变邻域随机场中的邻域半径估计
Neighborhood radius estimation in Variable-neighborhood Random Fields
摘要：
我们考虑由有限区域条件概率定义的随机场，该概率取决于随边界条件变化的区域的邻域。为了预测任何有限区域内的符号，有必要检查随机数的邻域符号，这些邻域符号可能根据它们的值而改变。类似于一维设置，我们称这些邻域符号为区域的上下文。这个框架是变长马尔可夫链概念的自然扩张，是由Rissanen（1983）在他的经典论文中引入的d维域。我们定义了一个算法来估计最小的球的半径包含上下文的基础上实现的字段。我们证明了这个估计的一致性。我们的证明是建设性的，并产生明确的上界的概率错误估计的范围内。
英文摘要：
We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region it is necessary to inspect a random number of neighborhood symbols which might change according to the value of them. In analogy to the one dimensional setting we call these neighborhood symbols the context of the region. This framework is a natural extension, to d-dimensional fields, of the notion of variable-length Markov chains introduced by Rissanen (1983) in his classical paper. We define an algorithm to estimate the radius of the smallest ball containing the context based on a realization of the field. We prove the consistency of this estimator. Our proofs are constructive and yield explicit upper bounds for the probability of wrong estimation of the radius of the context.
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