Causality and Statistical Learning

Granger causality for state space models

Granger causality, a popular method for determining causal influence between stochastic processes, is most commonly estimated via linear autoregressive modeling. However, this approach has a serious drawback: if the process being modeled has a moving average component, then the autoregressive model order is theoretically infinite, and in finite sample large empirical model orders may be necessary, resulting in weak Granger-causal inference. This is particularly relevant when the process has been filtered, downsampled, or observed with (additive) noise - all of which induce a moving average com…

Causality without potential outcomes and the dynamic approach

Several approaches to causal inference from observational studies have been proposed. Since the proposal of Rubin (1974) many works have developed a counterfactual approach to causality, statistically formalized by potential outcomes. Pearl (2000) has put forward a theory of structural causal models which gives an important role to graphical models and do not necessarily use potential outcomes. On the other hand, several authors have developed a dynamical approach in line with Granger (1969). We analyze prospective and retrospective causal questions and their different modalities. Following Da…

因果关系作为人工智能的统计良知：从珀尔的阶梯到可信机器

Causality as the Statistical Conscience of Artificial Intelligence: From Pearl's Ladder to Trustworthy Machines

本文论证因果推断是AI不可或缺的统计良知，通过统计必要性定理、统一因果统计估计框架以及三种AI失败模式的因果盲区分析，提出可信AI本质上是因果统计问题。

统计学中的挑战：因果关系与因果推断的十二个挑战

Challenges in Statistics: A Dozen Challenges in Causality and Causal Inference

本文指出因果关系与因果推断是统计学与多领域交叉的核心研究方向，虽过去三十年取得进展但仍有诸多开放问题，提出需从理论、方法、工具及跨领域合作等多方面推进该领域未来研究。

Conditional distribution variability measures for causality detection

In this paper we derive variability measures for the conditional probability distributions of a pair of random variables, and we study its application in the inference of causal-effect relationships. We also study the combination of the proposed measures with standard statistical measures in the the framework of the ChaLearn cause-effect pair challenge. The developed model obtains an AUC score of 0.82 on the final test database and ranked second in the challenge.

Extended Conditional Independence and Applications in Causal Inference

The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions the calculus that applies for the two cases separately (axioms of a separoid) still applies for the extended case. These results provide a rigorous basis for a wide range of statistical concepts, including ancillarity and sufficiency, and, in particular, the Decision Theoretic framework for statistical causality, which uses the language and calculus of conditi…

The Probability of Causation

Many legal cases require decisions about causality, responsibility or blame, and these may be based on statistical data. However, causal inferences from such data are beset by subtle conceptual and practical difficulties, and in general it is, at best, possible to identify the "probability of causation" as lying between certain empirically informed limits. These limits can be refined and improved if we can obtain additional information, from statistical or scientific data, relating to the internal workings of the causal processes. In this paper we review and extend recent work in this area, wh…

Causality and Generalizability: Identifiability and Learning Methods

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrum…

对称性与因果性：超越独立同分布（IID）数据的因果效应识别

Symmetries and Causality: Causal Effect Identification Beyond IID Data

本文提出基于数据对称性的因果推理数学语言，可复现IID数据的因果理论结果，扩展了超越IID数据的因果推理范围，适用于迁移与鲁棒性属性描述。

Non-Parametric Causality Detection: An Application to Social Media and Financial Data

According to behavioral finance, stock market returns are influenced by emotional, social and psychological factors. Several recent works support this theory by providing evidence of correlation between stock market prices and collective sentiment indexes measured using social media data. However, a pure correlation analysis is not sufficient to prove that stock market returns are influenced by such emotional factors since both stock market prices and collective sentiment may be driven by a third unmeasured factor. Controlling for factors that could influence the study by applying multivariate…

机器学习对自然科学是好是坏？

Is machine learning good or bad for the natural sciences?

