图灵程序丛书 —《数据科学入门》— Ch4-Ch7 线性代数、统计学、概率、假设与推断

Ch4-Ch7 线性代数、统计学、概率、假设与推断

此系列记录《数据科学入门》学习笔记

Ch 4 线性代数

4.1 向量

# 向量加减法
def vector_add(v, m):
    return [v_i + w_i for v_i, w_i in zip(v, w)]


def vector_subtract(v, m):
    return [v_i - w_i for v_i, w_i in zip(v, w)]

# 一系列向量的加法
def vector_sum(vectors):
    result = vectors[0]
    for vector in vectors[1:]:
        result = vector_add(result, vector)
    return result

def vector_sum1(vectors):
    return reduce(vector_add, vectors)

vector_sum = patial(reduce, vector_add)

# 标量乘以向量
def scalar_multiply(c, v):
    return [c * v_i for v_i in v]

# 计算一系列长度相同的向量的均值
def vector_meam(vectors):
    n = len(vectors)
    return scalar_multiply(1/n, vector_sum(vectors))

# 两个向量的点乘
def dot(v, w):
    return sum(v_i * w_i for v_i, w_i in zip(v, w))

# 计算向量的平方
def sum_of_squares(v):
    return dot(v, v)

# 计算向量的长度、距离
import math
def magnitude(v):
    return math.sqrt(sum_of_squares(v))

def squared_distance(v, w):
    return sum_of_squares(vector_subtract(v, w))

def distance(v, w):
    return math.sqrt(squared_distance(v, w))

def distance(v, w):
    return magnitude(vector_substract(v, w))

4.2 矩阵

# 求维数
def shape(a):
    num_rows = len(a)
    num_cols = len(a[0]) if a else 0
    return num_rows, num_cols

# 返回矩阵的某一行或者某一列
def get_row(a, i):
    return a[i]

def get_col(a, j):
    return a[:,j]

def get_col(a, j):
    return [a_i[j] for a_i in a]

# 根据形状和用来生成元素的函数来创建矩阵
def make_matrix(num_rows, num_cols, entry_fn):
    return [[entry_fn(i, j) for j in range(num_cols)] for i in range(num_rows)]

def is_diagonal(i, j):
    return 1 if i == j else 0

identify_matrix = make_matrix(5, 5, is_diagonal)
identify_matrix
#[[1, 0, 0, 0, 0],
# [0, 1, 0, 0, 0],
# [0, 0, 1, 0, 0],
# [0, 0, 0, 1, 0],
# [0, 0, 0, 0, 1]]

Ch 5 统计学

5.1 描述单个数据集

num_friends = [100, 9, 1, 4, 25, 63, 5, 16, 5, 9, 5, 25, 2, 15, 26, 2, 6, 4, 15, 16, 4, 26, 22, 13, 16, 45,
               23, 8, 9, 15, 6, 12, 5, 85, 12, 14, 2, 17, 5, 13, 42, 51, 5, 4, 26, 2, 4, 9, 5, 12, 6, 19, 
               14, 3, 5, 4, 15, 62, 15, 21, 16, 12, 3, 26, 4, 5, 41, 18, 85, 6, 8, 8, 11, 92, 12, 21, 36, 8]


from collections import Counter
import matplotlib.pyplot as plt
from pylab import *  

friend_counts = Counter(num_friends)
xs = range(max(num_friends))
ys = [friend_counts[x] for x in xs]
plt.bar(xs, ys);
plt.axis([0, 101, 0, 10])
mpl.rcParams['font.sans-serif'] = ['SimHei'] 
plt.title('朋友的数量')
plt.xlabel('朋友个数')
plt.ylabel('人数')
plt.show()

print(len(num_friends))    # 78
print(max(num_friends))    # 100
print(min(num_friends))    # 1
print(sum(num_friends))    # 1441
print(mean(num_friends))   # 18.4743589
print(median(num_friends)) # 12.0


print(sorted(num_friends)[0])    # 1
print(sorted(num_friends)[1])    # 2
print(sorted(num_friends)[-1])   # 100
print(sorted(num_friends)[-2])   # 92