Machine Learning Summary (2)

Meaning of IID

An important point in machine learning: the error isIndependent and identically distributed, and obey the mean 0, the variance is ⊖ 2 \ominus^2 ⊖2 .
Explain:
What is Independence?
The data samples are independent of each other (do not affect each other), for example: Zhang San came to the bank for a loan, and the amount of his loan did not affect Li Si's loan amount and situation.The two data are independent of each other.
What is the same distribution?
The sample data must satisfy the same distribution.It cannot be that the data satisfies the normal distribution, and the data satisfies the Poisson distribution.For example: what we study is to predict the amount of loan that can be borrowed based on age and monthly salary.Then we have to ensure that these data (age, monthly salary, loan amount) are from the same bank.
What is a Gaussian distribution?
The Gaussian distribution is also called the normal distribution, as shown above.The high probability of the value is concentrated near the mean, and the probability of the values ​​on both sides is very small.
The following is the explanation of Baidu Encyclopedia!!!
If the random variable X obeys a mathematical expectation μ and variance ${\sigma }^2$ normal distribution, denoted as N(μ, ${\sigma }^2$).Its probability density function determines its position for the expected value μ of a normal distribution, and its standard deviation σ determines the magnitude of the distribution.The normal distribution when μ = 0 and σ = 1 is the standard normal distribution.

It is impossible for the data generated and collected in our lives to fully satisfyerrors are independent and identically distributed, and obey a mean of 0 and a variance of${\ominus }^2$ Gaussian distribution.

Conversion of Error Term

Put (1) into (2) to get


Both sides of the formula take the log at the same time, it will not changeSolved $\ominus$, but the problem can be simplified (from multiplication to addition)!!!

To be continued