scholarly journals On the conditional independence implication problem: A lattice-theoretic approach

2013 ◽  
Vol 202 ◽  
pp. 29-51 ◽  
Author(s):  
Mathias Niepert ◽  
Marc Gyssens ◽  
Bassem Sayrafi ◽  
Dirk Van Gucht
Keyword(s):  
Conditional Independence ◽  
Theoretic Approach ◽  
Implication Problem

scholarly journals A linear-algebraic tool for conditional independence inference

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Kentaro Tanaka ◽  
Milan Studeny ◽  
Akimichi Takemura ◽  
Tomonari Sei
Keyword(s):  
Computational Result ◽  
Conditional Independence ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Positive Density ◽  
Implication Problem ◽  
Algebraic Tool ◽  
Linear Algebraic Method

In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables. 

Conditioning

2021 ◽  
pp. 190-212
Author(s):  
James Davidson
Keyword(s):  
Conditional Expectation ◽  
Conditional Independence ◽  
Theoretic Approach ◽  
Conditional Distributions

This chapter deals in depth with the concept of conditional expectation. This is defined first in the traditional “naïve” manner, and then using the measure theoretic approach. A comprehensive set of properties of the conditional expectation are proved, generalizing several results of Ch. 9, and then multiple sub‐σ‎‎‐fields and nesting are considered, concluding with a treatment of conditional distributions and conditional independence.

CONDITIONAL INDEPENDENCE RELATIONS IN POSSIBILITY THEORY

2000 ◽  
Vol 08 (03) ◽  
pp. 253-269 ◽  
Author(s):  
JIŘINA VEJNAROVÁ
Keyword(s):  
Conditional Independence ◽  
Possibility Theory ◽  
Theoretic Approach ◽  
Formal Properties ◽  
Independence Relations

The goal of this paper is to survey and briefly discuss various rules of conditioning proposed in the framework of possibility theory, as well as various conditional independence relations suggested for these rules. These conditioning rules and conditional independence relations are confronted with formal properties of conditional independence. Special attention is paid to the conditioning in the sense of measure-theoretic approach (based on the notion of a t-norm) recently introduced by de Cooman. It is shown that this approach to conditioning and the related conditional independence notion generalizes and unifies some of the previously suggested rules and conditional independence relations. The properties of the proposed conditional independence relation completely correspond to those possessed by stochastic conditional independence.

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