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This article introduces the relevant knowledge of "python over-fitting case analysis". In the operation of actual cases, many people will encounter such a dilemma, so let the editor lead you to learn how to deal with these situations. I hope you can read it carefully and be able to achieve something!

The following figure visually shows the most serious over-fitting situation:

The model fits almost all the points, that is, the accuracy on the training set is close to 100%. What are the characteristics of this kind of model? Take a look at the parameters of this model:

1.24700471e-13.-2.35752755e-11, 2.06759733e-09,-1.11665116e-07.

4.15722794e-06.-1.13161697e-04, 2.33087852e-03,-3.70886530e-02.

4.61321531e-01.-4.50943817e+00, 3.46373724e+01,-2.07949995e+02.

9.65158102e+02.-3.40164962e+03, 8.85765503e+03,-1.63366853e+04.

1.99303609e+04.-1.41930185e+04, 4.37094529e+03, 2.87198980e+00.

A total of 20, which is exactly equal to the number of points that need to be fitted.

The above figure is fitted by Lagrangian interpolation method, with the help of scipy package to complete the interpolation, the code is shown below.

Data preparation phase:

From scipy.interpolate import lagrange

Import numpy as np

Import matplotlib.pyplot as plt

# number of samples used

N = 20

# seed ensures that a fixed random number is generated each time

Np.random.seed (2)

Eps = np.random.rand (n) * 2

# construct sample data

X = np.linspace (0,20, n)

Y = np.linspace (2,14, n) + eps

Call Lagrange interpolation to get the interpolation function p, and then input the interpolation point x to complete the interpolation to get the interpolation point (xx,yy).

# call Lagrangian interpolation to get the interpolation function p

P = lagrange (x, y)

Xx = x

Yy = p (xx)

A polynomial model is obtained by Lagrangian interpolation, and the number of parameters is equal to the number of samples.

Above we restore a method of fitting all sample points.

In order to improve the generalization ability of the model in machine learning, it is necessary to simplify the model parameters, in other words, to regularize the parameters, which is also in line with Occam's razor law, that is, the simple and effective principle.

The commonly used L1 regular will make the parameters sparse, and it will return the weights of some of them to 0. 5. Of course, as far as the data points to be fitted today are concerned, if the parameters of the model are directly simplified to 2, the fitting effect will not be bad.

Choose sklearn's simplest linetype regression model:

From sklearn import linear_model

Reg = linear_model.LinearRegression ()

Reg.fit (x.reshape (len (x),-1), y)

# get 2 parameter values

Reg.coef_,reg.intercept_

(array ([0.62182096]), 2.644854261121125)

Then the fitting effect under plot:

Plt.figure (figsize= (122.8))

Plt.scatter (x, y, color= "r")

# Lagrangian interpolation complex model

Plt.plot (xx, yy, color= "b", label='lagrange')

# Linetype regression minimalist model

Plt.plot (xx,xx*reg.coef_+reg.intercept_,color='green',label='linear_model')

Plt.show ()

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