Peter Spirtes

ICML Conference 2025 Conference Paper

Latent Variable Causal Discovery under Selection Bias

• Haoyue Dai
• Yiwen Qiu
• Ignavier Ng
• Xinshuai Dong
• Peter Spirtes
• Kun Zhang 0001

Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle latent variables, none have been adapted for selection bias. We make an attempt by studying rank constraints, which, as a generalization to conditional independence constraints, exploits the ranks of covariance submatrices in linear Gaussian models. We show that although selection can significantly complicate the joint distribution, interestingly, the ranks in the biased covariance matrices still preserve meaningful information about both causal structures and selection mechanisms. We provide a graph-theoretic characterization of such rank constraints. Using this tool, we demonstrate that the one-factor model, a classical latent variable model, can be identified under selection bias. Simulations and real-world experiments confirm the effectiveness of using our rank constraints.

TMLR Journal 2025 Journal Article

Long-Term Fairness Inquiries and Pursuits in Machine Learning: A Survey of Notions, Methods, and Challenges

• Usman Gohar
• Zeyu Tang
• Jialu Wang
• Kun Zhang
• Peter Spirtes
• Yang Liu
• Lu Cheng

The widespread integration of Machine Learning systems in daily life, particularly in high-stakes domains, has raised concerns about the fairness implications. While prior works have investigated static fairness measures, recent studies reveal that automated decision-making has long-term implications and that off-the-shelf fairness approaches may not serve the purpose of achieving long-term fairness. Additionally, the existence of feedback loops and the interaction between models and the environment introduces additional complexities that may deviate from the initial fairness goals. In this survey, we review existing literature on long-term fairness from different perspectives and present a taxonomy for long-term fairness studies. We highlight key challenges and consider future research directions, analyzing both current issues and potential further explorations.

ICML Conference 2025 Conference Paper

Permutation-based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data

• Xinshuai Dong
• Ignavier Ng
• Boyang Sun
• Haoyue Dai
• Guang-Yuan Hao
• Shunxing Fan
• Peter Spirtes
• Yumou Qiu

Recent advances have shown that statistical tests for the rank of cross-covariance matrices play an important role in causal discovery. These rank tests include partial correlation tests as special cases and provide further graphical information about latent variables. Existing rank tests typically assume that all the continuous variables can be perfectly measured, and yet, in practice many variables can only be measured after discretization. For example, in psychometric studies, the continuous level of certain personality dimensions of a person can only be measured after being discretized into order-preserving options such as disagree, neutral, and agree. Motivated by this, we propose Mixed data Permutation-based Rank Test (MPRT), which properly controls the statistical errors even when some or all variables are discretized. Theoretically, we establish the exchangeability and estimate the asymptotic null distribution by permutations; as a consequence, MPRT can effectively control the Type I error in the presence of discretization while previous methods cannot. Empirically, our method is validated by extensive experiments on synthetic data and real-world data to demonstrate its effectiveness as well as applicability in causal discovery (code will be available at https: //github. com/dongxinshuai/scm-identify).

ICLR Conference 2025 Conference Paper

Prompting Fairness: Integrating Causality to Debias Large Language Models

• Jingling Li
• Zeyu Tang 0002
• Xiaoyu Liu
• Peter Spirtes
• Kun Zhang 0001
• Liu Leqi
• Yang Liu 0018

Large language models (LLMs), despite their remarkable capabilities, are susceptible to generating biased and discriminatory responses. As LLMs increasingly influence high-stakes decision-making (e.g., hiring and healthcare), mitigating these biases becomes critical. In this work, we propose a causality-guided debiasing framework to tackle social biases, aiming to reduce the objectionable dependence between LLMs' decisions and the social information in the input. Our framework introduces a novel perspective to identify how social information can affect an LLM's decision through different causal pathways. Leveraging these causal insights, we outline principled prompting strategies that regulate these pathways through selection mechanisms. This framework not only unifies existing prompting-based debiasing techniques, but also opens up new directions for reducing bias by encouraging the model to prioritize fact-based reasoning over reliance on biased social cues. We validate our framework through extensive experiments on real-world datasets across multiple domains, demonstrating its effectiveness in debiasing LLM decisions, even with only black-box access to the model.

