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We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such…

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations (p<n, p: the number of variables and n: the number of observations). However, modern datasets including…

Large contingency tables summarizing categorical variables arise in many areas. For example in biology when a large number of biomarkers are cross-tabulated according to their discrete expression level. Interactions of the variables are…

Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing…

We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct…

Causal relationships among variables are commonly represented via directed acyclic graphs. There are many methods in the literature to quantify the strength of arrows in a causal acyclic graph. These methods, however, have undesirable…

I describe a planning methodology for domains with uncertainty in the form of external events that are not completely predictable. The events are represented by enabling conditions and probabilities of occurrence. The planner is…

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…

Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…

Due to unmeasured confounding, it is often not possible to identify causal effects from a postulated model. Nevertheless, we can ask for partial identification, which usually boils down to finding upper and lower bounds of a causal quantity…

An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…

The stochastic dynamics of biochemical networks are usually modelled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically, and numerical methods typically produce estimates with…

Mathematical programming formulations of influence diagrams can bridge the gap between representing and solving decision problems. However, they suffer from both modeling and computational limitations. Aiming to address modeling…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Many important quantities of interest are only partially identified from observable data: the data can limit them to a set of plausible values, but not uniquely determine them. This paper develops a unified framework for covariate-assisted…

Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and…

In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…

Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of…

Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…

Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in…