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Page 1594 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Sarkaria (6-PUNJ; Chandigarh) 2003c:05082 05C15 06A07 68R10 68T37 Mati, FrantiSek (CZ-AOS-I; Prague) Lengths of semigraphoid inferences.  ...  This is the first known example of an exponentially long semigraphoid inference. A comparison is made between local and global inferences.  ... 

On an additive partial correlation operator and nonparametric estimation of graphical models

Kuang-Yao Lee, Bing Li, Hongyu Zhao
2016 Biometrika  
interdependence, which leads to more accurate statistical inference.  ...  We establish the consistency of the proposed estimator.  ...  National Science Foundation; Hongyu Zhao's research was supported in part by both the National Science Foundation and the National Institutes of Health.  ... 
doi:10.1093/biomet/asw028 pmid:29422689 pmcid:PMC5793672 fatcat:4yllodfgzvanffj7dp5dmht4ny

Temporal Inference with Finite Factored Sets [article]

Scott Garrabrant
2021 arXiv   pre-print
We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally.  ...  Rather than using directed acyclic graphs, we make use of factored sets, which are sets expressed as Cartesian products.  ...  Let S = Ω ∪ {00, 01, 10, 11} be the set of all bit strings of length either 2 or 3.  ... 
arXiv:2109.11513v1 fatcat:xm4rxwqmmvdldhpgamonluiz6y

Marginals of DAG-Isomorphic Independence Models [chapter]

Peter R. de Waal
2009 Lecture Notes in Computer Science  
The original independence model can then be viewed as the marginal of the model with latent variables.  ...  We investigate if a given probabilistic independence model can be augmented with latent variables to a new independence model that is isomorphic with a graphical independence model of a directed acyclic  ...  Gill for suggesting this problem in the context of probabilistic graphical models, and an anonymous referee for valuable comments that helped to improve Sections 3 and 4.  ... 
doi:10.1007/978-3-642-02906-6_18 fatcat:4yyycsnsh5dxncjs4zzcedj6tu

Graphoids and natural conditional functions

Daniel Hunter
1991 International Journal of Approximate Reasoning  
A natural conditional function (NCF) is a function from possible states of the world to natural numbers, representing the degrees of implausibility of the different states.  ...  This paper shows that the relation of conditional independence, when defined in terms of NCFs, has a natural representation in terms of influence diagrams.  ...  Furthermore, M of necessity is a semigraphoid.  ... 
doi:10.1016/0888-613x(91)90026-i fatcat:mwtigwoogjfxtfa7pjku3z3axm

Consistency Guarantees for Greedy Permutation-Based Causal Inference Algorithms [article]

Liam Solus, Yuhao Wang, Caroline Uhler
2021 arXiv   pre-print
Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed acyclic graphs or Markov equivalence classes of directed acyclic graphs  ...  A walk is performed on the edges of the polytope maximizing the sparsity of the associated directed acyclic graphs.  ...  Let S p denote the space of all permutations of length p.  ... 
arXiv:1702.03530v4 fatcat:ydvrljejezdjrdemzbanjxibi4

Greedy Relaxations of the Sparsest Permutation Algorithm [article]

Wai-Yin Lam, Bryan Andrews, Joseph Ramsey
2022 arXiv   pre-print
There has been an increasing interest in methods that exploit permutation reasoning to search for directed acyclic causal models, including the "Ordering Search" of Teyssier and Kohler and GSP of Solus  ...  We extend the methods of the latter by a permutation-based operation, tuck, and develop a class of algorithms, namely GRaSP, that are efficient and pointwise consistent under increasingly weaker assumptions  ...  The variables in the example are as follows: (1) Velocity of the wind in the tunnel, (2) chord length of the airfoil, (3) angle of attack of the airfoil, (4) displacement of the wind away from the airfoil  ... 
arXiv:2206.05421v1 fatcat:nt6lv4wnvjcitlwiz5lufl6d2i

Causal Markov condition for submodular information measures [article]

