Markov blanket)

Markov blanket)

Recently, when I came into contact with the concept of markovblanket, I found that there was not much information on the Internet and there were very few easy-to-understand explanations. After I checked some information, I decided to write a summary.

When talking about Markov blanket, there will be a bunch of similar concepts in terms of names, such as Markov chain (MC) and Hidden Markov Model (Hidden Markov Model, hmm) and markovrandom field (MRF. In fact, unlike these concepts, a Markov blanket is a local concept rather than an overall model level concept. For more information, see [He Xian. Research on Markov blanket discovery algorithms based on Bayesian Networks [D]. University of electronic science and technology, 2012.

First, let's look at the Markov blanket'sDefinition:

 

The definition of this pure symbol looks abstract. In an image, the complete set of a random variable U is divided into three mutually exclusive parts. The variable X and the Set A and B have no intersection between the three subsets, the Union set is the complete set U. If the variable X has nothing to do with the Set B when the set a is given, it is called the Markov blanket of the variable X. In formula (2-16), set MB is set a as I said, {U-MB-{x} is set B as I said, the symbol "bytes" indicates "independent", and the symbol "|" indicates that, given XX conditions, the formula (2-16) is readable as "when a set of MB is given, variable X is independent of {U-MB-{x ".

For example, the full set of U is the whole society, X is your individual, and MB is the person in your life circle. According to philosophy, everything is related. However, you do not have any relationship with everyone in society, but indirectly relate to them through your life circle, that is to say, given your life circle, you have nothing to do with the rest of the society (independent ).

Specifically, when the complete set mentioned above is the various nodes of a trusted Bayesian Network (BN:

This term is rigorous. In other words, in a trusted Bayesian Network, a node's Markov blanket includes its parents, all its children, and its spouse, that is, the person who gave birth to the child and the person who participated in the birth of the child and his current wife (because you will find that not all the children are children of T and spouse ). In other words, in fact, we use traditional Chinese family composition to explain the most image, with the family's male master as the core (T in the figure). The family includes grandparents (x1, x2, that is, t's parents), the couple (t himself, X8), the Children (X6, X7, X7), and The Children (X7, X7, but now I am raising T, and I have no ex-wife. ^_^ ). It is worth noting that there can be more than one spouse for each node (that is, to allow polygenia, if an arrow from X4 to X6 is added, X4 is also the spouse of T ), you can also have no spouse (I .e., single, x4. although there are two children, but currently single). Of course, the assumption here is that the Gender is also changing at any time. Who is you looking for a Markov blanket, who is male ^_^

So what is the use of a Markov blanket? Feature Selection is mentioned in this article (of course, this is only one of the purposes ):

In other words, a person's Markov blanket is the person associated with you (defined by the formula 2-16 ). If you want to investigate this person, you cannot investigate everyone in the whole society (a lot of feature redundancy ), in fact, we only need to find out the Markov blanket demographic survey of this person (Feature Selection ). In particular, if this society is a Bayesian Network, Markov blanket groups only include their own families. This is equivalent to a person who only has a relationship with his family and has nothing to do with others, is a simplified model. You can check the concept of Bayesian Networks.

So how can we find out the Markov blanket crowd of this person? Let's go and see the original document ......

Last, let's talk a little bit.Bayesian NetworkIt is a directed acyclic graph (DAG). As shown in 2-2, the links between nodes are directed arrows and cannot be circled along the arrow. Bayesian networks are the promotion of Markov chains. Markov Chains define only one chain, while Bayesian networks do not define a chain. However, both follow the Markov hypothesis, that is, a node only depends on its previous node (first-order Markov hypothesis ). For Markov chains, Hidden Markov models, and Bayesian Networks, you can take a look at the beauty of mathematics. The chapter "statistical language models" involves Markov chains, specifically the chapter "Hidden Markov models ", another chapter is "Markov chain extension-Bayesian Network", which is easy to understand and will not be described here.

The trusted Bayesian network is mentioned several times. In chapter 3rd of the document, credibility is defined:

I do not know whether the above definition refers to "trusted" in "trusted Bayesian Networks". My personal understanding of "trusted" means that this Bayesian Network is a real Bayesian Network, this satisfies the Markov hypothesis.

Source: csdn
Original: 78424522

Markov blanket)