I want to implement a single perceptron for linear regression using the following formulas:
The input data for the first case is one column (x(392, 1); y(392, 1)) and for the second case is (x(392, 7); y(392, 1)). The NaN values have been removed and x values have been standardized x-x.mean()/x.std()
This is my Python implementation:
class LinearRegression(object):
def __init__(self, x, y, n_iter):
self.x = x
self.y = y
self.n_iter = n_iter
self.cost_iteration = []
# Initializing model parameters (w, b) to zeros
self.weights = np.zeros((1, self.x.shape[1])) # w: weights
self.biases = np.zeros((1, 1)) # b: bias
def feedforward(self):
# return the feedforward value for x
#self.weights, self.biases = self.update_params()
z = self.x @ self.weights.T + self.biases
return z
def loss(self):
# return the loss value for given x and y
z = self.feedforward()
loss = self.y-z
cost = np.sum(loss**2)/self.y.shape[0]
return loss, cost
def backpropagation(self):
# return the derivatives with respect to weight matrix and biases
loss, cost = self.loss()
db = -2*np.sum(loss)/self.y.shape[0] # dJ/db
dw = -2*np.dot(self.x.T, loss)/self.y.shape[0] # dJ/dw
return dw, db
def update_params(self):
# update weights and biases based on the output
dw, db = self.backpropagation()
self.weights -= dw.T
self.biases -= db
return self.weights, self.biases
def fit(self):
# fit method for the training data
for iter in range(self.n_iter):
self.update_params()
print(self.biases)
l, c = self.loss()
self.cost_iteration.append (c)
return self.cost_iteration
The final cost should be approximately 23.9 and 11.6 for the two models, respectively. But I can't figure out why it's not the case when I use my code.
