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On the Semi-Markov Equivalence of Causal Models [article]

Benoit Desjardins
2013 arXiv   pre-print
Without causal sufficiency, an infinite semi-Markov equivalence class of models has only been characterized by the fact that each model in the equivalence class entails the same marginal statistical dependencies  ...  In this paper, we study the variability of structure of causal models within a semi-Markov equivalence class and propose a systematic approach to construct models entailing any specific marginal statistical  ...  But this approach fails to consider the exten sive variability of graphical structure in sets of semi Markov equivalent causal models.  ... 
arXiv:1301.7370v1 fatcat:46kp36ggdbbpbbfaaxdvus4c3u

Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processes [article]

S. E. Marzen, J. P. Crutchfield
2020 arXiv   pre-print
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground.  ...  Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.  ...  Army Research Office under contract W911NF-13-1-0390 and grant W911NF-18-1-0028, the U.S. Department of Energy under grant de-sc0017324, and the Moore Foundation.  ... 
arXiv:2005.03750v1 fatcat:fwxzmon3zzep7ojzm3bcjmztsm

Structure and Randomness of Continuous-Time, Discrete-Event Processes

Sarah E. Marzen, James P. Crutchfield
2017 Journal of statistical physics  
We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models---memoryful, state-dependent versions of renewal  ...  Calculating these quantities requires introducing novel mathematical objects (ϵ-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.  ...  ACKNOWLEDGMENTS The authors thank Santa Fe Institute for its hospitality during visits, A. Boyd, C. Hillar, and D. Upper for useful discussions, and T. Elliott for the example of  ... 
doi:10.1007/s10955-017-1859-y fatcat:ub4yyks6crg2jaoubkuzajiuei

Informational and Causal Architecture of Continuous-time Renewal Processes

Sarah Marzen, James P. Crutchfield
2017 Journal of statistical physics  
We introduce the minimal maximally predictive models (ϵ-machines) of processes generated by certain hidden semi-Markov models.  ...  We present a complete analysis of the ϵ-machines of continuous-time renewal processes and, then, extend this to processes generated by unifilar hidden semi-Markov models and semi-Markov models.  ...  Berkeley Chancellor's Fellowship, and the MIT Physics of Living Systems Fellowship.  ... 
doi:10.1007/s10955-017-1793-z fatcat:6deeel5vyfhd5pfr3or3wnrn5y

ASP-based Discovery of Semi-Markovian Causal Models under Weaker Assumptions [article]

Zhalama and Jiji Zhang and Frederick Eberhardt and Wolfgang Mayer and Mark Junjie Li
2019 arXiv   pre-print
In this paper, we study weakenings of Faithfulness for constraint-based discovery of semi-Markovian causal models, which accommodate the possibility of latent variables, and show that both (1) and (2)  ...  However, this line of work has so far only considered the discovery of causal models without latent variables.  ...  Acknowledgments JZ was supported by GRF LU13602818 from the RGC of Hong Kong. FE was supported by NSF grant 1564330.  ... 
arXiv:1906.02385v1 fatcat:6d5h4yu4qnfdrh7l7lvg3bouea

IDA with Background Knowledge

Zhuangyan Fang, Yangbo He
2020 Conference on Uncertainty in Artificial Intelligence  
In this paper, we consider the problem of estimating all possible causal effects from observational data with two types of background knowledge: direct causal information and nonancestral information.  ...  Based on the proposed rules, we present a fully local algorithm to estimate all possible causal effects with direct causal information.  ...  This research was supported by National Key R&D Program of China (2018YFB1004300) and NSFC (11671020).  ... 
dblp:conf/uai/FangH20 fatcat:hwttgwdp2zclzny3hgawtqsjbe

Information symmetries in irreversible processes

Christopher J. Ellison, John R. Mahoney, Ryan G. James, James P. Crutchfield, Jörg Reichardt
2011 Chaos  
Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional correlations.  ...  We analyze example irreversible processes whose epsilon-machine presentations change size under time reversal, including one which has a finite number of recurrent causal states in one direction, but an  ...  or the Department of Defense.  ... 
doi:10.1063/1.3637490 pmid:21974670 fatcat:hbvuix622nc4lj52gl2dr5mzvq

Faithfulness of Probability Distributions and Graphs [article]