ICML Conference 2025 Conference Paper

Reflection-Window Decoding: Text Generation with Selective Refinement

• Zeyu Tang 0002
• Zhenhao Chen
• Xiangchen Song
• Loka Li
• Yunlong Deng
• Yifan Shen 0004
• Guangyi Chen 0002
• Peter Spirtes

The autoregressive decoding for text generation in large language models (LLMs), while widely used, is inherently suboptimal due to the lack of a built-in mechanism to perform refinement and/or correction of the generated content. In this paper, we consider optimality in terms of the joint probability over the generated response, when jointly considering all tokens at the same time. We theoretically characterize the potential deviation of the autoregressively generated response from its globally optimal counterpart that is of the same length. Our analysis suggests that we need to be cautious when noticeable uncertainty arises during text generation, which may signal the sub-optimality of the generation history. To address the pitfall of autoregressive decoding for text generation, we propose an approach that incorporates a sliding reflection window and a pausing criterion, such that refinement and generation can be carried out interchangeably as the decoding proceeds. Our selective refinement framework strikes a balance between efficiency and optimality, and our extensive experimental results demonstrate the effectiveness of our approach.

ICLR Conference 2025 Conference Paper

When Selection Meets Intervention: Additional Complexities in Causal Discovery

• Haoyue Dai
• Ignavier Ng
• Jianle Sun
• Zeyu Tang 0002
• Gongxu Luo
• Xinshuai Dong
• Peter Spirtes
• Kun Zhang 0001

We address the common yet often-overlooked selection bias in interventional studies, where subjects are selectively enrolled into experiments. For instance, participants in a drug trial are usually patients of the relevant disease; A/B tests on mobile applications target existing users only, and gene perturbation studies typically focus on specific cell types, such as cancer cells. Ignoring this bias leads to incorrect causal discovery results. Even when recognized, the existing paradigm for interventional causal discovery still fails to address it. This is because subtle differences in _when_ and _where_ interventions happen can lead to significantly different statistical patterns. We capture this dynamic by introducing a graphical model that explicitly accounts for both the observed world (where interventions are applied) and the counterfactual world (where selection occurs while interventions have not been applied). We characterize the Markov property of the model, and propose a provably sound algorithm to identify causal relations as well as selection mechanisms up to the equivalence class, from data with soft interventions and unknown targets. Through synthetic and real-world experiments, we demonstrate that our algorithm effectively identifies true causal relations despite the presence of selection bias.

ICLR Conference 2024 Conference Paper

A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables

• Xinshuai Dong
• Biwei Huang
• Ignavier Ng
• Xiangchen Song
• Yujia Zheng 0001
• Songyao Jin
• Roberto Legaspi
• Peter Spirtes

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of measured variables), based on rank information of covariance matrix over measured variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases. Our code will be publicly available.

JMLR Journal 2024 Journal Article

Causal-learn: Causal Discovery in Python

• Yujia Zheng
• Biwei Huang
• Wei Chen
• Joseph Ramsey
• Mingming Gong
• Ruichu Cai
• Shohei Shimizu
• Peter Spirtes

Causal discovery aims at revealing causal relations from observational data, which is a fundamental task in science and engineering. We describe causal-learn, an open-source Python library for causal discovery. This library focuses on bringing a comprehensive collection of causal discovery methods to both practitioners and researchers. It provides easy-to-use APIs for non-specialists, modular building blocks for developers, detailed documentation for learners, and comprehensive methods for all. Different from previous packages in R or Java, causal-learn is fully developed in Python, which could be more in tune with the recent preference shift in programming languages within related communities. The library is available at https://github.com/py-why/causal-learn. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

ICLR Conference 2024 Conference Paper

Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View

• Haoyue Dai
• Ignavier Ng
• Gongxu Luo
• Peter Spirtes
• Petar Stojanov
• Kun Zhang 0001

