Introduction to data science —— Optimization of mathematical basis

The first 1 Turn off ： Basis of model optimization

The first 2 Turn off ： gradient descent

Our mission ： Use gradient descent to fit the input data x,y .

def student(x, y):
    epsilon = 0.00001  #  Iterative threshold , Stop the iteration when the difference between the two iterative loss functions is less than the threshold 
    alpha = 0.01  #  Learning rate 
    a = 0
    b = 0
    m = len(x)
    error0 = 0
    error1 = 0
    # ********* Begin *********#
    while True    
    # ********* End *********#

Introduction to data science —— Probability of mathematical basis

The first 1 Turn off ： Bayes of probability basis

The first 2 Turn off ： Probability based data distribution

Introduction to data science —— Statistics of fundamentals of Mathematics

The first 1 Turn off ： Data description of statistical basis

Our mission ： Calculate relevant indicators for the input data .

def student(data):

    #********* Begin *********#
    n = len(data)
    sorted_v = sorted(data)
    midpoint = n // 2
    if n % 2 == 1:
        print( sorted_v[midpoint])
    else:
        lo = midpoint - 1
        hi = midpoint
        print( (sorted_v[lo] + sorted_v[hi]) / 2)
    
    
    #********* End *********#
    

The first 2 Turn off ： Correlation of statistical basis

Our mission ： Write a program that can calculate covariance .

def de_mean(x):
    x_bar = sum(x) / len(x)
    return [x_i - x_bar for x_i in x]
    
def dot(v, w):
    return sum(v_i * w_i for v_i, w_i in zip(v, w))
    
def student(x, y):
    # ********* Begin *********#
    n= len(x)
    d=round(dot(de_mean(x), de_mean(y)) / (n - 1),2)
    print(d)
    
    
    
    # ********* End *********#

Introduction to data science —— Matrix of mathematical basis

The first 1 Turn off ： What is a matrix ？

Our mission ： Use the list to create a 20 That's ok 20 Columns of the matrix .

# ********** Begin ********** #
#  The created matrix is assigned to  matrix
matrix = [[0]*20 for x in range(20)]
for x in range(len(matrix)):
    matrix[x][x] = 1 

# ********** End ********** #
print(matrix)

The first 2 Turn off ： Matrix operation based on line substitution

Our mission ： Design a function to realize the multiplication between matrices .

def matxMultiply(A, B):
        # ********** Begin ********** #
        multiply = []
        if len(A[0]) != len(B):
            raise ValueError
           
        result = [list(row) for row in zip(*B)]
     
        for Al in range(len(A)):
            row =[]
            for Bl in range(len(result)):
                num = 0   
                for Br in range(len(result[0])):
                    num +=  A[Al][Br] * result[Bl][Br]
                row.append(num)
            multiply.append(row)
        return multiply
        # ********** Begin ********** #
a = [[2,5,8,0],[1,9,5,8],[3,9,4,8]]
b = [[3,5],[6,8],[11,30],[1,1]]
print(matxMultiply(a,b))

Introduction to data science —— Vector of mathematical basis

The first 1 Turn off ： Mathematics in Data Science

The first 2 Turn off ： What is a vector ?

Our mission ： Create a three-dimensional vector and a four-dimensional vector .

#  Please write complete code according to the programming requirements on the left 
# ********** Begin ********** #
list1 = [70, 170, 40]
list2 = [95, 80, 75, 62] 
print (list1)
print (list2)
# ********** End ********** #

The first 3 Turn off ： Vector operations

Our mission ： Supplement the code on the right to realize the following vector operation ：
- First calculate the sum of two vectors ;
- Multiply by a scalar .

a = eval(input())
b = eval(input())
c = 0.5
    #********** Begin **********#
def scalar_multiply(c, v):
    return [c * v_i for v_i in v]
def vector_add(v, w):
    return [v_i + w_i for v_i, w_i in zip(v, w)]
add_result = vector_add(a,b)
result = scalar_multiply(c, add_result)
    #********** End **********#
print(result)