We merge computational mechanics' definition of causal states (predictively-equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely-applicable method that infers causal structure directly from observations of a system's behaviors whether they are over discrete or continuous events or time. A structural representation -- a finite- or infinite-state kernel $ε$-machine -- is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker-Plank equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably-infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally-driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high dimensional data.
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Institute for Statistical Mathematics（统计数理研究所）；ETH Zürich（苏黎世联邦理工学院）
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations which can be applied to points drawn from the respective distributions. We refer to our approach as {\em kernel probabilistic programming}. We illustrate it on synthetic data, and show how it can be used for nonparametric structural equation models, with an application to causal inference.
IBM Research（IBM研究院）；Istituto Italiano di Tecnologia（意大利理工学院）
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition-free algorithm that orchestrates two inexact solvers for simultaneously learning both the input and output components of separable matrix-valued kernels. As a key application enabled by our framework, we show how high-dimensional…
IBM Research（IBM研究院）；Italian Institute of Technology（意大利理工学院）
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition-free algorithm that orchestrates two inexact solvers for simultaneously learning both the input and output components of separable matrix-valued kernels. As a key application enabled by our framework, we show how high-dimensional…
The Institute of Scientific and Industrial Research, Osaka University（大阪大学产业科学研究所）；Graduate School of Science, Osaka University（大阪大学研究生院）；Graduate School of Informatics, Kyoto University（京都大学情报学研究科）
Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based on non-Gaussianity of the observed data distribution. However, most of these are limited to continuous data. In this paper, we present a novel causal model for binary data and propose a new approach to derive an identifiable causal structure governing the data based on skew Bernoulli distributions of external noise. Experimental evaluation shows excellent pe…
Discovering Mixtures of Structural Causal Models from Time Series Data
Halıcıoğlu Data Science Institute, University of California, San Diego（加利福尼亚大学圣迭戈分校哈利西奥格鲁数据科学学院）；Department of Computer Science and Engineering, University of California, San Diego（加利福尼亚大学圣迭戈分校计算机科学与工程系）
University of Melbourne（墨尔本大学）；University of Tartu（塔尔图大学）
This paper proposes an approach to analyze an event log of a business process in order to generate case-level recommendations of treatments that maximize the probability of a given outcome. Users classify the attributes in the event log into controllable and non-controllable, where the former correspond to attributes that can be altered during an execution of the process (the possible treatments). We use an action rule mining technique to identify treatments that co-occur with the outcome under some conditions. Since action rules are generated based on correlation rather than causation, we the…
Anti-discrimination is an increasingly important task in data science. In this paper, we investigate the problem of discovering both direct and indirect discrimination from the historical data, and removing the discriminatory effects before the data is used for predictive analysis (e.g., building classifiers). We make use of the causal network to capture the causal structure of the data. Then we model direct and indirect discrimination as the path-specific effects, which explicitly distinguish the two types of discrimination as the causal effects transmitted along different paths in the networ…
DeepMind（深度思维）；University of Oxford（牛津大学）；Imperial College London（帝国理工学院）
Causal models of agents have been used to analyse the safety aspects of machine learning systems. But identifying agents is non-trivial -- often the causal model is just assumed by the modeler without much justification -- and modelling failures can lead to mistakes in the safety analysis. This paper proposes the first formal causal definition of agents -- roughly that agents are systems that would adapt their policy if their actions influenced the world in a different way. From this we derive the first causal discovery algorithm for discovering agents from empirical data, and give algorithms …
Amazon Research Tübingen（亚马逊图宾根研究院）；Monash University（莫纳什大学）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's behaviour. This is a challenging problem for two reasons: First, observational effects are often unrepresentative of the underlying causal effect because they are skewed by the presence of confounding factors. Second, naive empirical estimations of a rule's effect have a high variance, and, hence, their maximisation can lead to random results. To address th…
Discovering Latent Causal Graphs from Spatiotemporal Data
Department of Computer Science and Engineering, University of California, San Diego, La Jolla, USA（计算机科学与工程系，加州大学圣地亚哥分校，拉乔拉，美国）；Halıcıoglu Data Science Institute, University of California, San Diego, La Jolla, USA（Halıcıoglu数据科学研究所，加州大学圣地亚哥分校，拉乔拉，美国）；Scripps Institution of Oceanography, University of California, San Diego, La Jolla, USA（斯克里普斯海洋研究所，加州大学圣地亚哥分校，拉乔拉，美国）
