The instructor said, “To include the bias into the matrix multiplication is to add an entire column with number one in the data table and a row with the bias, which is -1.5 in the model”.
Could you tell me the reason why he picked 1 to add to the entire table in the bias column?
The bias values of 1 will be multiplied by the bias weight.
It allows this computation:
f = x*w + b
To be implemented as:
f = x * w + 1 * b
… by using a single dot-product operation, when you include ‘b’ as an additional element in the ‘w’ vector.
Reasoning step 1)
What you want is to check if ‘Lottery×1 + Win×1 -1.5’ is greater than 0.
Reasoning step 2)
‘Lottery×1 + Win×1 -1.5’ can be viewed as ‘Lottery×1 + Win×1 +1×-1.5’
Reasoning step 3)
You can think of the table on the left as a 9x3 matrix which we call A. Similarly, you can also think of the table on the right as a 3x1 matrix which we call B.
Reasoning step 4)
The matrix multiplication C=A×B is a 9x1 matrix, each row of which corresponds to ‘Lottery×1 + Win×1 +1×-1.5’ for each mail.
Keep it up!!