Bastian Steudel, Dominik Janzing, Bernhard Schoelkopf
2010 arXiv   pre-print
., the length of a text after applying existing data compression schemes.  ...  Our experiments on real data demonstrate the performance of compression based causal inference.  ...  Nevertheless I satisfies the semigraphoid axioms and can thus be considered as a measure of independence.  ... 
arXiv:1002.4020v1 fatcat:xua3zfuu5jeofojgphublv43xe

Constructing the dependency structure of a multiagent probabilistic network

S.K.M. Wong, C.J. Butz
2001 IEEE Transactions on Knowledge and Data Engineering  
That is, every probabilistic conditional independency logically implied by the minimal cover can be inferred from the dependency structure and every probabilistic conditional independency inferred from  ...  The main result of this paper is that the constructed dependency structure is a perfect-map of the minimal cover.  ...  The relation È x has P k rows, one row for each sequence of zeros and ones of length k. (Recall that k is the number of sets in hep such that I P F F F k x À .)  ... 
doi:10.1109/69.929898 fatcat:yfj5xu52ljf4xbtyojpest7fsa

The Gaussian conditional independence inference problem [article]

Tobias Boege, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Thomas Kahle, Volker Kaibel
2022
The inference problem then becomes a question of the geometry of certain real varieties inside of the cone of positive-definite matrices. This thesis studies the Gauss [...]  ...  Conditional independence relations are formally studied in branches of artificial intelligence by means of logical inference rules.  ...  length of an input object?  ... 
doi:10.25673/86275 fatcat:ltjuwngiyzhbpgoy45wwcjzp7y

Total positivity in Markov structures [article]

Shaun Fallat, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny Wermuth, Piotr Zwiernik
2016 arXiv   pre-print
In particular, we show that any independence model generated by an MTP2 distribution is a compositional semigraphoid which is upward-stable and singleton-transitive.  ...  We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence.  ...  This article represents research initiated at the American Institute of Mathematics workshop "Positivity, Graphical Models, and the Modeling of Complex Multivariate Dependencies" in October 2014.  ... 
arXiv:1510.01290v2 fatcat:luxrzdfdq5gnbhubb3iesz25cq

A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics [article]

Tobias Fritz
2020 arXiv   pre-print
, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.  ...  Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory  ...  attempted to construct quantum analogues of Bayesian inference and Bayesian networks.  ... 
arXiv:1908.07021v7 fatcat:h2ll5fe4wnfazdan4pjh3oocmy

Estimating causal structure using conditional DAG models [article]

Chris J. Oates, Jim Q. Smith, Sach Mukherjee
2014 arXiv   pre-print
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs".  ...  We give causal semantics for this model class and prove that, under certain assumptions, the direction of causal influence is identifiable from the joint observational distribution of the primary and secondary  ...  We focus on structural inference in the sense of estimation of the presence or absence of edges in the causal graph rather than estimation of quantitative causal effects.  ... 
arXiv:1411.2755v1 fatcat:t4ngrd4hzzcrvojvf42td6v22a

Page 2085 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Mare§, Milan (with Mesiar, Radko) Verbally generated fuzzy quantities and their aggregation. 2003j:03071 MataS, FrantiSek Lengths of semigraphoid inferences.  ...  English and Chinese summaries) 2003k:60005 Li, Shou Wei (with Shi, Kai Quan) The neural network with fuzzy inference function.  ... 

Estimating Causal Structure Using Conditional DAG Models

Chris J. Oates, Jim Q. Smith, Sach Mukherjee
2016 Journal of machine learning research  
This paper considers inference of causal structure in a class of graphical models called conditional DAGs.  ...  The secondary variables are used to aid in the estimation of the structure of causal relationships between the primary variables.  ...  Pearl and Verma (1987) proposed such a set of rules (the semigraphoid axioms) that any reasonable set of assertions about how one set of variables might be irrelevant to the prediction of a second, given  ... 
dblp:journals/jmlr/OatesSM16 fatcat:japc22pchbcudfgwmgdgrkjpb4
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