Beginning Anomaly Detection Using

mean squared error, named so because the function 

given input 

θ, the weights, finds the average difference squared between the predicted 

value and the actual value. The parameter h

θ

 represents the model with the weight 

parameter 

θ passed in, so h

θ

(x

i

) gives the predicted value for x

i

 with model’s weights 

θ. The 

parameter y

i

 represents the actual prediction for the data point at index i. If the parameter 

you are passing in includes both weight and bias, then it will look more like Figure 

3-12

.

Note that h

w, b

(x

i

) will have the formula in Figure 

3-13

.

The cost function reflects the overall performance of the model with the current 

weight parameter, so the most ideal value output from the cost function will be as small 

as possible. Since the cost function is a measure of how far the model’s predictions 

are from the actual value, you want to make the output from the cost function as small 

as possible since that means your predictions were almost what the actual prediction 

should be.

To minimize the cost function, you need to tell the model how to adjust the weights, 

but how do you do that? If you think back to calculus, optimization problems involved 

finding the derivative and solving for the critical points (points where the derivative of 

the original equation is 0). In your case, you want to find the