%matplotlib inline
import math,sys,os,numpy as np
from numpy.random import random
from matplotlib import pyplot as plt, rcParams, animation, rc
from __future__ import print_function, division
from ipywidgets import interact, interactive, fixed
from ipywidgets.widgets import *
rc('animation', html='html5')
rcParams['figure.figsize'] = 3, 3
%precision 4
np.set_printoptions(precision=4, linewidth=100)
def lin(a,b,x): return a*x+b
a=3.
b=8.
n=30
x = random(n)
y = lin(a,b,x)
x
array([ 0.2764, 0.3057, 0.4897, 0.787 , 0.6627, 0.6034, 0.3722, 0.1886, 0.4145, 0.6801, 0.5178, 0.4675, 0.3708, 0.9557, 0.1604, 0.4065, 0.8752, 0.6775, 0.1818, 0.2346, 0.591 , 0.9049, 0.9551, 0.3547, 0.7319, 0.5636, 0.7542, 0.7464, 0.2111, 0.1858])
y
array([ 8.8293, 8.9171, 9.4692, 10.3611, 9.9881, 9.8102, 9.1167, 8.5659, 9.2436, 10.0403, 9.5534, 9.4025, 9.1125, 10.8671, 8.4813, 9.2196, 10.6257, 10.0326, 8.5453, 8.7038, 9.7731, 10.7148, 10.8654, 9.064 , 10.1956, 9.6907, 10.2627, 10.2393, 8.6334, 8.5573])
plt.scatter(x,y)
<matplotlib.collections.PathCollection at 0x7f57280e7dd0>
def sse(y,y_pred): return ((y-y_pred)**2).sum()
def loss(y,a,b,x): return sse(y, lin(a,b,x))
def avg_loss(y,a,b,x): return np.sqrt(loss(y,a,b,x)/n)
a_guess=-1.
b_guess=1.
avg_loss(y, a_guess, b_guess, x)
9.1365
lr=0.01
# d[(y-(a*x+b))**2,b] = 2 (b + a x - y) = 2 (y_pred - y)
# d[(y-(a*x+b))**2,a] = 2 x (b + a x - y) = x * dy/db
def upd():
global a_guess, b_guess
y_pred = lin(a_guess, b_guess, x)
dydb = 2 * (y_pred - y)
dyda = x*dydb
a_guess -= lr*dyda.mean()
b_guess -= lr*dydb.mean()
fig = plt.figure(dpi=100, figsize=(5, 4))
plt.scatter(x,y)
line, = plt.plot(x,lin(a_guess,b_guess,x))
plt.close()
def animate(i):
line.set_ydata(lin(a_guess,b_guess,x))
for i in range(10): upd()
return line,
ani = animation.FuncAnimation(fig, animate, np.arange(0, 40), interval=100)
ani