The problem based learning is a popular teaching strategy for teachers.…

Reinforcement learning is a learning paradigm for solving sequential decision-making problems. Recent years have witnessed remarkable progress in reinforcement learning upon the fast development of deep neural networks. Along with the…

Placement and routing are two indispensable and challenging (NP-hard) tasks in modern chip design flows. Compared with traditional solvers using heuristics or expert-well-designed algorithms, machine learning has shown promising prospects…

Network representation learning (NRL) is an effective graph analytics technique and promotes users to deeply understand the hidden characteristics of graph data. It has been successfully applied in many real-world tasks related to network…

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…

Applying new computing paradigms like quantum computing to the field of machine learning has recently gained attention. However, as high-dimensional real-world applications are not yet feasible to be solved using purely quantum hardware,…

This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as…