M-Step
3 points possible (graded)
Fixing , we want to update such that our lower bound is maximized.
What is the optimal ? For simplicity, assume we only have two data points and for this particular question. Answer in terms of , , and , , which are defined to be
(For ease of input, use subscripts instead superscripts, i.e. type x_i for . Type gamma_ki for .)
unanswered
What is the optimal ? Answer in terms of , , and , which are defined as above to be , and .
(Type hatmu_k for . As above, for ease of input, use subscripts instead superscripts, i.e. type x_i for . Type gamma_ki for .)
unanswered
What is the optimal ? Answer in terms of and , which are defined as above to be ,
(As above, type gamma_ki for .)
Note: that you must account for the constraint that where .
Note: If you know that some aspect of your formula equals an exact constant, simplify and use this number, i.e. .