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Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…

Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…

We revisit the elegant observation of T. Cover '65 which, perhaps, is not as well-known to the broader community as it should be. The first goal of the tutorial is to explain---through the prism of this elementary result---how to solve…

We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this…

Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. Two standard algorithms -- label propagation and graph neural networks -- both operate by repeatedly passing information along edges,…

Recent works on representation learning for graph structured data predominantly focus on learning distributed representations of graph substructures such as nodes and subgraphs. However, many graph analytics tasks such as graph…

Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…

Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…

Graph representation learning based on graph neural networks (GNNs) can greatly improve the performance of downstream tasks, such as node and graph classification. However, the general GNN models do not aggregate node information in a…

This paper presents an entirely unsupervised interest point training framework by jointly learning detector and descriptor, which takes an image as input and outputs a probability and a description for every image point. The objective of…

Learning the structure of a causal graphical model using both observational and interventional data is a fundamental problem in many scientific fields. A promising direction is continuous optimization for score-based methods, which,…

Graph neural networks (GNNs) have excelled in various graph learning tasks, particularly node classification. However, their performance is often hampered by noisy measurements in real-world graphs, which can corrupt critical patterns in…

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…

We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics…

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…

Computational efficiency is a major bottleneck in using classic graph-based approaches for semi-supervised learning on datasets with a large number of unlabeled examples. Known techniques to improve efficiency typically involve an…

We apply network Lasso to semi-supervised regression problems involving network structured data. This approach lends quite naturally to highly scalable learning algorithms in the form of message passing over an empirical graph which…

Combinatorial optimization (CO) layers in machine learning (ML) pipelines are a powerful tool to tackle data-driven decision tasks, but they come with two main challenges. First, the solution of a CO problem often behaves as a piecewise…

Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…

Unsupervised learning allows us to leverage unlabelled data, which has become abundantly available, and to create embeddings that are usable on a variety of downstream tasks. However, the typical lack of interpretability of unsupervised…