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Caroline Uhler - One of the best experts on this subject based on the ideXlab platform.

  • Causal Structure discovery from distributions arising from mixtures of dags
    arXiv: Machine Learning, 2020
    Co-Authors: Basil Saeed, Snigdha Panigrahi, Caroline Uhler
    Abstract:

    We consider distributions arising from a mixture of Causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of Structure learning based on samples from such distributions. Since the mixing variable is latent, we consider Causal Structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a "union" of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this Causal information can be used to cluster samples according to each mixture component.

  • ordering based Causal Structure learning in the presence of latent variables
    arXiv: Statistics Theory, 2019
    Co-Authors: Daniel Irving Bernstein, Basil Saeed, Chandler Squires, Caroline Uhler
    Abstract:

    We consider the task of learning a Causal graph in the presence of latent confounders given i.i.d.~samples from the model. While current algorithms for Causal Structure discovery in the presence of latent confounders are constraint-based, we here propose a score-based approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the \emph{Sparsest Poset} formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for Causal Structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.

  • abcd strategy budgeted experimental design for targeted Causal Structure discovery
    International Conference on Artificial Intelligence and Statistics, 2019
    Co-Authors: Raj Agrawal, Chandler Squires, Karren D Yang, Karthikeyan Shanmugam, Caroline Uhler
    Abstract:

    Determining the Causal Structure of a set of variables is critical for both scientific inquiry and decision-making. However, this is often challenging in practice due to limited interventional data. Given that randomized experiments are usually expensive to perform, we propose a general framework and theory based on optimal Bayesian experimental design to select experiments for targeted Causal discovery. That is, we assume the experimenter is interested in learning some function of the unknown graph (e.g., all descendants of a target node) subject to design constraints such as limits on the number of samples and rounds of experimentation. While it is in general computationally intractable to select an optimal experimental design strategy, we provide a tractable implementation with provable guarantees on both approximation and optimization quality based on submodularity. We evaluate the efficacy of our proposed method on both synthetic and real datasets, thereby demonstrating that our method realizes considerable performance gains over baseline strategies such as random sampling.

Tom Heskes - One of the best experts on this subject based on the ideXlab platform.

  • Learning Causal Structure from mixed data with missing values using Gaussian copula models
    Statistics and Computing, 2018
    Co-Authors: Perry Groot, Tom Heskes
    Abstract:

    We consider the problem of Causal Structure learning from data with missing values, assumed to be drawn from a Gaussian copula model. First, we extend the ‘Rank PC’ algorithm, designed for Gaussian copula models with purely continuous data (so-called nonparanormal models), to incomplete data by applying rank correlation to pairwise complete observations and replacing the sample size with an effective sample size in the conditional independence tests to account for the information loss from missing values. When the data are missing completely at random (MCAR), we provide an error bound on the accuracy of ‘Rank PC’ and show its high-dimensional consistency. However, when the data are missing at random (MAR), ‘Rank PC’ fails dramatically. Therefore, we propose a Gibbs sampling procedure to draw correlation matrix samples from mixed data that still works correctly under MAR. These samples are translated into an average correlation matrix and an effective sample size, resulting in the ‘Copula PC’ algorithm for incomplete data. Simulation study shows that: (1) ‘Copula PC’ estimates a more accurate correlation matrix and Causal Structure than ‘Rank PC’ under MCAR and, even more so, under MAR and (2) the usage of the effective sample size significantly improves the performance of ‘Rank PC’ and ‘Copula PC.’ We illustrate our methods on two real-world datasets: riboflavin production data and chronic fatigue syndrome data.

