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# ------------------------------------------------------------------
# _____ _ _ _
# | ___(_) __| | | ___
# | |_ | |/ _` | |/ _ \
# | _| | | (_| | | __/
# |_| |_|\__,_|_|\___| Regression cooker
# ------------------------------------------------------------------
# Formation Introduction au Deep Learning (FIDLE)
# CNRS/SARI/DEVLOG 2020 - S. Arias, E. Maldonado, JL. Parouty
# ------------------------------------------------------------------
# Initial version by JL Parouty, feb 2020
import numpy as np
import math
import random
import datetime, time
import matplotlib
import matplotlib.pyplot as plt
from IPython.display import display,Markdown,HTML
class RegressionCooker():
__version__ = '0.1'
def __init__(self, mplstyle='../fidle/mplstyles/custom.mplstyle'):
print('\nFIDLE 2020 - Regression Cooker')
print('Version :', self.__version__)
print('Run time : {}'.format(time.strftime("%A %-d %B %Y, %H:%M:%S")))
if mplstyle is not None:
matplotlib.style.use(mplstyle)
@classmethod
def about(cls):
print('\nFIDLE 2020 - Regression Cooker)')
print('Version :', cls.version)
@classmethod
def vector_infos(cls,name,V):
"""
Show some nice infos about a vector
args:
name : vector name
V : vector
"""
m=V.mean(axis=0).item()
s=V.std(axis=0).item()
print("{:16} : mean={:8.3f} std={:8.3f} min={:8.3f} max={:8.3f}".format(name,m,s,V.min(),V.max()))
def get_dataset(self,n):
"""
Return a dataset of n observation
args:
n : dataset size
return:
X,Y : with X shapes = (n,1) Y shape = (n,)
"""
xob_min = 0 # x min and max
xob_max = 10
a_min = -30 # a min and max
a_max = 30
b_min = -10 # b min and max
b_max = 10
noise_min = 10 # noise min and max
noise_max = 50
a0 = random.randint(a_min,a_max)
b0 = random.randint(b_min,b_max)
noise = random.randint(noise_min,noise_max)
# ---- Construction du jeu d'apprentissage ---------------
# X,Y : données brutes
X = np.random.uniform(xob_min,xob_max,(n,1))
N = noise * np.random.normal(0,1,(n,1))
Y = a0*X + b0 + N
return X,Y
def plot_dataset(self,X,Y,title='Dataset :',width=12,height=6):
"""
Plot dataset X,Y
args:
X : Observations
Y : Values
"""
nb_viz = min(1000,len(X))
display(Markdown(f'### {title}'))
print(f"X shape : {X.shape} Y shape : {Y.shape} plot : {nb_viz} points")
plt.figure(figsize=(width, height))
plt.plot(X[:nb_viz], Y[:nb_viz], '.')
plt.show()
self.vector_infos('X',X)
self.vector_infos('Y',Y)
def __plot_theta(self, i, theta,x_min,x_max, loss,gradient,alpha):
Xd = np.array([[x_min], [x_max]])
Yd = Xd * theta.item(1) + theta.item(0)
plt.plot(Xd, Yd, color=(1.,0.4,0.3,alpha))
if i<0:
print( " #i Loss Gradient Theta")
else:
print(" {:3d} {:+7.3f} {:+7.3f} {:+7.3f} {:+7.3f} {:+7.3f}".format(i,loss,gradient.item(0),gradient.item(1),theta.item(0),theta.item(1)))
def __plot_XY(self, X,Y,width=12,height=6):
nb_viz = min(1000,len(X))
plt.figure(figsize=(width, height))
plt.plot(X[:nb_viz], Y[:nb_viz], '.')
