Machine learning--Probabilistic graph model

The probabilistic graph model (PGM) is a model for describing the real situation. The core is conditional probability, which is essentially the use of prior knowledge to establish an association constraint relationship between random variables, and finally to achieve the purpose of convenient seeking conditional probabilities.

1. Starting from the phenomenon---the world is a random variable

The world is a random variable.

First, the world is unknown and there are many possibilities.

Second, everything in the world is interconnected.

Thirdly, a random variable is a mapping, and the process of mapping the observed sample to a numerical value is called a random variable.

The above three principles give us the means to quantify the world, and we can use this to turn an abstract question into a mathematical problem. And the use of mathematical means to identify problems and solve problems. Everything in the world is unknown, and all are random variables. How many babies will be born tomorrow? Wuhan is a random variable, and tomorrow's baby's genes are also random variables, the children's IQ is random variables, the entrance examination score is a random variable, the monthly salary geometry is a random variable. But are these random variables completely irrelevant? Boy, High IQ, low score of college entrance examination, the probability of high monthly salary and how many? Obviously, with each increase in random variables, the sample space will explode in exponential form. How do we quickly calculate the probability of a given set of random variable observations? The probability plot gives the answer.

　　

2. Probabilistic Graphs---self-bringing intelligent models

In fact, when I look at the CRF, I often think that the word segmentation based on CRF uses the adjacent information of words; the image processing based on edge detection uses the neighboring information of pixels; Is neighboring information enough? Is it just enough to consider the information that comes with neighboring pixels to restore an observation (sentence or image) to its original meaning? Yes, the richest relationship must be in the adjacent information, compared to the edge of the division of the common line absolutely indelible, hmm division of speech is also a good result .... But what if the non-adjacent information is introduced into judgment? When I was wondering how to introduce nonadjacent information, deep learning and CNN appeared out of thin air, and had to admit that the person who designed it was extremely clever, using the next sampling to create a more distant pixel connection, and using convolution to accumulate the effects of the previous results to the present moment (the essence of convolution is stacking + metamorphism). In this way, the non-adjacent information is used. But isn't that the only way? Obviously not, there is a less automatic, but not intractable method, called PGM.

or from the fast calculation of conditional probabilities to talk about PGM. The first is the representation, the expression of the probability map is a ... Figure... Of course there will be nodes, there will be edges. The node is a random variable (everything is random) and the Edge is a dependency (now only on the graph). A typical probability plot is as follows:

A person's course score depends on the IQ and the difficulty of the exam, the quality of its recommendation depends on the score, a person's SAT scores can now only consider relying on IQ. So how should p (d,i,g,l,s) be calculated?

Or more popular, a smart person, in a difficult exam to get a high score, but got a very bad letter of recommendation, and his SAT test is the probability of high score?

We hide some details, a person recommendation letter sucks, his sat high score probability is how much? Or, what is the probability that a person has a low SAT score and a bull in his hand?

This is difficult to calculate if the dependencies between random variables are not considered. But if there is a well-constructed probability map, the above problem can be transformed into conditional probability problem.

By observing the experiment, we can get a series of conditional probabilities, through this conditional probability, and the Bayesian conditional probability chain rule, then we can ask for the probability of the set of random variables we want.

OK, the toy example is over, let's take a little bit of it. How to infer the genotype of a person's blood type (A B ab O) and their parents blood type (Aaao ab BB BO ...), first of all, we can establish a probability map, all blood type B, genotype g, are random variables (nodes).

　　

Machine learning--Probabilistic graph model