Gene regulatory network inference (GRNI) is a challenging problem, particularly owing to the presence of zeros in single-cell RNA sequencing data: some are biological zeros representing no gene expression, while some others are technical zeros arising from the sequencing procedure (aka dropouts), which may bias GRNI by distorting the joint distribution of the measured gene expressions. Existing approaches typically handle dropout error via imputation, which may introduce spurious relations as the true joint distribution is generally unidentifiable. To tackle this issue, we introduce a causal graphical model to characterize the dropout mechanism, namely, Causal Dropout Model. We provide a simple yet effective theoretical result: interestingly, the conditional independence (CI) relations in the data with dropouts, after deleting the samples with zero values (regardless if technical or not) for the conditioned variables, are asymptotically identical to the CI relations in the original data without dropouts. This particular test-wise deletion procedure, in which we perform CI tests on the samples without zeros for the conditioned variables, can be seamlessly integrated with existing structure learning approaches including constraint-based and greedy score-based methods, thus giving rise to a principled framework for GRNI in the presence of dropouts. We further show that the causal dropout model can be validated from data, and many existing statistical models to handle dropouts fit into our model as specific parametric instances. Empirical evaluation on synthetic, curated, and real-world experimental transcriptomic data comprehensively demonstrate the efficacy of our method.

NeurIPS Conference 2024 Conference Paper

Identifying Latent State-Transition Processes for Individualized Reinforcement Learning

• Yuewen Sun
• Biwei Huang
• Yu Yao
• Donghuo Zeng
• Xinshuai Dong
• Songyao Jin
• Boyang Sun
• Roberto Legaspi

The application of reinforcement learning (RL) involving interactions with individuals has grown significantly in recent years. These interactions, influenced by factors such as personal preferences and physiological differences, causally influence state transitions, ranging from health conditions in healthcare to learning progress in education. As a result, different individuals may exhibit different state-transition processes. Understanding individualized state-transition processes is essential for optimizing individualized policies. In practice, however, identifying these state-transition processes is challenging, as individual-specific factors often remain latent. In this paper, we establish the identifiability of these latent factors and introduce a practical method that effectively learns these processes from observed state-action trajectories. Experiments on various datasets show that the proposed method can effectively identify latent state-transition processes and facilitate the learning of individualized RL policies.

NeurIPS Conference 2024 Conference Paper

On the Parameter Identifiability of Partially Observed Linear Causal Models

• Xinshuai Dong
• Ignavier Ng
• Biwei Huang
• Yuewen Sun
• Songyao Jin
• Roberto Legaspi
• Peter Spirtes
• Kun Zhang

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research—we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime.

ICLR Conference 2024 Conference Paper

Procedural Fairness Through Decoupling Objectionable Data Generating Components

• Zeyu Tang 0002
• Jialu Wang
• Yang Liu 0018
• Peter Spirtes
• Kun Zhang 0001

We reveal and address the frequently overlooked yet important issue of _disguised procedural unfairness_, namely, the potentially inadvertent alterations on the behavior of neutral (i.e., not problematic) aspects of data generating process, and/or the lack of procedural assurance of the greatest benefit of the least advantaged individuals. Inspired by John Rawls's advocacy for _pure procedural justice_ (Rawls, 1971; 2001), we view automated decision-making as a microcosm of social institutions, and consider how the data generating process itself can satisfy the requirements of procedural fairness. We propose a framework that decouples the objectionable data generating components from the neutral ones by utilizing reference points and the associated value instantiation rule. Our findings highlight the necessity of preventing _disguised procedural unfairness_, drawing attention not only to the objectionable data generating components that we aim to mitigate, but also more importantly, to the neutral components that we intend to keep unaffected.

ICML Conference 2024 Conference Paper

Score-Based Causal Discovery of Latent Variable Causal Models

• Ignavier Ng
• Xinshuai Dong
• Haoyue Dai
• Biwei Huang
• Peter Spirtes
• Kun Zhang 0001

Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e. g. conditional independence or rank deficiency tests), they may face empirical challenges such as testing-order dependency, error propagation, and choosing an appropriate significance level. These issues can potentially be mitigated by properly designed score-based methods, such as Greedy Equivalence Search (GES) (Chickering, 2002) in the specific setting without latent variables. Yet, formulating score-based methods with latent variables is highly challenging. In this work, we develop score-based methods that are capable of identifying causal structures containing causally-related latent variables with identifiability guarantees. Specifically, we show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models. We further provide a characterization of the degrees of freedom for the marginal over the observed variables under multiple structural assumptions considered in the literature, and accordingly develop both exact and continuous score-based methods. This offers a unified view of several existing constraint-based methods with different structural assumptions. Experimental results validate the effectiveness of the proposed methods.

