Quiz 2: Question about HMM's

Quiz 2: Question about HMM's

by Haeata Balfour Ash -
Number of replies: 2

Hi, in the below question, I don't understand how we arrive at the correct answers. In particular I don't follow why t5 is necessary. My understanding for HMM's is we only depend on the last k tags, and since k = 1, t3 is the only relevant tag

Considering an order-1 HMM model to tag a word sequence with tags t𝑘, select all of the following expressions which are equal to 𝑃(t4| t2 t3 t5 t6):


In reply to Haeata Balfour Ash

Re: Quiz 2: Question about HMM's

by Jean-Cédric Chappelier -
> since k = 1, t3 is the only relevant tag
No, not at all! This is something I explained several times in the review and hands-on sessions, as well as already once on this forum: see my reply to https://moodle.epfl.ch/mod/forum/discuss.php?d=95289

Now the above question, although strongly related, is not exactly the same. So if you want a formal proof, here is comes:
𝑃(t_4| t_2 t_3 t_5 t_6) = \frac{𝑃(t_4 t_5 t_6| t_2 t_3)}{𝑃(t_5 t_6| t_2 t_3 )}=\frac{𝑃(t_4 | t_2 t_3)𝑃(t_5| t_2 t_3 t_4)𝑃(t_6| t_2 t_3 t_4 t_5)}{\sum_t 𝑃(T_4=t, t_5, t_6| t_2 t_3)}=\frac{𝑃(t_4 | t_3)𝑃(t_5| t_4)𝑃(t_6| t_5)}{\sum_t 𝑃(T_4=t | t_3)𝑃(t_5| T_4=t)𝑃(t_6| t_5)}=\frac{𝑃(t_4 | t_3)𝑃(t_5| t_4)}{\sum_t 𝑃(T_4=t | t_3)𝑃(t_5| T_4=t)}
from where you can derive any of the above three; for instance:
𝑃(t_4| t_3 t_5) = \frac{𝑃(t_4 t_5|  t_3)}{𝑃(t_5|  t_3 )}=\frac{𝑃(t_4 |  t_3)𝑃(t_5| t_3 t_4)}{\sum_t 𝑃(T_4=t, t_5|  t_3)}=\frac{𝑃(t_4 | t_3)𝑃(t_5| t_4)}{\sum_t 𝑃(T_4=t | t_3)𝑃(t_5| T_4=t)}