Machine Learning Specialization : Regression and Classification : Week 3: Optional Lab 02 : Evaluating g(z) where z is a vector

Course Q&A Machine Learning Specialization Supervised ML: Regression and Classification
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In the Optional Lab 02 of Course 1 Week 3, does anyone know how the function g(z) is evaluated when z is a vector of scalar values, where each scalar component value is computed from using the linear regression model with a previously unknown vector of input feature values \vec x^{(i)}, for some i , where i = 1 to m?

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Hi @ai_is_cool

The function g(z) is applied to the output of the linear regression model z = w⋅x + b. When z is a vector (as in this case), the sigmoid function is applied element-wise to each value in the vector. So, every computed z[i] gets transformed into a probability between 0 and 1.

Hope it helps!

1 Like
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Thanks @Alireza_Saei for your reply.

Yes that helps although I was thinking more mathematically how e^{-z} is evaluated when z is a vector of scalar values.

Do you know if there is even such an operation mathematically?

Mathematically this operation doesn’t exist unless you consider a matrix with a single column and more than 1 row.

It would be interesting to create an array z in Python using the NumPy module and try passing it to the function math.exp(…).

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Hi @ai_is_cool ,

For deep learning, the function np.exp() is preferred as it deals with array like input.

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There are lots of math library functions that work element-wise on all values in a scalar, vector, or matrix.

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Do you mean Python library modules?