CLeaR Conference 2022 Conference Paper

A Uniformly Consistent Estimator of non-Gaussian Causal Effects Under the $k$-Triangle-Faithfulness Assumption

• Shuyan Wang
• Peter Spirtes

Kalisch and Bühlmann (2007) showed that for linear Gaussian models, under the Causal Markov Assumption, the Strong Causal Faithfulness Assumption, and the assumption of causal sufficiency, the PC algorithm is a uniformly consistent estimator of the Markov Equivalence Class of the true causal DAG for linear Gaussian models; it follows from this that for the identifiable causal effects in the Markov Equivalence Class, there are uniformly consistent estimators of causal effects as well. The $k$-Triangle-Faithfulness Assumption is a strictly weaker assumption that avoids some implausible implications of the Strong Causal Faithfulness Assumption and also allows for uniformly consistent estimates of Markov Equivalence Classes (in a weakened sense), and of identifiable causal effects. However, both of these assumptions are restricted to linear Gaussian models. We propose the Generalized $k$-Triangle Faithfulness, which can be applied to any smooth distribution. In addition, under the Generalized $k$-Triangle Faithfulness Assumption, we describe the Edge Estimation Algorithm that provides uniformly consistent estimators of causal effects in some cases (and otherwise outputs “can’t tell"), and the \textitVery Conservative $SGS$ Algorithm that (in a slightly weaker sense) is a uniformly consistent estimator of the Markov equivalence class of the true DAG.

NeurIPS Conference 2022 Conference Paper

Independence Testing-Based Approach to Causal Discovery under Measurement Error and Linear Non-Gaussian Models

• Haoyue Dai
• Peter Spirtes
• Kun Zhang

Causal discovery aims to recover causal structures generating the observational data. Despite its success in certain problems, in many real-world scenarios the observed variables are not the target variables of interest, but the imperfect measures of the target variables. Causal discovery under measurement error aims to recover the causal graph among unobserved target variables from observations made with measurement error. We consider a specific formulation of the problem, where the unobserved target variables follow a linear non-Gaussian acyclic model, and the measurement process follows the random measurement error model. Existing methods on this formulation rely on non-scalable over-complete independent component analysis (OICA). In this work, we propose the Transformed Independent Noise (TIN) condition, which checks for independence between a specific linear transformation of some measured variables and certain other measured variables. By leveraging the non-Gaussianity and higher-order statistics of data, TIN is informative about the graph structure among the unobserved target variables. By utilizing TIN, the ordered group decomposition of the causal model is identifiable. In other words, we could achieve what once required OICA to achieve by only conducting independence tests. Experimental results on both synthetic and real-world data demonstrate the effectiveness and reliability of our method.

UAI Conference 2018 Conference Paper

Causal Discovery with Linear Non-Gaussian Models under Measurement Error: Structural Identifiability Results

• Kun Zhang 0001
• Mingming Gong
• Joseph D. Ramsey
• Kayhan Batmanghelich
• Peter Spirtes
• Clark Glymour

Causal discovery methods aim to recover the causal process that generated purely observational data. Despite its successes on a number of real problems, the presence of measurement error in the observed data can produce serious mistakes in the output of various causal discovery methods. Given the ubiquity of measurement error caused by instruments or proxies used in the measuring process, this problem is one of the main obstacles to reliable causal discovery. It is still unknown to what extent the causal structure of relevant variables can be identified in principle. This study aims to take a step towards filling that void. We assume that the underlining process or the measurement-error free variables follows a linear, non-Guassian causal model, and show that the so-called ordered group decomposition of the causal model, which contains major causal information, is identifiable. The causal structure identifiability is further improved with different types of sparsity constraints on the causal structure. Finally, we give rather mild conditions under which the whole causal structure is fully identifiable.

