How to calculate Softmax Regression probabilities?

Question

The scatter plot of Iris Dataset is shown in the figure below. Assume Softmax Regression is used to classify Iris to Setosa, Versicolor, or Viriginica using just petal length and petal width. If all the weights required for Softmax Regression initialized to 0.5 and the network includes bias nodes:

1) Write the weight vectors and equations for calculating the class probabilities.

2) We have a new iris and we have measured petal length = 4.5  and petal width = 1.6. Using the above initial model, what would be the result of classification?

3) If we change all the weights related to the class blue to 1 and keep all other weights 0.5, what will be the predicted class?

Answer 1

Please look at the following solution:

Comments

Hey Guys, on the last page, the third part, the result of z3 should be "1+4.1+1.6=7.1", instead of 6.1.   (Although it doesn't affect the final result )

Actually, that was the original version I submitted to our professor, but I mistakenly changed it before making the video.
Thanks for the correction from my classmate Prabh Singh! And good luck on the final exams everyone!

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The question doesn't make any mention of a bias, so we just assume it is 1?