Faced with data-driven policies, individuals will manipulate their features to obtain favorable decisions. While earlier works cast these manipulations as undesirable gaming, recent works have adopted a more nuanced causal framing in which manipulations can improve outcomes of interest, and setting coherent mechanisms requires accounting for both predictive accuracy and improvement of the outcome. Typically, these works focus on known causal graphs, consisting only of an outcome and its parents. In this paper, we introduce a general framework in which an outcome and n observed features are rel…
A tutorial on discovering and quantifying the effect of latent causal sources of multimodal EHR data
Department of Biomedical Informatics Vanderbilt University Medical Center（生物医学信息学系范德堡大学医学中心）；Department of Biomedical Informatics University of Pittsburgh（生物医学信息学系匹兹堡大学）；Departments of Medicine & Biomedical Informatics Vanderbilt University Medical Center（医学与生物医学信息学系范德堡大学医学中心）；Departments of Biomedical Informatics & Computer Science Vanderbilt University Medical Center & Vanderbilt University（生物医学信息学与计算机科学系范德堡大学医学中心及范德堡大学）
German Aerospace Center（德国航空航天中心）；Institute of Data Science（数据科学研究所）；Technische Universität Berlin（柏林工业大学）
The paper introduces a novel conditional independence (CI) based method for linear and nonlinear, lagged and contemporaneous causal discovery from observational time series in the causally sufficient case. Existing CI-based methods such as the PC algorithm and also common methods from other frameworks suffer from low recall and partially inflated false positives for strong autocorrelation which is an ubiquitous challenge in time series. The novel method, PCMCI$^+$, extends PCMCI [Runge et al., 2019b] to include discovery of contemporaneous links. PCMCI$^+$ improves the reliability of CI tests …
Applied AI Lab（应用人工智能实验室）；University of Oxford（牛津大学）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）
Latent world models allow agents to reason about complex environments with high-dimensional observations. However, adapting to new environments and effectively leveraging previous knowledge remain significant challenges. We present variational causal dynamics (VCD), a structured world model that exploits the invariance of causal mechanisms across environments to achieve fast and modular adaptation. By causally factorising a transition model, VCD is able to identify reusable components across different environments. This is achieved by combining causal discovery and variational inference to lea…
University of Southern California（南加州大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Animals exhibit an innate ability to learn regularities of the world through interaction. By performing experiments in their environment, they are able to discern the causal factors of variation and infer how they affect the world's dynamics. Inspired by this, we attempt to equip reinforcement learning agents with the ability to perform experiments that facilitate a categorization of the rolled-out trajectories, and to subsequently infer the causal factors of the environment in a hierarchical manner. We introduce {\em causal curiosity}, a novel intrinsic reward, and show that it allows our age…
Discovering Causal Relations and Equations from Data
Universitat de València（瓦伦西亚大学）；German Aerospace Center（德国航空航天中心）；Technische Universität Berlin（柏林工业大学）；University of Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Bournemouth University（伯恩茅斯大学）；Heidelberg University（海德堡大学）；KTH Royal Institute of Technology（KTH皇家理工学院）；New York University（纽约大学）
Beyond Stationarity in Time Series: Discovering Causal Structures and Latent Regimes via Markov Blankets
Univ. Grenoble Alpes（格勒诺布尔大学）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔国立高等工程学院）；LIG（信息与信号处理实验室）；Sorbonne Université（索邦大学）；INSERM（法国国家健康与医学研究院）；Institut Pierre Louis d’Epidémiologie et de Santé Publique（皮埃尔·路易流行病学与公共卫生研究所）
A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization
Discovering and Reasoning of Causality in the Hidden World with Large Language Models
TMLR Group, Hong Kong Baptist University（香港 Baptist 大学 TMLR 组）；Mohamed bin Zayed University of Artificial Intelligence（Mohamed bin Zayed 人工智能大学）；Department of Philosophy, Carnegie Mellon University（哲学系，卡内基梅隆大学）；School of Computer Science, The University of Sydney（悉尼大学计算机科学学院）；School of Mathematics and Statistics, The University of Melbourne（墨尔本大学数学与统计学学院）；The Chinese University of Hong Kong（香港中文大学）
Istituto Italiano di Tecnologia（意大利理工学院）；Università di Genova（热那亚大学）
Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to name a few. The key idea is that exploring task relatedness (structure) can lead to improved performances. In this paper, we propose and study a novel sparse, non-parametric approach exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued functions. We develop a suitable regularization framework which can be formulated as a convex optim…
School of EECS, Queen Mary University of London (QMUL)（伦敦玛丽女王大学电子工程与计算机科学学院）；The Alan Turing Institute（图灵研究所）
