I'm facing some issues trying to find the linear regression line using Gradient Descent, getting to weird results. Here is the function:
def gradient_descent(m_k, c_k, learning_rate, points):
n = len(points)
dm, dc = 0, 0
for i in range(n):
x = points.iloc[i]['alcohol']
y = points.iloc[i]['total']
dm += -(2/n) * x * (y - (m_k * x + c_k)) # Partial der in m
dc += -(2/n) * (y - (m_k * x + c_k)) # Partial der in c
m = m_k - dm * learning_rate
c = c_k - dc * learning_rate
return m, c
And combined with a for loop
l_rate = 0.0001
m, c = 0, 0
epochs = 1000
for _ in range(epochs):
m, c = gradient_descent(m, c, l_rate, dataset)
plt.scatter(dataset.alcohol, dataset.total)
plt.plot(list(range(2, 10)), [m * x + c for x in range(2,10)], color='red')
plt.show()
Gives this result:
The problem is though that taking advantage of sklearn to compute the slope and intercept, ie
model = LinearRegression(fit_intercept=True).fit(np.array(dataset['alcohol']).copy().reshape(-1, 1),
np.array(dataset['total']).copy())
I get something completely different:
Any idea why? Looking on SO I've found out that a possible problem could be a too high learning rate, but as stated above I'm currently using 0.0001
Sklearn's LinearRegression doesn't use gradient descent - it uses Ordinary Least Squares (OLS) Regression which is a non-iterative method .
For your model, you might consider randomly initialising m, c rather than starting with 0,0. You could also consider adjusting the learning rate or using an adaptive learning rate.
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