  • ICDM - Robust Estimation of Gaussian Copula Causal Structure from Mixed Data with Missing Values
    2017 IEEE International Conference on Data Mining (ICDM), 2017
    Co-Authors: Perry Groot, Tom Heskes
    Abstract:

    We consider the problem of Causal Structure learning from data with missing values, assumed to be drawn from a Gaussian copula model. First, we extend the 'Rank PC' algorithm, designed for Gaussian copula models with purely continuous data (so-called nonparanormal models), to incomplete data by applying rank correlation to pairwise complete observations and replacing the sample size with an effective sample size in the conditional independence tests to account for the information loss from missing values. The resulting approach works when the data are missing completely at random (MCAR). Then, we propose a Gibbs sampling procedure to draw correlation matrix samples from mixed data under missingness at random (MAR). These samples are translated into an average correlation matrix, and an effective sample size, resulting in the 'Copula PC' algorithm for incomplete data. Simulation study shows that: 1) the usage of the effective sample size significantly improves the performance of 'Rank PC' and 'Copula PC'; 2) 'Copula PC' estimates a more accurate correlation matrix and Causal Structure than 'Rank PC' under MCAR and, even more so, under MAR. Also, we illustrate our methods on a real-world data set about gene expression.

James Cussens - One of the best experts on this subject based on the ideXlab platform.

  • Online Causal Structure Learning in the Presence of Latent Variables.
    arXiv: Artificial Intelligence, 2019
    Co-Authors: Durdane Kocacoban, James Cussens
    Abstract:

    We present two online Causal Structure learning algorithms which can track changes in a Causal Structure and process data in a dynamic real-time manner. Standard Causal Structure learning algorithms assume that Causal Structure does not change during the data collection process, but in real-world scenarios, it does often change. Therefore, it is inappropriate to handle such changes with existing batch-learning approaches, and instead, a Structure should be learned in an online manner. The online Causal Structure learning algorithms we present here can revise correlation values without reprocessing the entire dataset and use an existing model to avoid relearning the Causal links in the prior model, which still fit data. Proposed algorithms are tested on synthetic and real-world datasets, the latter being a seasonally adjusted commodity price index dataset for the U.S. The online Causal Structure learning algorithms outperformed standard FCI by a large margin in learning the changed Causal Structure correctly and efficiently when latent variables were present.

  • ICMLA - Online Causal Structure Learning in the Presence of Latent Variables
    2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA), 2019
    Co-Authors: Durdane Kocacoban, James Cussens
    Abstract:

    We present two online Causal Structure learning algorithms which can track changes in a Causal Structure and process data in a dynamic real-time manner. Standard Causal Structure learning algorithms assume that Causal Structure does not change during the data collection process, but in real-world scenarios, it often does change. The algorithms proposed here can revise correlation values without reprocessing the entire dataset and use an existing model to avoid relearning the Causal links in the prior model, which still fit data. Proposed algorithms are tested on synthetic datasets. The online Causal Structure learning algorithms outperformed standard FCI by a large margin in learning the changed Causal Structure correctly and efficiently when latent variables were present.

Perry Groot - One of the best experts on this subject based on the ideXlab platform.

  • Learning Causal Structure from mixed data with missing values using Gaussian copula models
    Statistics and Computing, 2018
    Co-Authors: Perry Groot, Tom Heskes
    Abstract:

    We consider the problem of Causal Structure learning from data with missing values, assumed to be drawn from a Gaussian copula model. First, we extend the ‘Rank PC’ algorithm, designed for Gaussian copula models with purely continuous data (so-called nonparanormal models), to incomplete data by applying rank correlation to pairwise complete observations and replacing the sample size with an effective sample size in the conditional independence tests to account for the information loss from missing values. When the data are missing completely at random (MCAR), we provide an error bound on the accuracy of ‘Rank PC’ and show its high-dimensional consistency. However, when the data are missing at random (MAR), ‘Rank PC’ fails dramatically. Therefore, we propose a Gibbs sampling procedure to draw correlation matrix samples from mixed data that still works correctly under MAR. These samples are translated into an average correlation matrix and an effective sample size, resulting in the ‘Copula PC’ algorithm for incomplete data. Simulation study shows that: (1) ‘Copula PC’ estimates a more accurate correlation matrix and Causal Structure than ‘Rank PC’ under MCAR and, even more so, under MAR and (2) the usage of the effective sample size significantly improves the performance of ‘Rank PC’ and ‘Copula PC.’ We illustrate our methods on two real-world datasets: riboflavin production data and chronic fatigue syndrome data.