Kayvan Sadeghi
2017 arXiv   pre-print
This allows us to provide sufficient conditions for a given independence model to be Markov to a graph with the minimum possible number of edges, and more importantly, necessary and sufficient conditions  ...  A main question in graphical models and causal inference is whether, given a probability distribution P (which is usually an underlying distribution of data), there is a graph (or graphs) to which P is  ...  Acknowledgments The original idea of this paper was inspired by discussions at the American Institute of Mathematics workshop "Positivity, Graphical Models, and the Modeling of Complex Multivariate Dependencies  ... 
arXiv:1701.08366v2 fatcat:yvgu5zwzwrhptgar2g7yejwuhi

Conditions and Assumptions for Constraint-based Causal Structure Learning [article]

Kayvan Sadeghi, Terry Soo
2022 arXiv   pre-print
We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph.  ...  We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph.  ...  and to Jonas Peters for hosting a first author's visit, during which some of the ideas used in this paper were discussed.  ... 
arXiv:2103.13521v3 fatcat:hl4b6gymrrbplhboruebrlikki

Prediction and Dissipation in Nonequilibrium Molecular Sensors: Conditionally Markovian Channels Driven by Memoryful Environments

Sarah E. Marzen, James P. Crutchfield
2020 Bulletin of Mathematical Biology  
hidden semi-Markov) environmental inputs in nonequilibrium steady state.  ...  Success in deriving these formulae relies on identifying the environment's causal states, the input's minimal sufficient statistics for prediction.  ...  of a unifilar hidden semi-Markov model.  ... 
doi:10.1007/s11538-020-00694-2 pmid:31993762 fatcat:tyybv4qmffeprpnk4pobqm3hmm

Algorithms for Discovery of Multiple Markov Boundaries

Alexander Statnikov, Nikita I Lytkin, Jan Lemeire, Constantin F Aliferis
2013 Journal of machine learning research  
and give insight on local causal structure.  ...  Over the last decade many sound algorithms have been proposed to identify a single Markov boundary of the response variable.  ...  subset of data samples (training set), classification models based on the above variables are also developed in the training set, and the reported performance of classification models is estimated in  ... 
pmid:25285052 pmcid:PMC4184048 fatcat:xtopmlggcrdsrcyjpit5ydkqbm

Discrete Information Dynamics with Confidence via the Computational Mechanics Bootstrap: Confidence Sets and Significance Tests for Information-Dynamic Measures

David Darmon
2020 Entropy  
Via Monte Carlo simulation, we compare the inferential properties of the computational mechanics bootstrap to a Markov model bootstrap.  ...  The computational mechanics bootstrap is shown to have desirable inferential properties for a collection of model systems and generally outperforms the Markov model bootstrap.  ...  Conflicts of Interest: The author declares no conflict of interest. Abbreviations The following abbreviation is used in this manuscript: CSSR Causal State Splitting Reconstruction  ... 
doi:10.3390/e22070782 pmid:33286553 fatcat:3h62sdqslzcqxc3gu5xqa5hhzm

Causal Graphical Models with Latent Variables: Learning and Inference [chapter]

Stijn Meganck, Philippe Leray, Bernard Manderick
2007 Lecture Notes in Computer Science  
We will do this by proposing an alternative representation for semi-Markovian causal models.  ...  Previously an algorithm has been constructed that by combining elements from both techniques allows to learn a semi-Markovian causal models from a mixture of observational and experimental data.  ...  Acknowledgements This work was partially supported by the IST Programme of the European Community, under the PASCAL network of Excellence, IST-2002-506778.  ... 
doi:10.1007/978-3-540-75256-1_4 fatcat:jritqd44njevjh3a64au433awy

Unifying DAGs and UGs [article]

Jose M. Peña
2018 arXiv   pre-print
We also present an equivalent factorization property. Finally, we present a causal interpretation of the new models.  ...  Moreover, up to two edges are allowed between any pair of nodes. Specifically, we present local, pairwise and global Markov properties for the new graphical models and prove their equivalence.  ...  The following lemma shows that the existence of a semi-directed cycle is not sufficient to declare an UDAG non-equivalent to any LWF CG.  ... 
arXiv:1708.08722v8 fatcat:mkblo7fa25f6zkm7m6axru3r34

Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?

Joshua B. Ruebeck, Ryan G. James, John R. Mahoney, James P. Crutchfield
2018 Chaos  
Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process.  ...  Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation.  ...  Army Research Laboratory and the U. S. Army Research Office under contracts W911NF-13-1-0390 and W911NF-13-1-0340. JR was funded by the 2016 NSF Research Experience for Undergraduates program.  ... 
doi:10.1063/1.5003041 pmid:29390624 fatcat:vgwkyy4z6jb37pbkighycoslbu
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