Use pytorch to bulid multi-linear,but the result i get is not what i want?

Question

import sklearn
    from sklearn.datasets import load_boston
    import torch
    import torch.nn as nn

    boston = load_boston()

    num_epochs = 10

    linear_model = nn.Linear(13,1,bias = True)
    criterion = nn.MSELoss()
    optimizer = torch.optim.SGD(linear_model.parameters(), lr=0.01)

    for epoch in range(num_epochs):

        inputs = torch.from_numpy(boston.data)
        targets = torch.from_numpy(boston.target)
        targets = targets.float()
        inputs = inputs.float()

        outputs = linear_model(inputs)
        loss = criterion(outputs,targets)

        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        print('epoch:{}/{} ...... loss:{:.4f}'.format(epoch,num_epochs,loss.item()))

Answer 1

The problem with your code seems to be data normalization, or, the lack of it.

I edited your code to add data normalization ((x - mean) / std), set epochs to 50 and switched the optimiser to Adam so it converges faster.

import sklearn
from sklearn.datasets import load_boston
import torch
import numpy as np
import torch.nn as nn

def normalize(X):
    mean = np.mean(X)
    std = np.std(X)
    return ((X - mean) / std), mean, std

boston = load_boston()

m_in = np.zeros(13)
s_in = np.zeros(13)

b_in = boston.data
b_out = boston.target

for i in range(13):
    b_in[:, i], m_in[i], s_in[i] = normalize(b_in[:, i])

b_out, m_out, s_out = normalize(b_out)

num_epochs = 50

linear_model = nn.Linear(13, 1, bias=True)
criterion = nn.MSELoss()
optimizer = torch.optim.Adam(linear_model.parameters(), lr=0.01)

linear_model.train()
for epoch in range(num_epochs):
    inputs = torch.from_numpy(b_in)
    targets = torch.from_numpy(b_out)
    targets = targets.float().unsqueeze(1)
    inputs = inputs.float()

    outputs = linear_model(inputs)
    loss = criterion(outputs, targets)

    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    print('epoch: {}/{} ...... loss: {:.4f}'.format(epoch, num_epochs, loss.item()))

The new output looks like this:

epoch: 0/50 ...... loss: 1.2610
epoch: 1/50 ...... loss: 1.1395
epoch: 2/50 ...... loss: 1.0332
epoch: 3/50 ...... loss: 0.9421
epoch: 4/50 ...... loss: 0.8660
epoch: 5/50 ...... loss: 0.8040
epoch: 6/50 ...... loss: 0.7548
epoch: 7/50 ...... loss: 0.7164
epoch: 8/50 ...... loss: 0.6863
epoch: 9/50 ...... loss: 0.6623
epoch: 10/50 ...... loss: 0.6421
epoch: 11/50 ...... loss: 0.6240
epoch: 12/50 ...... loss: 0.6068
epoch: 13/50 ...... loss: 0.5895
epoch: 14/50 ...... loss: 0.5717
epoch: 15/50 ...... loss: 0.5532
epoch: 16/50 ...... loss: 0.5339
epoch: 17/50 ...... loss: 0.5143
epoch: 18/50 ...... loss: 0.4946
epoch: 19/50 ...... loss: 0.4752
epoch: 20/50 ...... loss: 0.4565
epoch: 21/50 ...... loss: 0.4389
epoch: 22/50 ...... loss: 0.4226
epoch: 23/50 ...... loss: 0.4079
epoch: 24/50 ...... loss: 0.3949
epoch: 25/50 ...... loss: 0.3835
epoch: 26/50 ...... loss: 0.3736
epoch: 27/50 ...... loss: 0.3652
epoch: 28/50 ...... loss: 0.3580
epoch: 29/50 ...... loss: 0.3517
epoch: 30/50 ...... loss: 0.3461
epoch: 31/50 ...... loss: 0.3410
epoch: 32/50 ...... loss: 0.3361
epoch: 33/50 ...... loss: 0.3315
epoch: 34/50 ...... loss: 0.3270
epoch: 35/50 ...... loss: 0.3226
epoch: 36/50 ...... loss: 0.3183
epoch: 37/50 ...... loss: 0.3142
epoch: 38/50 ...... loss: 0.3103
epoch: 39/50 ...... loss: 0.3068
epoch: 40/50 ...... loss: 0.3036
epoch: 41/50 ...... loss: 0.3008
epoch: 42/50 ...... loss: 0.2984
epoch: 43/50 ...... loss: 0.2963
epoch: 44/50 ...... loss: 0.2945
epoch: 45/50 ...... loss: 0.2930
epoch: 46/50 ...... loss: 0.2917
epoch: 47/50 ...... loss: 0.2904
epoch: 48/50 ...... loss: 0.2892
epoch: 49/50 ...... loss: 0.2881

The features in the dataset seem to have different ranges and this poses a problem for the learning algorithm. By normalizing the data, we make it much easier for the model to learn.

[1] This is a great article that explains why normalization is needed: https://towardsdatascience.com/understand-data-normalization-in-machine-learning-8ff3062101f0