Several structure learning algorithms have been proposed towards discovering causal or Bayesian Network (BN) graphs. The validity of these algorithms tends to be evaluated by assessing the relationship between the learnt and the ground truth graph. However, there is no agreed scoring metric to determine this relationship. Moreover, this paper shows that some of the commonly used metrics tend to be biased in favour of graphs that minimise edges. While graphs that are less complex are desirable, some of the metrics favour underfitted graphs, thereby encouraging limited propagation of evidence. T…
Johns Hopkins University（约翰斯·霍普金斯大学）；Microsoft Research（微软研究院）；New York University（纽约大学）
How can neural networks perform so well on compositional tasks even though they lack explicit compositional representations? We use a novel analysis technique called ROLE to show that recurrent neural networks perform well on such tasks by converging to solutions which implicitly represent symbolic structure. This method uncovers a symbolic structure which, when properly embedded in vector space, closely approximates the encodings of a standard seq2seq network trained to perform the compositional SCAN task. We verify the causal importance of the discovered symbolic structure by showing that, w…
Reconstructing the causal relationships behind the phenomena we observe is a fundamental challenge in all areas of science. Discovering causal relationships through experiments is often infeasible, unethical, or expensive in complex systems. However, increases in computational power allow us to process the ever-growing amount of data that modern science generates, leading to an emerging interest in the causal discovery problem from observational data. This work evaluates the LPCMCI algorithm, which aims to find generators compatible with a multi-dimensional, highly autocorrelated time series w…
ETH Zurich（苏黎世联邦理工学院）；MPI Tübingen（图宾根马克斯·普朗克研究所）；EPFL（洛桑联邦理工学院）
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may translate to faster, more accurate, and more flexible models, which may directly relate to real-world impact. In this dissertation, we consider two different research areas that concern structuring a learning algorithm's solution: when the structure is known and when it has to be discovered.
University of Oxford（牛津大学）；Department of Statistics（统计系）；DeepMind（DeepMind（深度思维））
Discovering the causal structure among a set of variables is a fundamental problem in many areas of science. In this paper, we propose Kernel Conditional Deviance for Causal Inference (KCDC) a fully nonparametric causal discovery method based on purely observational data. From a novel interpretation of the notion of asymmetry between cause and effect, we derive a corresponding asymmetry measure using the framework of reproducing kernel Hilbert spaces. Based on this, we propose three decision rules for causal discovery. We demonstrate the wide applicability of our method across a range of diver…
This paper introduces an algorithm for discovering implicit and delayed causal relations between events observed by a robot at arbitrary times, with the objective of improving data-efficiency and interpretability of model-based reinforcement learning (RL) techniques. The proposed algorithm initially predicts observations with the Markov assumption, and incrementally introduces new hidden variables to explain and reduce the stochasticity of the observations. The hidden variables are memory units that keep track of pertinent past events. Such events are systematically identified by their informa…
Babylon Health（巴比伦健康）；University College London（伦敦大学学院）
Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based on the assumption that all variables have been jointly measured in a single dataset. In many cases this assumption fails. Previous approaches to overcoming this shortcoming devised algorithms that returned all joint causal structures consistent with the conditional independence information contained in each individual dataset. But, as conditional independen…
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 latent confounders. This task requires solutions that come from different areas of statistics and machine learning. We combine elements of variational Bayesian methods, expectation-maximisation, hill-climbing search, and structure learning under the assumption of causal insufficiency. We propose two learning strategies; one that maximises model selection accur…
Discovering and exploiting the causal structure in the environment is a crucial challenge for intelligent agents. Here we explore whether causal reasoning can emerge via meta-reinforcement learning. We train a recurrent network with model-free reinforcement learning to solve a range of problems that each contain causal structure. We find that the trained agent can perform causal reasoning in novel situations in order to obtain rewards. The agent can select informative interventions, draw causal inferences from observational data, and make counterfactual predictions. Although established formal…
ETH Zürich（苏黎世联邦理工学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；IBM Research Zürich（苏黎世IBM研究院）
Inferring causal structures from experimentation is a central task in many domains. For example, in biology, recent advances allow us to obtain single-cell expression data under multiple interventions such as drugs or gene knockouts. However, the targets of the interventions are often uncertain or unknown and the number of observations limited. As a result, standard causal discovery methods can no longer be reliably used. To fill this gap, we propose a Bayesian framework (BaCaDI) for discovering and reasoning about the causal structure that underlies data generated under various unknown experi…
