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The inaccessibility of controlled randomized trials due to inherent constraints in many fields of science has been a fundamental issue in causal inference. In this paper, we focus on distinguishing the cause from effect in the bivariate…

Traditional machine learning assumes samples in tabular data to be independent and identically distributed (i.i.d). This assumption may miss useful information within and between sample relationships in representation learning. This paper…

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world…

Entanglement in continuous-variable non-Gaussian states provides irreplaceable advantages in many quantum information tasks. However, the sheer amount of information in such states grows exponentially and makes a full characterization…

With the wide-spread availability of complex relational data, semi-supervised node classification in graphs has become a central machine learning problem. Graph neural networks are a recent class of easy-to-train and accurate methods for…

Probabilistic theory and differential equation are powerful tools for the interpretability and guidance of the design of machine learning models, especially for illuminating the mathematical motivation of learning latent variable from…

Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…

Recent years have seen rapid progress at the intersection between causality and machine learning. Motivated by scientific applications involving high-dimensional data, in particular in biomedicine, we propose a deep neural architecture for…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic…

Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the…

The marginal correlation between two variables is a measure of their linear dependence. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The…

In semi-supervised learning on graphs, response variables observed at one node are used to estimate missing values at other nodes. The methods exploit correlations between nearby nodes in the graph. In this paper we prove that many such…

Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…

We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…

This paper considers the problem of learning the parameters in Bayesian networks of discrete variables with known structure and hidden variables. Previous approaches in these settings typically use expectation maximization; when the network…

Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets. While existing approaches…

The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean…

We construct a "hyperparameter matrix" statistical method for performing the joint analyses of multiple correlated astronomical data sets, in which the weights of data sets are determined by their own statistical properties. This method is…

Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…