使用Scikit-Learn学习乘法

Question

I have written a program that learns to add,

from sklearn import linear_model
from random import randint
reg=linear_model.LinearRegression()
x=[[randint(0,100),randint(0,100)] for i in range(1000)]
Y=[i[0]+i[1] for i in x]
reg.fit(x, Y)
print(reg.pred([[56, 23]])
# OUTPUT : 79

Please help me with this program if i want it to do multiplication, i get very low accuracy.

Please make as less changes as possible to the program as i am a newbie.

!!Thanks in Advance!!

Answer 1

Well you have multiple solutions to your problem.
To achieve 0 error, you need to learn a model that can learn this kind of complexity. You probably want to use simple models like Linear Regression, and therefore, you should expand your data using polynomial features . See sklearn.processing.PolynomialFeatures here .

Alternative solutions can involve more complicated models such as Neural Networks . You can simply use multi-layer network with 2-3 hidden layers, and linear output layer so that the output will be unbounded. This method will be less preferred for this kind of problem since it is more complex and not guaranteed to perform the best on your problem.

Note :
If you do choose to try a network for this simple problem, make sure to use a Mean loss .

Example :

First, lets load some tools.
We will use linear regression and a pre-processing toolkit by scikit-learn.

from sklearn import linear_model
from sklearn import preprocessing
from random import randint
import numpy as np

Addition problem

# Lets generate some random data
x=[[randint(0,100),randint(0,100)] for i in range(1000)]

# and compute the deterministic addition function
Y=[i[0]+i[1] for i in x]

Since x+y is a linear combination of x and y , we do not need to do any feature extraction on our data. Minimization objective in linear regression is np.sum((x * w -Y) ** 2) where we minimize over w. Optimal parameters for this model are [1, 1] .

# First, we create an instance of the regressor
reg_add=linear_model.LinearRegression()

# then, fit it to the data
reg_add.fit(x, Y)

# and finally, test it on some sample
sample = [[56, 23]]
print('Addition: X={}, Y_hat={}'.format(sample,reg_add.predict(sample)))

Output:

Addition: X=[[56, 23]], Y_hat=[79.]

Multiplication problem

# Again, lets generate some random data
x=[[randint(0,100),randint(0,100)] for i in range(1000)]

# And compute the multiplication of all coordinates for each sample
Y=np.array([i[0]*i[1] for i in x])

Now, a simple linear regressor cannot fit accurately to the data, since x[0]*x[1] is not a linear combination of elements in the sample. However, if we choose polynomial feature extraction, we can. Polynomial features are all polynomial combinations of the coordinates up the a defined degree, including degree 0 .

# Lets create an instance of the processor, using polynomial features of degree=2
pp = preprocessing.PolynomialFeatures(2)

# transform the original data
x2 = pp.fit_transform(x)

# Then, create a linear regressor,
reg_mult=linear_model.LinearRegression()

# Fit it to the processed data and the results
reg_mult.fit(x2, Y)

# and test it on a new example.
sample = [[2, 4]]
print('Multiplication: X={}, Y_hat={}'.format(sample,reg_mult.predict(pp.transform(sample))))

Output:

Multiplication: X=[[2, 4]], Y_hat=[8.]