Linear model (2)--Generalized linear model

Outline:

1. Review multivariate linear regression
2. The basic form of generalized linear model
3. Logarithmic linear regression
4. Learning and reference

1. Review multivariate linear regression

In the last essay, the basic form of a linear model--multivariate linear regression--is described as follows:

Figure A

In multivariate linear regression, the predicted values of the model are all distributed in a straight line, so the model can work well only when the real distribution of the sample points is roughly the same as the shape of the desired line. The situation is roughly two:

Figure II

In Figure two, we think that the distribution of the sample point is linearly variable, so our model's predicted value directly approximation to the real value of the sample point y itself, but in real life, many times the distribution of sample points is not as shown in Figure two, then we have a model that can be extended to the linear model to adapt to more realistic situation? Let's say we have a collection of sample points like figure three;

Might

Before we learn how to get the predicted value of a model to approximate three straight lines, let's take a look at what a generalized linear model is.

2. Basic forms of generalized linear models

The basic form of the generalized linear model four:

Figure Four

Among them, G (·) As the link function, the function is to associate the predicted value of the linear regression model with the true value Y, which is a monotone, functional, four model called "Generalized linear Model".

Frankly speaking, the generalized linear model is to give the predictive value of the linear regression model to wear a small vest, for example, suppose there is a sample point set, sample point distribution Three, that is, the real value y is on the exponential scale change, we hope that the predicted value of linear regression will approximate three of the distribution, then, We should be based on the real value of the sample point y is an exponential variation of this feature, the predictive value of the linear regression model to wear the exponential change of the vest, and G (·) This function is to play the role of a vest.

Figure Five

3. Logarithmic linear regression

Logarithmic linear regression is g (·) =ln (·) The case of a sample point set that can be adapted to the true tag value y of a collection of samples when three changes are present.

When G (·) =ln (·) When y=e^ (wt*x+b), the concrete derivation of procedure six shows:

Figure Six

4. Learning and references

Zhou Zhihua Teacher's "machine learning", Tsinghua University Press.

Linear model (2)--Generalized linear model