Exercise 2014.6.24 Sequential Data Modeling
Name
No.
x0 x1 x2
x3 x4 x5
知恵ちゃんは夏祭りに行った．彼女は笑ったり，泣いたり，黙り込んだりと大忙し．彼女がお
祭を好きかどうか確信が持てない．その行動確率をHMMでモデル化した．以下のHMMを用
いて，次ページ以降の問題に答えよ．
Tomoe-chan went to the summer festival. Sometimes she laughed, sometimes she cried,
and sometimes she was totally silent. But I am not sure whether she ‘hate’ or ‘like’ the
festival. We modeled her behavioral probability with HMM. Please answer some
questions in the following pages based on HMM below.
Like
1 .0 
x0  x3
20
x0
0  x2  x4
x2
x0  x2  x4
x4
x0  x2  x4
SInitial
𝑃(𝐶𝑟𝑦𝑖𝑛𝑔)=
x x
1 .0  1 4
20
Hate
x1
𝑃(𝐿𝑎u𝑔ℎ𝑖𝑛𝑔)= x  x
𝑃(𝐿𝑎u𝑔ℎ𝑖𝑛𝑔)= x
𝑃(𝑆𝑖l𝑒𝑛𝑐𝑒)=
x0  x3
20
1
x1  x4
20
𝑃(𝑆𝑖l𝑒𝑛𝑐𝑒)=
𝑃(𝐶𝑟𝑦𝑖𝑛𝑔)=
x x
1 .0  2 5
20
3
 x5
x3
x1  x3  x5
x5
x1  x3  x5
Submit to : B7F, Augmented Human Communication Lab, Submit Box
Deadline : 7/1 AM9:00 , Questions to TA (Mailto: [email protected])
x2  x5
20
1
Exercise 2014.6.24 Sequential Data Modeling
① 1ページ目のHMMの変数に値を代入し，次の空欄を埋めよ．
Please assign values for each variables of HMM in page 1. Then, estimate the
figure below.
※分数で記入 (Fill it out with fraction)
Hate
SInitial
Like
𝑃(𝐿𝑎u𝑔ℎ𝑖𝑛𝑔)=
𝑃(𝑆𝑖l𝑒𝑛𝑐𝑒)=
𝑃(𝐶𝑟𝑦𝑖𝑛𝑔)=
𝑃(𝐿𝑎u𝑔ℎ𝑖𝑛𝑔)=
𝑃(𝑆𝑖l𝑒𝑛𝑐𝑒)=
𝑃(𝐶𝑟𝑦𝑖𝑛𝑔)=
2
Exercise 2014.6.24 Sequential Data Modeling
② 次の空欄を埋めよ．
Please estimate the following things.
※分数で記入 (Fill it out with fraction)
𝑃(𝐿𝑖k𝑒|SInitial ) =
𝑃(𝐻𝑎t𝑒|SInitial ) =
𝑃(𝐿𝑖k𝑒|𝐿𝑖k𝑒)=
𝑃(𝐿𝑖k𝑒|𝐻𝑎t𝑒)=
𝑃(𝐻𝑎t𝑒|𝐿𝑖k𝑒)=
𝑃(𝐻𝑎t𝑒|𝐻𝑎t𝑒)=
𝑃(𝐿𝑎u𝑔ℎ𝑖𝑛𝑔|𝐿𝑖k𝑒)=
𝑃(𝐿𝑎u𝑔ℎ𝑖𝑛𝑔|𝐻𝑎t𝑒)=
𝑃(𝑆𝑖l𝑒𝑛𝑐𝑒|𝐿𝑖k𝑒)=
𝑃(𝑆𝑖l𝑒𝑛𝑐𝑒|𝐻𝑎t𝑒)=
𝑃(𝐶𝑟𝑦𝑖𝑛𝑔|𝐿𝑖k𝑒)=
𝑃(𝐶𝑟𝑦𝑖𝑛𝑔|𝐻𝑎t𝑒)=
③ HMMsの‘隠れ’は，知恵ちゃんの何が隠れているか？何故，そう考えたか？
What is hidden in Tomoe-chan’s hidden Markov models? And why you think so?
3
Exercise 2014.6.24 Sequential Data Modeling
④ 格子図を書き， backward algorithm を用いて，以下の確率を求めよ．
Please draw lattice diagram and evaluate the probability below using
backward algorithm.
𝑃(𝐿𝑎u𝑔ℎ𝑖𝑛𝑔, 𝐿𝑎u𝑔ℎ𝑖𝑛𝑔, 𝐶𝑟𝑦𝑖𝑛𝑔)=
𝑃(𝐶𝑟𝑦𝑖𝑛𝑔, 𝐿𝑎u𝑔ℎ𝑖𝑛𝑔, 𝑆𝑖l𝑒𝑛𝑐𝑒)=
4
Exercise 2014.6.24 Sequential Data Modeling
⑤ 以下のような行動が観測されたときの，知恵ちゃんの感情状態を推定せよ．
When following behaviors are observed, estimate the underlying Tomoechan’s emotional state/condition.
‘Silence’ → ‘Crying’ → ‘Silence’ → ‘Laughing’ → ‘Laughing’ → ‘Silence’
※計算式を必ず書くこと(Write a calculating formula necessarily)
→
→
→
→
→
5
Exercise 2014.6.24 Sequential Data Modeling
＜おまけ問題 ( Extra question )＞
身の回りの事象をHMMsでモデル化せよ．
Please find any sequential event around you, and construct the HMMs.
6