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In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…

Causal induction, i.e., identifying unobservable mechanisms that lead to the observable relations among variables, has played a pivotal role in modern scientific discovery, especially in scenarios with only sparse and limited data. Humans,…

Computer Vision and Pattern Recognition · Computer Science 2021-03-29 Chi Zhang , Baoxiong Jia , Mark Edmonds , Song-Chun Zhu , Yixin Zhu

Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…

Machine Learning · Computer Science 2022-06-20 Zijun Cui , Naiyu Yin , Yuru Wang , Qiang Ji

There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…

Statistics Theory · Mathematics 2025-09-30 Marco Battiston , Lorenzo Cappello

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional…

Artificial Intelligence · Computer Science 2014-11-17 N. L. Zhang , D. Poole

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find \textit{invariant representations} of the data. These are representations of the covariates such that…

Machine Learning · Computer Science 2022-08-16 Advait Parulekar , Karthikeyan Shanmugam , Sanjay Shakkottai

The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce…

Quantum Physics · Physics 2019-07-24 Elie Wolfe , Robert W. Spekkens , Tobias Fritz

This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…

Machine Learning · Statistics 2022-06-22 Zhendong Wang , Ruijiang Gao , Mingzhang Yin , Mingyuan Zhou , David M. Blei

Inferring causal effects of a treatment, intervention or policy from observational data is central to many applications. However, state-of-the-art methods for causal inference seldom consider the possibility that covariates have missing…

Methodology · Statistics 2020-02-26 Imke Mayer , Julie Josse , Félix Raimundo , Jean-Philippe Vert

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as…

Machine Learning · Computer Science 2024-12-02 Yuhang Liu , Zhen Zhang , Dong Gong , Mingming Gong , Biwei Huang , Anton van den Hengel , Kun Zhang , Javen Qinfeng Shi

This paper introduces a new framework for recovering causal graphs from observational data, leveraging the observation that the distribution of an effect, conditioned on its causes, remains invariant to changes in the prior distribution of…

Machine Learning · Computer Science 2026-02-04 Nang Hung Nguyen , Phi Le Nguyen , Thao Nguyen Truong , Trong Nghia Hoang , Masashi Sugiyama

Pursuing causality from data is a fundamental problem in scientific discovery, treatment intervention, and transfer learning. This paper introduces a novel algorithmic method for addressing nonparametric invariance and causality learning in…

Statistics Theory · Mathematics 2025-11-18 Yihong Gu , Cong Fang , Peter Bühlmann , Jianqing Fan

When domain knowledge is limited and experimentation is restricted by ethical, financial, or time constraints, practitioners turn to observational causal discovery methods to recover the causal structure, exploiting the statistical…

Granger causality is widely used for causal structure discovery in complex systems from multivariate time series data. Traditional Granger causality tests based on linear models often fail to detect even mild non-linear causal…

Machine Learning · Computer Science 2025-10-23 Ziyi Zhang , Shaogang Ren , Xiaoning Qian , Nick Duffield

Learning causal structure from observational data is a fundamental challenge in machine learning. However, the majority of commonly used differentiable causal discovery methods are non-identifiable, turning this problem into a continuous…

Machine Learning · Computer Science 2022-09-30 Yu Wang , An Zhang , Xiang Wang , Yancheng Yuan , Xiangnan He , Tat-Seng Chua

Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian…

Machine Learning · Computer Science 2024-08-21 Ignavier Ng , Yujia Zheng , Xinshuai Dong , Kun Zhang

Down-sampling training data has long been shown to improve the generalization performance of a wide range of machine learning systems. Recently, down-sampling has proved effective in genetic programming (GP) runs that utilize the lexicase…

Neural and Evolutionary Computing · Computer Science 2022-06-01 Ryan Boldi , Thomas Helmuth , Lee Spector

Causal inference is difficult in the presence of unobserved confounders. We introduce the instrumented common confounding (ICC) approach to (nonparametrically) identify causal effects with instruments, which are exogenous only conditional…

Econometrics · Economics 2022-09-20 Christian Tien

Notions of counterfactual invariance (CI) have proven essential for predictors that are fair, robust, and generalizable in the real world. We propose graphical criteria that yield a sufficient condition for a predictor to be…

Machine Learning · Computer Science 2024-08-12 Francesco Quinzan , Cecilia Casolo , Krikamol Muandet , Yucen Luo , Niki Kilbertus

Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…

Machine Learning · Statistics 2023-07-19 Chih-Yuan Chiu , Kshitij Kulkarni , Shankar Sastry