二元贝叶斯网的线性性质
Linearity Properties of Bayes Nets with Binary Variables
摘要：
众所周知，在线性模型中：（1）对观测变量的边际分布的可检验约束条件区分了某些情况，在这些情况下，一个未观测的原因共同影响几个观测变量;（2）“工具变量”技术有时允许估计一个变量对另一个变量的影响，即使变量之间的关联可能被未观测的共同原因混淆;（3）协会可以直接从与路径或跋涉中的每条边相关联的参数值计算由路径或跋涉连接的两个变量的关联（或一个变量给定另一个变量的条件概率分布）;（4）可以从与每条跋涉相关联的参数计算由多个跋涉产生的两个变量的关联;（5）两个变量在第三个条件下的独立性意味着变量在所有单位上的和在每个原始条件变量的所有单位上的和的条件下的相应独立性。还已知性质（2）-（5）不适用于所有具有二进制变量的贝叶斯网。我们证明了（1）对所有二元变量的贝叶斯网成立，（5）对所有这种单跋涉连接的贝叶斯网成立。我们进一步表明，所有五个属性的贝叶斯网与任何DAG和二进制变量参数化噪声或和噪声-“与”门。
英文摘要：
It is "well known" that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of "instrumental variables" sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by a path or trek can be computed directly from the parameter values associated with each edge in the path or trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables.These properties are exploited in search procedures. It is also known that properties (2)-(5) do not hold for all Bayes nets with binary variables. We show that (1) holds for all Bayes nets with binary variables and (5) holds for all singly trek-connected Bayes nets of that kind. We further show that all five properties hold for Bayes nets with any DAG and binary variables parameterized with noisy-or and noisy-and gates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