plt.tick_params(axis='both', which='both', bottom=False, left=False, labelbottom=False, labelleft=False)
plt.xlabel('x axis')
plt.ylabel('y axis')
def __plot_loss(self,loss, width=8,height=4):
plt.figure(figsize=(width, height))
plt.tick_params(axis='both', which='both', bottom=False, left=False, labelbottom=False, labelleft=False)
plt.ylim(0, 20)
plt.plot(range(len(loss)), loss)
plt.xlabel('Iterations')
plt.ylabel('Loss')
def basic_descent(self, X, Y, epochs=200, eta=0.01,width=12,height=6):
"""
Performs a gradient descent where the gradient is updated at the end
of each iteration for all observations.
args:
X,Y : Observations
epochs : Number of epochs (200)
eta : learning rate
width,height : graphic size
return:
theta : theta
"""
display(Markdown(f'### Basic gradient descent :'))
display(Markdown(f'**With :** '))
print('with :')
print(f' epochs = {epochs}')
print(f' eta = {eta}')
display(Markdown(f'**epochs :** '))
x_min = X.min()
x_max = X.max()
y_min = Y.min()
y_max = Y.max()
n = len(X)
# ---- Initialization
theta = np.array([[y_min],[0]])
X_b = np.c_[np.ones((n, 1)), X]
# ---- Visualization
self.__plot_XY(X,Y,width,height)
self.__plot_theta( -1, theta,x_min,x_max, None,None,0.1)
# ---- Training
loss=[]
for i in range(epochs+1):
gradient = (2/n) * X_b.T @ ( X_b @ theta - Y)
mse = ((X_b @ theta - Y)**2).mean(axis=None)
theta = theta - eta * gradient
loss.append(mse)
if (i % (epochs/10))==0:
self.__plot_theta( i, theta,x_min,x_max, mse,gradient,i/epochs)
# ---- Visualization
display(Markdown(f'**Visualization :** '))
plt.show()
display(Markdown(f'**Loss :** '))
self.__plot_loss(loss)
plt.show()
return theta
def minibatch_descent(self, X, Y, epochs=200, batchs=5, batch_size=10, eta=0.01,width=12,height=6):
"""
Performs a gradient descent where the gradient is updated at the end
of each iteration for all observations.
args:
X,Y : Observations
epochs : Number of epochs (200)
eta : learning rate
width,height : graphic size
return:
theta : theta
"""
display(Markdown(f'### Mini batch gradient descent :'))
display(Markdown(f'**With :** '))
print('with :')
print(f' epochs = {epochs}')
print(f' batchs = {batchs}')
print(f' batch size = {batch_size}')
print(f' eta = {eta}')
display(Markdown(f'**epochs :** '))
x_min = X.min()
x_max = X.max()
y_min = Y.min()
y_max = Y.max()
n = len(X)
# ---- Initialization
theta = np.array([[y_min],[0]])
X_b = np.c_[np.ones((n, 1)), X]
# ---- Visualization
self.__plot_XY(X,Y,width,height)
self.__plot_theta( -1, theta,x_min,x_max, None,None,0.1)
# ---- Training
def learning_schedule(t):
return 1 / (t + 100)
loss=[]
for epoch in range(epochs):
for i in range(batchs):
random_index = np.random.randint(n-batch_size)
xi = X_b[random_index:random_index+batch_size]
yi = Y[random_index:random_index+batch_size]
mse = ((xi @ theta - yi)**2).mean(axis=None)
gradient = 2 * xi.T.dot(xi.dot(theta) - yi)
eta = learning_schedule(epoch*150)
theta = theta - eta * gradient
loss.append(mse)
self.__plot_theta( epoch, theta,x_min,x_max, mse,gradient,epoch/epochs)
# draw_theta(epoch,mse,gradients, theta,0.1+epoch/(n_epochs+1))
# draw_theta(epoch,mse,gradients,theta,1)
# ---- Visualization
display(Markdown(f'**Visualization :** '))
plt.show()
display(Markdown(f'**Loss :** '))
self.__plot_loss(loss)
plt.show()
return theta