Linear Regression with polynomials - transformation problem

pelopo: <SCODE>from __future__ import print_function
from itertools import count

import torch
import torch.autograd
import torch.nn.functional as F
from torch.autograd import Variable

train_data = torch.Tensor([
   [40,  6,  4],
   [44, 10,  4],
   [46, 12,  5],
   [48, 14,  7],
   [52, 16,  9],
   [58, 18, 12],
   [60, 22, 14],
   [68, 24, 20],
   [74, 26, 21],
   [80, 32, 24]])
test_data = torch.Tensor([
    [6, 4],
    [10, 5],
    [4, 8]])

x_train = train_data[:,1:3]
y_train = train_data[:,0]

POLY_DEGREE = 4
input_size = 2
output_size = 1


def make_features(x):
    """Builds features i.e. a matrix with columns [x, x^2, x^3, x^4]."""
    x = x.unsqueeze(1)
    return torch.cat([x ** i for i in range(1, POLY_DEGREE+1)], 1)



def poly_desc(W, b):
    """Creates a string description of a polynomial."""
    result = 'y = '
    for i, w in enumerate(W):
        result += '{:+.2f} x^{} '.format(w, len(W) - i)
    result += '{:+.2f}'.format(b[0])
    return result


def get_batch():
    """Builds a batch i.e. (x, f(x)) pair."""
    x = make_features(x_train)

    return Variable(x), Variable(y_train)


# Define model
fc = torch.nn.Linear(input_size, output_size)

for batch_idx in range(1000):
    # Get data
    batch_x, batch_y = get_batch()

    # Reset gradients
    fc.zero_grad()

    # Forward pass
    output = F.smooth_l1_loss(fc(batch_x), batch_y)
    loss = output.data[0]

    # Backward pass
    output.backward()

    # Apply gradients
    for param in fc.parameters():
        param.data.add_(-0.1 * param.grad.data)

    # Stop criterion
    if loss < 1e-3:
        break

print('Loss: {:.6f} after {} batches'.format(loss, batch_idx))
print('==> Learned function:\t' + poly_desc(fc.weight.data.view(-1), fc.bias.data))
# print('==> Actual function:\t' + poly_desc(W_target.view(-1), b_target))<ECODE>

pelopo: I changed it a bit and now I don’t get any errors, but neither any values for loss or predicted values. I tried to replicate the case with sklearn and all is ok. I think I’m missing something simple, but just can’t see it. Any help would be appreciated. Code: <SCODE>import sklearn.linear_model as lm
from sklearn.preprocessing import PolynomialFeatures
import torch
import torch.autograd
import torch.nn.functional as F
from torch.autograd import Variable


train_data = torch.Tensor([
   [40,  6,  4],
   [44, 10,  4],
   [46, 12,  5],
   [48, 14,  7],
   [52, 16,  9],
   [58, 18, 12],
   [60, 22, 14],
   [68, 24, 20],
   [74, 26, 21],
   [80, 32, 24]])
test_data = torch.Tensor([
    [6, 4],
    [10, 5],
    [4, 8]])

x_train = train_data[:,1:3]
y_train = train_data[:,0]

POLY_DEGREE = 3
input_size = 2
output_size = 1

poly = PolynomialFeatures(input_size * POLY_DEGREE, include_bias=False)
x_train_poly = poly.fit_transform(x_train.numpy())


class Model(torch.nn.Module):

    def __init__(self):
        super(Model, self).__init__()
        self.fc = torch.nn.Linear(poly.n_output_features_, output_size)
                
    def forward(self, x):
        return self.fc(x)
            
model = Model()    
criterion = torch.nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.001)

losses = [] # Added

for i in range(1000):
    optimizer.zero_grad()
    outputs = model(Variable(torch.Tensor(x_train_poly)))
    loss = criterion(outputs, Variable(y_train))
    losses.append(loss.data[0])
    loss.backward()    
    optimizer.step()
    if loss.data[0] < 1e-4:
        break    

print('n_iter', i)
print(loss.data[0])
plt.plot(losses)
plt.show()
<ECODE> and below is the sklearn code that works <SCODE>regr = lm.LinearRegression()
poly = PolynomialFeatures(4, include_bias=False)
X_poly = poly.fit_transform(x_train.numpy())

regr.fit(x_train.numpy(), y_train.numpy())
pred = regr.predict(test_data.numpy())
pred
<ECODE> Output

AjayTalati: I can’t see what’s broken, but I like this nice pedagogical example! Hope you get it working!

Sangwon_Jake: Im keep getting loss:nan for every loss.data[0]