  • ICDM - Robust Estimation of Gaussian Copula Causal Structure from Mixed Data with Missing Values
    2017 IEEE International Conference on Data Mining (ICDM), 2017
    Co-Authors: Perry Groot, Tom Heskes
    Abstract:

    We consider the problem of Causal Structure learning from data with missing values, assumed to be drawn from a Gaussian copula model. First, we extend the 'Rank PC' algorithm, designed for Gaussian copula models with purely continuous data (so-called nonparanormal models), to incomplete data by applying rank correlation to pairwise complete observations and replacing the sample size with an effective sample size in the conditional independence tests to account for the information loss from missing values. The resulting approach works when the data are missing completely at random (MCAR). Then, we propose a Gibbs sampling procedure to draw correlation matrix samples from mixed data under missingness at random (MAR). These samples are translated into an average correlation matrix, and an effective sample size, resulting in the 'Copula PC' algorithm for incomplete data. Simulation study shows that: 1) the usage of the effective sample size significantly improves the performance of 'Rank PC' and 'Copula PC'; 2) 'Copula PC' estimates a more accurate correlation matrix and Causal Structure than 'Rank PC' under MCAR and, even more so, under MAR. Also, we illustrate our methods on a real-world data set about gene expression.

Ding Jia - One of the best experts on this subject based on the ideXlab platform.

  • Ultraviolet regularity from quantum gravitational indefinite Causal Structure
    arXiv: General Relativity and Quantum Cosmology, 2020
    Co-Authors: Ding Jia
    Abstract:

    Indefinite Causal Structure is generically present in theories of quantum gravity admitting a path integral formulation. We show that summing over Causal Structures eliminates ultraviolet divergences of matter QFT and resolves spacetime singularities using the non-perturbative World Quantum Gravity approach. Independent information-theoretic and model-independent considerations suggest that the mechanism of ultraviolet regularization by indefinite Causal Structure also applies to other theories of quantum gravity.

  • Quantum theories from principles without assuming a definite Causal Structure
    Physical Review A, 2018
    Co-Authors: Ding Jia
    Abstract:

    There has been a body of work deriving the complex Hilbert-space Structure of quantum theory from axioms/principles/postulates to deepen our understanding of quantum theory and to reveal ways to go beyond it to resolve foundational issues. Recent progress in incorporating indefinite Causal Structure into physical theories suggests that a more comprehensive understanding of both quantum theory and the theory beyond it accounts for indefinite Causal Structure. We formulate a framework of physical theories without assuming definite Causal Structure and identify postulates that single out the complex Hilbert-space Structure. More than one complex Hilbert-space theory is compatible with the postulates, which leaves room for further search for the best among these theories.

  • Reduction of correlations by quantum indefinite Causal Structure
    arXiv: Quantum Physics, 2018
    Co-Authors: Ding Jia
    Abstract:

    We show that quantum indefinite Causal Structure generically reduce two-party correlations. For significant indefiniteness in the Causal Structure captured by some general conditions, the correlation is shown to be reduced down to zero. The result offers an operational model-independent ultraviolet regularization mechanism. It may be applied to various approaches of quantum gravity that allow quantum indefinite spacetime Causal Structure.

  • Quantum field theory with indefinite Causal Structure
    arXiv: Quantum Physics, 2018
    Co-Authors: Ding Jia
    Abstract:

    Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may be relevant for a better understanding of these topics, a commonly accepted framework for studying QFT with quantum gravitational effects is missing. We present a theory for studying quantum fields in the presence of quantum indefinite Causal Structure. This theory incorporates quantum properties of spacetime Causal Structure in a model independent way, and exposes universal features of quantum spacetime which are independent of the details about its microscopic degrees of freedom (strings, loops, Causal sets...).