ETH Zurich（苏黎世联邦理工学院）；Mila（米拉人工智能研究所）；Universite de Montréal（蒙特利尔大学）；GlaxoSmithKline（葛兰素史克）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Google Research（谷歌研究院）；KTH Stockholm（瑞典皇家理工学院）；DeepMind（深度思维）
Discovering causal structures from data is a challenging inference problem of fundamental importance in all areas of science. The appealing properties of neural networks have recently led to a surge of interest in differentiable neural network-based methods for learning causal structures from data. So far, differentiable causal discovery has focused on static datasets of observational or fixed interventional origin. In this work, we introduce an active intervention targeting (AIT) method which enables a quick identification of the underlying causal structure of the data-generating process. Our…
University of Amsterdam（阿姆斯特丹大学）；Microsoft Research Cambridge（微软剑桥研究院）
We consider the problem of discovering causal relations from independence constraints selection bias in addition to confounding is present. While the seminal FCI algorithm is sound and complete in this setup, no criterion for the causal interpretation of its output under selection bias is presently known. We focus instead on local patterns of independence relations, where we find no sound method for only three variable that can include background knowledge. Y-Structure patterns are shown to be sound in predicting causal relations from data under selection bias, where cycles may be present. We …
Harvard University（哈佛大学）；KU Leuven（鲁汶大学）；IMT School for Advanced Studies（IMT高等研究院）
This paper introduces an innovative Bayesian machine learning algorithm to draw interpretable inference on heterogeneous causal effects in the presence of imperfect compliance (e.g., under an irregular assignment mechanism). We show, through Monte Carlo simulations, that the proposed Bayesian Causal Forest with Instrumental Variable (BCF-IV) methodology outperforms other machine learning techniques tailored for causal inference in discovering and estimating the heterogeneous causal effects while controlling for the familywise error rate (or - less stringently - for the false discovery rate) at…
Guangdong University of Technology（广东工业大学）；RIKEN（理化学研究所）；Shiga University（滋贺大学）；Pazhou Lab（琶洲实验室）；Peking University（北京大学）；Okayama University（冈山大学）；Foshan University（佛山科学技术学院）
Discovering causal structures among latent factors from observed data is a particularly challenging problem. Despite some efforts for this problem, existing methods focus on the single-domain data only. In this paper, we propose Multi-Domain Linear Non-Gaussian Acyclic Models for Latent Factors (MD-LiNA), where the causal structure among latent factors of interest is shared for all domains, and we provide its identification results. The model enriches the causal representation for multi-domain data. We propose an integrated two-phase algorithm to estimate the model. In particular, we first loc…
University of Sydney（悉尼大学）；University of Technology Sydney（悉尼科技大学）；Ingham Institute（英厄姆研究所）
Discovering causal structure among a set of variables is a fundamental problem in many domains. However, state-of-the-art methods seldom consider the possibility that the observational data has missing values (incomplete data), which is ubiquitous in many real-world situations. The missing value will significantly impair the performance and even make the causal discovery algorithms fail. In this paper, we propose an approach to discover causal structures from incomplete data by using a novel encoder and reinforcement learning (RL). The encoder is designed for missing data imputation as well as…
Georgia Institute of Technology（佐治亚理工学院）；Carnegie Mellon University（卡内基梅隆大学）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）；BioMap（百图生科）
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able …
School of Software, Shandong University（山东大学软件学院）；SDU-NTU Joint Centre for AI Research, Shandong University（山东大学-南洋理工大学人工智能联合研究中心）；Chongqing Uni. of Posts and Telecom.（重庆邮电大学）；MOE Key Laboratory of Big Data Intelligent Computing, Chongqing Uni. of Posts and Telecom.（重庆邮电大学大数据智能计算教育部重点实验室）
Discovering relevant, but possibly hidden, variables is a key step in constructing useful and predictive theories about the natural world. This brief note explains the connections between three approaches to this problem: the recently introduced information-bottleneck method, the computational mechanics approach to inferring optimal models, and Salmon's statistical relevance basis.
Discovering causal relationships between different variables from time series data has been a long-standing challenge for many domains such as climate science, finance, and healthcare. Given the complexity of real-world relationships and the nature of observations in discrete time, causal discovery methods need to consider non-linear relations between variables, instantaneous effects and history-dependent noise (the change of noise distribution due to past actions). However, previous works do not offer a solution addressing all these problems together. In this paper, we propose a novel causal …
Differentiable Causal Discovery For Latent Hierarchical Causal Models
University of California San Diego（加利福尼亚大学圣迭戈分校）；Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
