A set of variables is the Markov blanket of a random variable if it contains
all the information needed for predicting the variable. If the blanket cannot
be reduced without losing useful information, it is called a Markov boundary.
Identifying the Markov boundary of a random variable is advantageous because
all variables outside the boundary are superfluous. Hence, the Markov boundary
provides an optimal feature set. However, learning the Markov boundary from
data is challenging for two reasons. If one or more variables are removed from
the Markov boundary, variables outside the boundary may start providing
information. Conversely, variables within the boundary may stop providing
information. The true role of each candidate variable is only manifesting when
the Markov boundary has been identified. In this paper, we propose a new
Tsetlin Machine (TM) feedback scheme that supplements Type I and Type II
feedback. The scheme introduces a novel Finite State Automaton - a
Context-Specific Independence Automaton. The automaton learns which features
are outside the Markov boundary of the target, allowing them to be pruned from
the TM during learning. We investigate the new scheme empirically, showing how
it is capable of exploiting context-specific independence to find Markov
boundaries. Further, we provide a theoretical analysis of convergence. Our
approach thus connects the field of Bayesian networks (BN) with TMs,
potentially opening up for synergies when it comes to inference and learning,
including TM-produced Bayesian knowledge bases and TM-based Bayesian inference.

本文提出了一种新的 Tsetlin Machine (TM) 反馈机制，引入了一个上下文特定独立自动机，该自动机学习目标变量 Markov 边界之外的特征，从而在学习过程中将它们从 TM 中剪枝，通过实证研究展示了该机制如何利用上下文特定独立来找到 Markov 边界，并为其收敛性提供了理论分析，从而将贝叶斯网络领域与 TMs 相关联，为推理和学习提供协同作用的可能性，包括由 TM 生成的贝叶斯知识库和基于 TM 的贝叶斯推断。

使用马尔科夫边界引导剪枝学习极简特斯林机器子句

Learning Minimalistic Tsetlin Machine Clauses with Markov  Boundary-Guided Pruning

Recent characterisations of self-organising systems depend upon the presence
of a Markov blanket: a statistical boundary that mediates the interactions
between what is inside of and outside of a system. We leverage this idea to
provide an analysis of partitions in neuronal systems. This is applicable to
brain architectures at multiple scales, enabling partitions into single
neurons, brain regions, and brain-wide networks. This treatment is based upon
the canonical micro-circuitry used in empirical studies of effective
connectivity, so as to speak directly to practical applications. This depends
upon the dynamic coupling between functional units, whose form recapitulates
that of a Markov blanket at each level. The nuance afforded by partitioning
neural systems in this way highlights certain limitations of modular
perspectives of brain function that only consider a single level of
description.

基于马尔可夫毯概念，对神经元系统的分区进行分析，凸显模块化认知的限制。

大脑中的马尔科夫毯

Markov Blankets in the Brain

In this work we present a review of the state of the art of information
theoretic feature selection methods. The concepts of feature relevance,
redundance and complementarity (synergy) are clearly defined, as well as Markov
blanket. The problem of optimal feature selection is defined. A unifying
theoretical framework is described, which can retrofit successful heuristic
criteria, indicating the approximations made by each method. A number of open
problems in the field are presented.

本文介绍了信息论特征选择方法的现状，阐明了特征相关性、冗余性和补充性（协同作用）的概念，以及马尔科夫毯子。定义了最优特征选择的问题。我们描述了一个统一的理论框架，它可以使成功的启发式标准符合相应方法所做的近似。还介绍了该领域中的一些未解决问题。

基于互信息的特征选择方法综述

A Review of Feature Selection Methods Based on Mutual Information

Developing feature selection algorithms that move beyond a pure correlational
to a more causal analysis of observational data is an important problem in the
sciences. Several algorithms attempt to do so by discovering the Markov blanket
of a target, but they all contain a forward selection step which variables must
pass in order to be included in the conditioning set. As a result, these
algorithms may not consider all possible conditional multivariate combinations.
We improve on this limitation by proposing a backward elimination method that
uses a kernel-based conditional dependence measure to identify the Markov
blanket in a fully multivariate fashion. The algorithm is easy to implement and
compares favorably to other methods on synthetic and real datasets.

为了解决科学研究中纯关联分析的局限性而发展的特征选择算法，提出了一种基于核的条件相关度量的向后淘汰方法，并且在合成与实际数据集上比起其他方法表现更为优秀。