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XGBoostExplain.py 6.42 KiB
import pickle
import numpy as np
import matplotlib
from matplotlib import pyplot as plt
import scipy
from sklearn import svm
import random
def f_pred(Theta,h,X):
x = np.arange(-7,7,0.2)
y = x*np.tan(Theta) + h
if -np.pi/2 < Theta and Theta < np.pi/2:
return 2*np.array([np.interp(item[0],x,y) < item[1] for item in X])-1
else:
return 2*np.array([np.interp(item[0],x,y) > item[1] for item in X])-1
def f_pred1(Theta,h,item):
x = np.arange(-7,7,0.2)
y = x*np.tan(Theta) + h
return 2*int(np.interp(item[0],x,y) < item[1] ) -1
def PlotF(F,ax,n,bar,text):
c = ax.pcolormesh(X1, Y1, F,alpha=0.5, vmin=-1, vmax=1)
ax.scatter(x1_samples[:,0],x1_samples[:,1], marker='o',label= 'Electron (-1)')
ax.scatter(x2_samples[:,0],x2_samples[:,1], marker='o',label= 'Pion (+1)')
ax.set_xlim([-3,3])
ax.set_ylim([-4,4])
ax.set_ylabel("Detector 2 "+ r'$(x_2)$')
ax.set_xlabel("Detector 1 "+ r'$(x_1)$')
if text is True:
textstr = "Iteration "+ r'$ i=$' +str(n)
props = dict(boxstyle='round', facecolor='wheat', alpha=0.9)
ax.text(0.3,0.9, textstr, horizontalalignment='center', verticalalignment='center', transform=ax.transAxes, bbox=props)
if bar is True:
cbar = fig.colorbar(c, ax=ax)
cbar.set_label('Classification', rotation=270, labelpad=15)
return cbar
ax.legend(loc = 'lower right')
def CreatePoints():
mu_vec1 = np.array([0,0])
cov_mat1 = np.array([[2,0],[0,2]])
x1_samples = np.random.multivariate_normal(mu_vec1, cov_mat1, 100)
mu_vec1 = mu_vec1.reshape(1,2).T # to 1-col vector
mu_vec2 = np.array([1,2])
cov_mat2 = np.array([[1,0],[0,1]])
x2_samples = np.random.multivariate_normal(mu_vec2, cov_mat2, 100)
mu_vec2 = mu_vec2.reshape(1,2).T
with open("XGExplain.pkl", 'wb') as f:
pickle.dump([mu_vec1 , cov_mat1, x1_samples, mu_vec1 ,mu_vec2 ,cov_mat2,x2_samples , mu_vec2 ], f)
#CreatePoints()
with open("XGExplain.pkl", 'rb') as file:
mu_vec1 , cov_mat1, x1_samples, mu_vec1 ,mu_vec2 ,cov_mat2,x2_samples , mu_vec2 = pickle.load(file)
X = np.concatenate((x1_samples,x2_samples), axis = 0)
Y = np.array([-1]*100 + [1]*100)
Theta = np.arange(-np.pi,np.pi,0.1)
Hight = np.arange(-4,4,0.1)
x1 = np.linspace(-5, 5, 100)
y1 = np.linspace(-5, 5, 100)
X1, Y1 = np.meshgrid(x1, y1)
def Plot1():
global fig
fig, axs = plt.subplot_mosaic([['a)','b)']], constrained_layout=True, figsize=(10,4))
mini = np.array([[np.sum((Y-f_pred(T,H,X))**2) for T in Theta] for H in Hight])
Theta_min = Theta[np.unravel_index(mini.argmin(), mini.shape)[1]]
H_min = Hight[np.unravel_index(mini.argmin(), mini.shape)[0]]
xx = np.arange(-7,7,0.2)
yy = xx*np.tan(Theta_min) + H_min
axs['a)'].plot(xx, yy, 'k-')
F = np.array([[f_pred1(Theta_min,H_min,[x,y]) for x in x1] for y in y1 ])
cbar = PlotF(F,axs['a)'],0,True,False)
axs['a)'].legend(loc = 'lower right')
cbar.set_label(r'$F(x_1,x_2)$', rotation=270, labelpad=15)
textstr = r'$\vert y_i -f(\mathbf{x}_i) \vert = 2 $'
props = dict(boxstyle='round', facecolor='w', alpha=1)
