Related papers: A Non-Parametric Bayesian Method for Inferring Hid…

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…

Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates,…

We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth…

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…

We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…

This paper describes a Bayesian method for combining an arbitrary mixture of observational and experimental data in order to learn causal Bayesian networks. Observational data are passively observed. Experimental data, such as that produced…

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…

We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…

In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…

High-throughput scientific studies involving no clear a'priori hypothesis are common. For example, a large-scale genomic study of a disease may examine thousands of genes without hypothesizing that any specific gene is responsible for the…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

There are several existing algorithms that under appropriate assumptions can reliably identify a subset of the underlying causal relationships from observational data. This paper introduces the first computationally feasible score-based…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of…

Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for…

The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…

Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov…

Discovering and parameterising latent confounders represent important and challenging problems in causal structure learning and density estimation respectively. In this paper, we focus on both discovering and learning the distribution of…

Learning causal relationships among a set of variables, as encoded by a directed acyclic graph, from observational data is complicated by the presence of unobserved confounders. Instrumental variables (IVs) are a popular remedy for this…

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…