import numpy as np
import matplotlib.pyplot as plt

np.random.seed(666)
X = np.random.normal(0,1,size=(200,2))
y = np.array(X[:,0]**2+X[:,1]**2 <1.5,dtype='int')

plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()...

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

iris = datasets.load_iris()

X = iris.data
y = iris.target

X = X[y<2, :2]
y = y[y<2]

X.shape

(100, 2)

y.shape

(100,)

plt.scatter(X[y==0,0],X[y==0,1],color='...

解决分类问题

• 回归问题怎么解决分类问题？
  将样本的特征和样本发生的概率联系起来，概率是一个数

import numpy as np
import matplotlib.pyplot as plt

def sigmoid(t):
    return 1 / (1 + np.exp(-t))

x = np.linspace(-10,10,500)
y = sigmoid(x)

plt.plot(x,y)
plt.show()

问题：

对于给定的样本数据集X,y，我们如何找到参数theta，使...

Least Absolute Shrinkage and Selection Operator Regression

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(42)
x = np.random.uniform(-3.0,3.0,size=100)
X = x.reshape(-1,1)
y = 0.5 * x + 3 + np.random.normal(0,1,size=100)

plt.scatter...

模型正则化：限制参数的大小

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(42)
x = np.random.uniform(-3.0,3.0,size=100)
X = x.reshape(-1,1)
y = 0.5 * x + 3 + np.random.normal(0,1,size=100)

plt.scatter(x, y)
plt.show()

# 使用多项式回归

from sklearn....

模型误差 = 偏差（Bias）+ 方差（Variance）+ 不可避免的误差

偏差和方差通常是矛盾的：降低偏差，会提高方差，降低方差会提高偏差

机器学习的主要挑战，来自于方差

解决高方差的通常手段

1. 降低模型复杂度
2. 减少数据维度；降噪
3. 增加样本数
4. 使用验证集
5. 模型正则化

解决方法是将数据分成三份，训练数据、验证数据、测试数据

import numpy as np
from sklearn import datasets

/Users/shirukai/anaconda3/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88
  return...

import numpy as np
import matplotlib.pyplot as plt

X = np.empty((100,2))

X[:,0] = np.random.uniform(0.,100.,size=100)

X[:,1] = 0.75 * X[:,0] + 3. + np.random.normal(0,5,size=100)

plt.scatter(X[:,0],X[:,1])
plt.show()

from sklearn.decomposition ...

import numpy as np
from sklearn.metrics import r2_score


class LinearRegression:
    def __init__(self):
        """初始化Linear Regression模型"""
        self.coef_ = None  # 系数
        self.intercept_ = None  # 截距
        self._theta = None

    def fit_normal(self...