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PyTorch Tutorial - Linear Model

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Lecture2 -- Bilibili: PyTorch Tutorial; Lecturer: Hongpu Liu

Linear Model

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# 1. import libraries
import numpy as np
import matplotlib.pyplot as plt

# 2. Dataset
x_data = [1,2,3]
y_data = [2,4,6]

# 3. Design Model
def forward(x,w):
    return x*w

# 4. define loss function
def loss(x, y, y_pred):
    # y_pred = forward(x)
    loss = (y_pred - y) **2
    return loss

# create lists to store weights and mse result
w_list = []
mse_list = []

# Exhaustive Attack method/Brute Force Method
# get MSE under different weights
for w in np.arange(0.0, 4.1, 0.1):
    l_sum = 0
    for x_val, y_val in zip(x_data, y_data):
        y_pred_val = forward(x_val, w)
        loss_val = loss(x_val, y_val, y_pred_val)
        l_sum += loss_val
        print("\t", x_val, y_val, y_pred_val, loss_val)
    print("MSE=", l_sum/len(x_data))
    w_list.append(w)
    mse_list.append(l_sum/len(x_data))

# visualization
plt.plot(w_list, mse_list)
plt.ylabel("Loss")
plt.xlabel('w')
plt.show()

Assignment

Try to use the model: y = x*w + b, and draw the cost graph.

Tips:

  • You can read the material of how to draw 3d graph. [link]
  • Function np.meshgrid() is very popular for drawing 3d graph, read the [docs] and utilize vectorization calculation.
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import numpy as np
import matplotlib.pyplot as plt

x_data = [1,2,3]
y_data = [2,4,6]

def forward(x,w,b):
    y = x*w+b
    return y 

def loss(y, y_pred):
    loss = (y_pred-y)**2
    return loss

w_list = []
b_list = []
mse_list = []
for w in np.arange(0.1, 4.1, 0.1):
    for b in np.arange(-2.0, 2.1, 0.1):
        print("w:", w, "b:", b)
        l_sum = 0
        for x_val, y_val in zip(x_data, y_data):
            y_pred_val = forward(x_val, w, b)
            loss_val = loss(y_val, y_pred_val)
            l_sum += loss_val
            print("\t", x_val, y_val, y_pred_val, loss_val)
        print("MSE=", l_sum/len(x_data))
        mse_list.append(l_sum/len(x_data))
        w_list.append(w)
        b_list.append(b)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot3D(w_list, b_list, mse_list)
plt.show()