UAI Conference 2013 Conference Paper

Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Models

• Peter Spirtes

The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this paper, I extend the Trek Separation Theorem in two ways: I prove that the same necessary and sufficient conditions apply even when the generating model is partially non-linear and contains some cycles. This justifies application of constraint-based causal search algorithms to data generated by a wider class of causal models that may contain non-linear and cyclic relations among the latent variables.

JMLR Journal 2010 Journal Article

Introduction to Causal Inference

• Peter Spirtes

The goal of many sciences is to understand the mechanisms by which variables came to take on the values they have (that is, to find a generative model), and to predict what the values of those variables would be if the naturally occurring mechanisms were subject to outside manipulations. The past 30 years has seen a number of conceptual developments that are partial solutions to the problem of causal inference from observational sample data or a mixture of observational sample and experimental data, particularly in the area of graphical causal modeling. However, in many domains, problems such as the large numbers of variables, small samples sizes, and possible presence of unmeasured causes, remain serious impediments to practical applications of these developments. The articles in the Special Topic on Causality address these and other problems in applying graphical causal modeling algorithms. This introduction to the Special Topic on Causality provides a brief introduction to graphical causal modeling, places the articles in a broader context, and describes the differences between causal inference and ordinary machine learning classification and prediction problems. [abs] [ pdf ][ bib ] &copy JMLR 2010. ( edit, beta )

NeurIPS Conference 2009 Conference Paper

Nonlinear directed acyclic structure learning with weakly additive noise models

• Arthur Gretton
• Peter Spirtes
• Robert Tillman

The recently proposed \emph{additive noise model} has advantages over previous structure learning algorithms, when attempting to recover some true data generating mechanism, since it (i) does not assume linearity or Gaussianity and (ii) can recover a unique DAG rather than an equivalence class. However, its original extension to the multivariate case required enumerating all possible DAGs, and for some special distributions, e. g. linear Gaussian, the model is invertible and thus cannot be used for structure learning. We present a new approach which combines a PC style search using recent advances in kernel measures of conditional dependence with local searches for additive noise models in substructures of the equivalence class. This results in a more computationally efficient approach that is useful for arbitrary distributions even when additive noise models are invertible. Experiments with synthetic and real data show that this method is more accurate than previous methods when data are nonlinear and/or non-Gaussian.

UAI Conference 2008 Conference Paper

Causal discovery of linear acyclic models with arbitrary distributions

• Patrik O. Hoyer
• Aapo Hyvärinen
• Richard Scheines
• Peter Spirtes
• Joseph D. Ramsey
• Gustavo Lacerda
• Shohei Shimizu

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 such models is a wellstudied problem. However, existing methods have significant limitations. Methods based on conditional independencies (Spirtes et al. 1993; Pearl 2000) cannot distinguish between independence-equivalent models, whereas approaches purely based on Independent Component Analysis (Shimizu et al. 2006) are inapplicable to data which is partially Gaussian. In this paper, we generalize and combine the two approaches, to yield a method able to learn the model structure in many cases for which the previous methods provide answers that are either incorrect or are not as informative as possible. We give exact graphical conditions for when two distinct models represent the same family of distributions, and empirically demonstrate the power of our method through thorough simulations.

UAI Conference 2008 Conference Paper

Discovering Cyclic Causal Models by Independent Components Analysis

• Gustavo Lacerda
• Peter Spirtes
• Joseph D. Ramsey
• Patrik O. Hoyer

We generalize Shimizu et al’s (2006) ICA-based approach for discovering linear non-Gaussian acyclic (LiNGAM) Structural Equation Models (SEMs) from causally sufficient, continuous-valued observational data. By relaxing the assumption that the generating SEM’s graph is acyclic, we solve the more general problem of linear non-Gaussian (LiNG) SEM discovery. LiNG discovery algorithms output the distribution equivalence class of SEMs which, in the large sample limit, represents the population distribution. We apply a LiNG discovery algorithm to simulated data. Finally, we give sufficient conditions under which only one of the SEMs in the output class is “stable”.