本文探讨了机器学习在自然科学中的双重影响，指出其本体论与认识论虽在因果推断中处理混淆因子时有益，但在模拟物理仿真和生成数据标签时会引入统计偏差，呼吁科学界重新审视ML的价值。

存在不可见混杂因素下的动力学因果关系

Dynamical causality under invisible confounders

针对不可见混杂因素下因果推断难的问题，提出基于延迟嵌入空间正交分解的CIC方法，可量化变量因果关系、重构混杂因素，解决高维系统因果检测及变量不可分问题，经真实数据集验证有效。

Regression and Causality

The causal effect of an intervention (treatment/exposure) on an outcome can be estimated by: i) specifying knowledge about the data-generating process; ii) assessing under what assumptions a target quantity, such as for example a causal odds ratio, can be identified given the specified knowledge (and given the measured data); and then, iii) using appropriate statistical estimation techniques to estimate the desired parameter of interest. As regression is the cornerstone of statistical analysis, it seems obvious to ask: is it appropriate to use estimated regression parameters for causal effect …

Grasping Causality for the Explanation of Criticality for Automated Driving

The verification and validation of automated driving systems at SAE levels 4 and 5 is a multi-faceted challenge for which classical statistical considerations become infeasible. For this, contemporary approaches suggest a decomposition into scenario classes combined with statistical analysis thereof regarding the emergence of criticality. Unfortunately, these associational approaches may yield spurious inferences, or worse, fail to recognize the causalities leading to critical scenarios, which are, in turn, prerequisite for the development and safeguarding of automated driving systems. As to i…

Estimating Transfer Entropy via Copula Entropy

Causal discovery is a fundamental problem in statistics and has wide applications in different fields. Transfer Entropy (TE) is a important notion defined for measuring causality, which is essentially conditional Mutual Information (MI). Copula Entropy (CE) is a theory on measurement of statistical independence and is equivalent to MI. In this paper, we prove that TE can be represented with only CE and then propose a non-parametric method for estimating TE via CE. The proposed method was applied to analyze the Beijing PM2.5 data in the experiments. Experimental results show that the proposed m…

Causal inference: critical developments, past and future

Causality is a subject of philosophical debate and a central scientific issue with a long history. In the statistical domain, the study of cause and effect based on the notion of `fairness' in comparisons dates back several hundred years, and yet statistical concepts and developments that form the area of causal inference are only decades old. In this paper, we review core tenets and methods of causal inference and key developments in the history of the field. We highlight connections with traditional `associational' statistical methods, including estimating equations and semiparametric theory…

Sparse Causal Discovery in Multivariate Time Series

Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discovery consists in fitting VAR models with an additional sparsity-promoting regularization. Along this line we here propose that sparsity should be enforced for the subgroups of coefficients that belong to each pair of time series, as the absence of a causal relation requires the co…

Learning Generalized Causal Structure in Time-series

The science of causality explains/determines 'cause-effect' relationship between the entities of a system by providing mathematical tools for the purpose. In spite of all the success and widespread applications of machine-learning (ML) algorithms, these algorithms are based on statistical learning alone. Currently, they are nowhere close to 'human-like' intelligence as they fail to answer and learn based on the important "Why?" questions. Hence, researchers are attempting to integrate ML with the science of causality. Among the many causal learning issues encountered by ML, one is that these a…

Validity of time reversal for testing Granger causality

Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-reversed data. They show that this procedure, time-reversed Granger causality (TRGC), robustly rejects causal interpretations on mixtures of independent signals. While promising results have been achieved in simulations, it was so far unknown whether time reversal leads to valid measu…

Graph Topological Aspects of Granger Causal Network Learning

We study Granger causality in the context of wide-sense stationary time series, where our focus is on the topological aspects of the underlying causality graph. We establish sufficient conditions (in particular, we develop the notion of a "strongly causal" graph topology) under which the true causality graph can be recovered via pairwise causality testing alone, and provide examples from the gene regulatory network literature suggesting that our concept of a strongly causal graph may be applicable to this field. We implement and detail finite-sample heuristics derived from our theory, and esta…

无穷小因果性

Infinitesimal Causality

本文在Frobenius Markov范畴中引入无穷小因果性的范畴化描述，通过切丛语义刻画干预作为复制/丢弃结构的切形变，并定义因果充分性为两种Frobenius结构的兼容性。