Article Contents: [TOC]
Everyone believed it: experimentalists thought it was a mathematical theorem, mathematical researchers thought it was an empirical formula.
—- Gabriel Lippmann
This paper is mainly to explain the least square method, ridge regression and other optimization methods to pave the way.
Normal distribution in life
The height of women in life,
Let’s say you have 200 blind dates, and your mom collected all their height information and counted how many people there were every 5 centimeters. Then using height as the horizontal axis and number of people as the vertical axis, the following graph is drawn:
This kind of data distribution is the normal distribution. The positive and Pacific distribution is like a hill, low at both ends and high in the middle. It is symmetrical, with most of the data concentrated in the mean and a small part distributed at both ends
In fact, people’s score heights do conform to a normal distribution. In 2017, the average height of adult males aged 18 and above in China was 167.1cm, so the height of 167.1 is the general height of males in China. If it is 150cm or 190cm, there are relatively few people at both ends of the distribution.
The amazing thing is that people’s height, arm length, lung capacity, and their test scores all match the normal distribution.
Why is that?
2 Origin of Name
eyesWhy is a normal distribution not called “positive”?
It starts with this thing, this thing down here
This thing is called the Galton nail board, and guess who invented it? Yes, Victorian Francis Galton. After he made this pegboard, he realized that this shape worked for a lot of data, so he named it “The Normal Distribution.”
The word “normal” is used to indicate that the distribution can represent a wide variety of data types.
3 Analysis details
In the Galton pegboard, as each bead rolls down and hits the pillar, it moves randomly to the left or right. Then one bead rolls down and picks its direction multiple times, and the final distribution is close to normal.
The key point is that when an event is affected by multiple random factors, the result seems to be a normal distribution.
A woman’s height may be influenced by her parents’ height, her eating habits, whether she likes to exercise, etc. These influences are like pillars in galton’s nail board.
It is also important to note that in the Galton nail board, all beads start in the same state.
4 has a partial distribution
In reality, there are many skewed distributions, such as in medical testing. One theory is that in cells, cell classification is multiplication rather than addition. So the log method turns multiplication into addition, so the log method can also turn biased data into a normal distribution.
Take log on the x-coordinate:
Life is the same, the left is poor, the right is rich. Faced with countless random choices in life, most people fall in the middle and become average. A few unlucky and lucky people became very poor and very rich, but most of us became ordinary people. The reason why we work hard is that we hope that every time we choose, we can make a better choice and make our future better. ‘!