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We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates…

Machine Learning · Statistics 2011-10-21 Andrew Gordon Wilson , David A. Knowles , Zoubin Ghahramani

Unobserved confounding is one of the main challenges when estimating causal effects. We propose a causal reduction method that, given a causal model, replaces an arbitrary number of possibly high-dimensional latent confounders with a single…

Machine Learning · Statistics 2023-02-24 Maximilian Ilse , Patrick Forré , Max Welling , Joris M. Mooij

Background and Aims: The methods with which prediction models are usually developed mean that neither the parameters nor the predictions should be interpreted causally. However, when prediction models are used to support decision making,…

Methodology · Statistics 2021-01-25 Lijing Lin , Matthew Sperrin , David A. Jenkins , Glen P. Martin , Niels Peek

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model…

Machine Learning · Statistics 2026-03-04 Emil Javurek , Dennis Frauen , Yuxin Wang , Stefan Feuerriegel

Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under…

Machine Learning · Statistics 2025-10-03 Mehrzad Saremi

No man is an island, as individuals interact and influence one another daily in our society. When social influence takes place in experiments on a population of interconnected individuals, the treatment on a unit may affect the outcomes of…

Methodology · Statistics 2017-08-30 Edward K. Kao

We study causal effect estimation under interference from network data. We work under the chain-graph formulation pioneered in Tchetgen Tchetgen et. al (2021). Our first result shows that polynomial time evaluation of treatment effects is…

Statistics Theory · Mathematics 2025-12-10 Sohom Bhattacharya , Subhabrata Sen

The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for a rigorous and efficient method of causal network inference. Here…

Information Theory · Computer Science 2015-05-19 Jie Sun , Dane Taylor , Erik M. Bollt

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

Machine Learning · Statistics 2018-11-06 Edwin V. Bonilla , Karl Krauth , Amir Dezfouli

Network interference occurs when treatments assigned to some units affect the outcomes of others. Traditional approaches often assume that the observed network correctly specifies the interference structure. However, in practice,…

Methodology · Statistics 2026-02-04 Bar Weinstein , Daniel Nevo

Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between…

Machine Learning · Computer Science 2022-07-12 Gonçalo R. A. Faria , André F. T. Martins , Mário A. T. Figueiredo

One major drawback of state-of-the-art artificial intelligence is its lack of explainability. One approach to solve the problem is taking causality into account. Causal mechanisms can be described by structural causal models. In this work,…

Machine Learning · Statistics 2021-09-07 Nico Reick , Felix Wiewel , Alexander Bartler , Bin Yang

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…

Machine Learning · Statistics 2014-11-03 Ricardo Silva , Robin Evans

While observational data are routinely used to estimate causal effects of biomedical treatments, doing so requires special methods to adjust for observed confounding. These methods invariably rely on untestable statistical and causal…

Methodology · Statistics 2026-03-02 Arman Oganisian

We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the…

Machine Learning · Statistics 2016-02-23 Daniel Hernández-Lobato , Pablo Morales-Mombiela , David Lopez-Paz , Alberto Suárez

We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…

Methodology · Statistics 2025-11-06 Andrea Cremaschi , Manuele Leonelli , Gherardo Varando

The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that…

Signal Processing · Electrical Eng. & Systems 2026-05-01 Daniel Waxman , Fernando Llorente , Petar M. Djurić

Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions…

Machine Learning · Statistics 2020-04-17 Jaron J. R. Lee , Ilya Shpitser

We present the first framework for Gaussian-process-modulated Poisson processes when the temporal data appear in the form of panel counts. Panel count data frequently arise when experimental subjects are observed only at discrete time…

Machine Learning · Statistics 2018-03-13 Hongyi Ding , Young Lee , Issei Sato , Masashi Sugiyama

Causal inference from observational data plays critical role in many applications in trustworthy machine learning. While sound and complete algorithms exist to compute causal effects, many of them assume access to conditional likelihoods,…

Machine Learning · Computer Science 2024-11-04 Md Musfiqur Rahman , Matt Jordan , Murat Kocaoglu