axs['a)'].text(0.3,0.9, textstr, horizontalalignment='center', verticalalignment='center', transform=axs['a)'].transAxes, bbox=props)
axs['a)'].arrow(-1,3, 0.45, -0.8, head_width=0.1, head_length=0.1, color='black')
for i in range(7):
Theta_min = random.choice(Theta)
H_min = random.choice(Hight)
xx = np.arange(-7,7,0.2)
yy = xx*np.tan(Theta_min) + H_min
axs['b)'].plot(xx, yy, 'k-')
axs['b)'].set_xlim([-3,3])
axs['b)'].set_ylim([-4,4])
axs['b)'].set_ylabel("Detector 2 "+ r'$(x_2)$')
axs['b)'].set_xlabel("Detector 1 "+ r'$(x_1)$')
axs['b)'].set_title("Classifier "+ r'$\phi \in \mathbf{\Phi}$' + "(all Possible Lines) ")
axs['b)'].legend(["Example of Possible Classifaication lines"],loc = 'lower right')
plt.savefig("XG_lines.pdf")
plt.show()
def RunXG(Y):
alpha = 0.1
f= np.array([0]*200 )
F = np.ones_like(X1)*0
Y = Y*2-1
Theta_List, H_list, F_list,G = [],[],[],[]
for i in range(41):
F_list.append(F)
global fig
fig, axs = plt.subplot_mosaic([['a)']], constrained_layout=True, figsize=(5,4))
PlotF(F_list[i], axs['a)'],i+1,True,True)
plt.show()
print(i)
g = np.array(2*(f-Y))
h = np.array([2]*200 )
mini = np.array([[np.sum(1/2*h*(-g/h-f_pred(T,H,X))**2) for T in Theta] for H in Hight])
Theta_min = Theta[np.unravel_index(mini.argmin(), mini.shape)[1]]
H_min = Hight[np.unravel_index(mini.argmin(), mini.shape)[0]]
Theta_List.append(Theta_min)
H_list.append(H_min)
f = f+alpha*f_pred(Theta_min,H_min,X)
F = F + alpha* np.array([[f_pred1(Theta_min,H_min,[x,y]) for x in x1] for y in y1 ])
with open("XGExplain2.pkl", 'wb') as f:
pickle.dump(F_list, f)
def Plot2():
fig, axs = plt.subplot_mosaic([['a)', 'b)', 'c)']], constrained_layout=True, figsize=(10,4))
PlotF(F_list[1], axs['a)'],1,False, True)
PlotF(F_list[5], axs['b)'],5,False, True)
PlotF(F_list[40], axs['c)'],40,True, True)
plt.savefig("XG_Iter.pdf")
plt.show()
def Plot3():
fig, axs = plt.subplot_mosaic([['b)','a)']], constrained_layout=True, figsize=(9,3))
xx = np.arange(-3,3,0.2)
yy = xx**2
yb = (-0.5+xx)*2
axs['a)'].plot(xx, yy, 'k-')
axs['a)'].scatter([1], [1], color = 'r', marker='o')
axs['a)'].plot(xx, yb, 'r-')
axs['a)'].set_xlim([-2,2])
axs['a)'].set_ylim([0,4])
axs['a)'].set_ylabel(r'$L(\Delta y_i)$')
axs['a)'].set_xlabel(r'$\Delta y_i$')
textstr = '\n'.join((
r'$ h_m(\mathbf{x}_i)= \frac{\partial^2L(\Delta y_i)}{\partial \Delta y_i ^2} = 2$',
r'$ g_0(\mathbf{x}_i)= 2$'))
props = dict(boxstyle='round', facecolor='wheat', alpha=0.9)
axs['a)'].text(0.5,0.7, textstr, horizontalalignment='center', verticalalignment='center', transform=axs['a)'].transAxes, bbox=props)
axs['a)'].arrow(0.5,2.25, +0.5-0.1, -1.25+0.3, head_width=0.1, head_length=0.1, color='black')
F = np.ones_like(X1)*0
cbar = PlotF(F,axs['b)'],0,True,True)
axs['b)'].legend(loc = 'lower right')
cbar.set_label(r'$\hat f_{(0)}(\mathbf{x})$', rotation=270, labelpad=15)
plt.savefig("XG_f0.pdf")
plt.show()
#RunXG(Y)
with open("XGExplain2.pkl", 'rb') as file:
F_list = pickle.load(file)
Plot1()
Plot2()
Plot3()