Implementing SGD(Stochastic Gradient Descent) for Linear Regression

METRIC:

LOSS FUNCTION:

Loss function
  1. Initially assume m = 0 and c = 0. Let L be our learning rate (a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function). L could be a small value like 0.0001 for good accuracy.
  2. Calculate the partial derivative of the loss function with respect to m, and plug in the current values of x, y, m and c in it to obtain the derivative value D.
Derivative of loss function with respective to m
Derivative of loss function with respective to c
  • we update the current value of m and c using the equations.
  • Repeat this process until our loss function is a small value(which means 0 error ,100%accuracy). The value of m and c that we are left with now will be the optimal values.

IMPLEMENTATION OF SGD :

  1. Stochastic Gradient Descent is sensitive to feature scaling, so it is highly recommended to scale your data.
  2. For example, scale each attribute on the input vector X to [0,1] or [-1,+1], or standardize it to have mean 0 and variance 1.
  3. Note that the same scaling must be applied to the test vector to obtain meaningful results. This can be easily done using StandardScaler.
print("R^2 score for
our model :", r2_score(Y_test, pred_test))
out[4]:R^2 score for our model : 0.7226745354368981

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kalikiri harichandhana

kalikiri harichandhana

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