机器学习 Pt.II: 二元分类¶

#%matplotlib notebook
from matplotlib.animation import FuncAnimation

#定义代价函数为最小二乘法时对b1的偏导
def gd_lsq_b1(b0,b1,j):
    if j==0:
        return sum((2*(expit(b1*x+b0)-y)*(expit(b1*x+b0)**2)*np.exp(-b1*x-b0)*x) for (x,y) in zip(xval,yval))
    else:
        return sum( - y/(expit(b1*x+b0))*(expit(b1*x+b0)**2)*np.exp(-b1*x-b0)*x+(1-y)/(1-expit(b1*x+b0))*(expit(b1*x+b0)**2)*np.exp(-b1*x-b0)*x for (x,y) in zip(xval,yval))

#定义代价函数为最小二乘法时对b0的偏导
def gd_lsq_b0(b0,b1,j):
    if j==0:
        return sum((2*(expit(b1*x+b0)-y)*(expit(b1*x+b0)**2)*np.exp(-b1*x-b0)) for (x,y) in zip(xval,yval))
    else: 
        return sum( - y/(expit(b1*x+b0))*(expit(b1*x+b0)**2)*np.exp(-b1*x-b0)+(1-y)/(1-expit(b1*x+b0))*(expit(b1*x+b0)**2)*np.exp(-b1*x-b0) for (x,y) in zip(xval,yval))


def dolsq(it,b0,b1,b0_,b1_,lsq_,j,alpha=0.2):
    b0_.append(b0)
    b1_.append(b1)
    #阶梯下降法求b0和b1,b0''=b0'-alpha*(partialL/partialb0)
    for i in range(it):
        b0=b0-gd_lsq_b0(b0,b1,j)*alpha
        b1=b1-gd_lsq_b1(b0,b1,j)*alpha
        #将迭代中得到的b0’’存储至数组b0_
        b0_.append(b0)
        b1_.append(b1)
        if j==0:
            lsq_.append(lsq(b0,b1))
        else:
            lsq_.append(mle(b0,b1))

    return(b0_,b1_,lsq_)

def animate_lsq(i,line,line2):
    #画出从初始值到第i次迭代的b0值
    line.set_data(b0_[:i],lsq_[:i])
    #画出从初始值到第i次迭代的b0值
    line2.set_data(b1_[:i],lsq_[:i])
    return (line,line2)

b1_init=0

def init_all(b0,b1,b0_,b1_,lsq_):
    b0_=[];b1_=[];lsq_=[]
    b0=0;b1=b1_init    
    return (b0,b1,b0_,b1_,lsq_)

b0_=[];b1_=[];lsq_=[]
#初始化b0和b1
b0=0;b1=b1_init  
#迭代40次
it=40
b0_lsq=[];b1_lsq=[]
for j in range(2):
    fig, ax = plt.subplots()
    b0,b1,b0_,b1_,lsq_=init_all(b0,b1,b0_,b1_,lsq_)
    line, = ax.plot([],[],"X")
    line2, = ax.plot([],[],"X")
    b0_,b1_,lsq_=dolsq(it,b0,b1,b0_,b1_,lsq_,j) 
    if (j==0):
        b0_lsq=b0_
        b1_lsq=b1_
    ax.set_xlim(-10,20)
    ax.set_ylim(min(lsq_)-1,max(lsq_)+1)
    anim=FuncAnimation(fig, animate_lsq, fargs=[line,line2],repeat=False,frames=range(it)) 
    anim.save('gd{:d}.gif'.format(j),fps=2,dpi=200)
    plt.close() # update

def animate_2d_lsq(i):
line.set_data(b0_[:i],b1_[:i])
line2.set_data(b0_lsq[:i],b1_lsq[:i])
return (line,line2)

fig, ax = plt.subplots(1,2,figsize=(10,5))

xx, yy = np.meshgrid(np.linspace(-7, 10, 100), np.linspace(-10, 18, 100))
ax[1].contour(xx, yy, mle(xx,yy), linewidths=2, levels=range(0,200,8), cmap='Blues',linestyles="dashed")
line,= ax[1].plot([],[],marker="x",c="r")

ax[0].contour(xx, yy, lsq(xx,yy), linewidths=2, levels=range(0,40), cmap='Blues',linestyles="dashed")
line2,= ax[0].plot([],[],marker="x",c="r")
anim=FuncAnimation(fig, animate_2d_lsq,repeat=True,frames=range(it)) 
anim.save("gd_2d.gif",fps=2,dpi=200)
plt.close() # update

b0_1=b0_[1:]
b1_1=b1_[1:]

#每次迭代的b''-b'的变化
plt.plot(np.array(b0_1)-np.array(b0_[:it]))
plt.plot(np.array(b1_1)-np.array(b1_[:it]))
plt.legend(("b0","b1"))