UAI Conference 2006 Conference Paper

A Theoretical Study of Y Structures for Causal Discovery

• Subramani Mani
• Gregory F. Cooper
• Peter Spirtes

UAI Conference 2006 Conference Paper

Adjacency-Faithfulness and Conservative Causal Inference

• Joseph D. Ramsey
• Jiji Zhang
• Peter Spirtes

JMLR Journal 2006 Journal Article

Learning the Structure of Linear Latent Variable Models

• Ricardo Silva
• Richard Scheine
• Clark Glymour
• Peter Spirtes

We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems. [abs] [ pdf ][ bib ] &copy JMLR 2006. ( edit, beta )

UAI Conference 2005 Conference Paper

A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables

• Jiji Zhang
• Peter Spirtes

UAI Conference 2005 Conference Paper

Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables

• Ayesha R. Ali
• Thomas S. Richardson 0001
• Peter Spirtes
• Jiji Zhang

UAI Conference 2003 Conference Paper

Learning Measurement Models for Unobserved Variables

• Ricardo Bezerra de Andrade e Silva
• Richard Scheines
• Clark Glymour
• Peter Spirtes

Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical domains. Previous work shows that, given a partition of observed variables such that members of a class share only a single latent common cause, standard search algorithms for causal Bayes nets can infer structural relations between latent variables. We introduce an algorithm for discovering such partitions when they exist. Uniquely among available procedures, the algorithm is (asymptotically) correct under standard assumptions in causal Bayes net search algorithms, requires no prior knowledge of the number of latent variables, and does not depend on the mathematical form of the relationships among the latent variables. We evaluate the algorithm on a variety of simulated data sets.

UAI Conference 2003 Conference Paper

Strong Faithfulness and Uniform Consistency in Causal Inference

• Jiji Zhang
• Peter Spirtes

UAI Conference 2001 Conference Paper

Semi-Instrumental Variables: A Test for Instrument Admissibility

• Tianjiao Chu
• Richard Scheines
• Peter Spirtes

AIIM Journal 1997 Journal Article

An evaluation of machine-learning methods for predicting pneumonia mortality

• Gregory F. Cooper
• Constantin F. Aliferis
• Richard Ambrosino
• John Aronis
• Bruce G. Buchanan
• Richard Caruana
• Michael J. Fine
• Clark Glymour

This paper describes the application of eight statistical and machine-learning methods to derive computer models for predicting mortality of hospital patients with pneumonia from their findings at initial presentation. The eight models were each constructed based on 9847 patient cases and they were each evaluated on 4352 additional cases. The primary evaluation metric was the error in predicted survival as a function of the fraction of patients predicted to survive. This metric is useful in assessing a model's potential to assist a clinician in deciding whether to treat a given patient in the hospital or at home. We examined the error rates of the models when predicting that a given fraction of patients will survive. We examined survival fractions between 0. 1 and 0. 6. Over this range, each model's predictive error rate was within 1% of the error rate of every other model. When predicting that approximately 30% of the patients will survive, all the models have an error rate of less than 1. 5%. The models are distinguished more by the number of variables and parameters that they contain than by their error rates; these differences suggest which models may be the most amenable to future implementation as paper-based guidelines.

UAI Conference 1995 Conference Paper

Causal Inference in the Presence of Latent Variables and Selection Bias

• Peter Spirtes
• Christopher Meek
• Thomas S. Richardson 0001

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

UAI Conference 1995 Conference Paper

Directed Cyclic Graphical Representations of Feedback Models

• Peter Spirtes

The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However, non-recursive structural equation models of the kinds used to model economic processes are naturally represented by directed cyclic graphs with independent errors, a characterization of conditional independence errors, a characterization of conditional independence constraints is obtained, and it is shown that the result generalizes in a natural way to systems in which the error variables or noises are statistically dependent. For non-linear systems with independent errors a sufficient condition for conditional independence of variables in associated distributions is obtained.

UAI Conference 1991 Conference Paper

Detecting Causal Relations in the Presence of Unmeasured Variables

• Peter Spirtes