[first song] machine learning of rebirth - linear regression

About 【 Head song 】 Linear regression theory and case practice Other units are only seen by fans , Students who want more learning resources pay attention to me ~

It's not easy to create , Before reference , Point a praise , Collection , You can't pay too much attention , Family

The first 1 Turn off ： Data loading and analysis

Task description

Our mission ： Write a small program that can load linear regression related data .

Programming requirements

The data in the actual combat content is a metadata , utilize pandas Read in the data file , And attach the name tag to the corresponding data , Respectively Population and Profit.

1. data = pd.read_csv(path, header= , names=[ ' ', ' ' ])

if __name__ == "__main__":
    path = os.getcwd() + '/ex1data1.txt'
    # utilize pandas Read in the data data, And the data attributes are named 'Population' and 'Profit'
    #********* begin *********#
    data=pd.read_csv(path,header=None,names=['Population','Profit'])
    #********* end *********#
    print(data.shape)

The first 2 Turn off ： Calculate the loss function

Programming requirements

According to the above formula , Write calculation loss function computeCost(X, y, theta), Finally back to cost.

• X： I. metadata matrix , namely Population data ;
• y： Target data , namely Profit data ;
• theta： Model parameters ;
• cost： Loss function value .

Test instructions

Test input ： nothing
Test output ：the cost is: 32.0727338775

def computeCost(X, y, theta):
    # Write the loss function calculation function according to the formula 
    #********* begin *********#
    inner=np.power(((X*theta.T)-y),2)
    cost=np.sum(inner)/(2*len(X))
    cost=round(cost,10)
    #********* end *********#
    return cost

  The first 3 Turn off ： Perform gradient descent to get a linear model

Programming requirements

According to the above formula , Write calculation loss function gradientDescent(X, y, theta, alpha, iters), Finally back to theta, cost.

• x： I. metadata matrix , namely Population data ;
• y： Target data , namely Profit data ;
• theta： Model parameters ;
• m： Data scale ;
• α: Learning rate .

Test instructions

Test input ： nothing
Test output ： The model parameters are :[[-3.241402141.1272942]]

def gradientDescent(X, y, theta, alpha, iters):
    temp = np.matrix(np.zeros(theta.shape))
    parameters = int(theta.ravel().shape[1])
    cost = np.zeros(iters)
    
    for i in range(iters):
        error = (X * theta.T) - y
        
        for j in range(parameters):
            #********* begin *********#
            term=np.multiply(error,X[:,j])
            temp[0,j]=theta[0,j]-((alpha/len(X))*np.sum(term))
            #********* end *********#
        theta = temp
        cost[i] = computeCost(X, y, theta)

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