Graduate School of Advanced Science and Engineering Waseda University
༤
༤㻌 ኈ㻌 ㄽ㻌 ᩥ㻌 ᴫ㻌 せ
Doctoral Thesis Synopsis
ㄽ ᩥ 㢟 ┠ T h e s i s T h e m e
A Study on Bayesian Optimal Estimation with Probabilistic Hidden Structure
Modeling
☜⋡ⓗ㞃ࢀᵓ㐀ࣔࢹࣜࣥࢢࢆ⏝࠸ࡓ Bayes ᭱ 㐺࡞᥎ᐃ㛵ࡍࡿ◊✲
⏦ ㄳ ⪅ (Applicant name)
Takayuki KATSUKI
ᮌ Ꮥ⾜
Department of Electrical Engineering and Bioscience, Research on Probabilistic Information Processing
Oct, 2016
ሗ ฎ ⌮ ࡢ 㔜 せ ᛶ ࡣ ࠊ ࢹ ࣮ ࢱ ࡢ ቑ ຍ ඹ ᪥ ᪥ ቑ ࡋ ࡚ ࠸ ࡿ ࠋ ࠶ ࡽ ࡺ ࡿ ࣔ ࣀ ࡀ ࢭ ࣥ ࢧ ࣮ ࢆ ഛ ࠼ ࠊ ࣥ ࢱ ࣮ ࢿ ࢵ ࢺ ⧅ ࡀ ࡿ ࡼ ࠺ ࡞ ࡾ ࠊ ࢡ ࢭ ࢫ ྍ ⬟ ࡞ 㔞 ࡢ ࢹ ࣮ ࢱ ࡀ ࠊ ᪥ ࠎ ⏕ ࡲ ࢀ ࡚ ࠸ ࡿ ࠋ ே 㛫 ࡶ ࡲ ࡓ ࢭ ࣥ ࢧ ࣮ ࡋ ࡚ ࡢ ᙺ ࢆ ᢸ ࠸ ࠊ ࣔ ࣂ
ࣝ ࢹ ࣂ ࢫ ࡸ ࢯ ࣮ ࢩ ࣕ ࣝ ࢿ ࢵ ࢺ ࣡ ࣮ ࢡ ࢆ ࡋ ࡚ 㔞 ࡢ ࢹ ࣮ ࢱ ࢆ ⏕ ࡳ ฟ ࡋ ࡚ ࠸ ࡿ ࠋ
ሗ ฎ ⌮ ࡛ ࡣ ࠊ ࡇ ࢀ ࡽ 㔞 ࡢ ࢹ ࣮ ࢱ ࢆ ✀ ࠎ ࡢ ┠ ⓗ ά ⏝ ࡍ ࡿ ࠋ
ከ ࡃ ࡢ ሗ ฎ ⌮ ࡣ ࠊほ ࡉ ࢀ ࡓ ࢹ ࣮ ࢱ ࡽ ே 㛫 ࡀ ゎ 㔘 ྍ ⬟ ࡞ ᙧ ࡢ ኚ ࢆ ⾜ ࠺ ࠋ
࠼ ࡤ ࠊ ほ ࡉ ࢀ ࡓ ᩥ ❶ ࡽ ࡑ ࡢ ࢺ ࣆ ࢵ ࢡ ࢆ ぢ ฟ ࡍ ࡇ ࠊ ࠼ ࡽ ࢀ ࡓ ⏬ ീ ࡿ
≀ య ࣛ ࣋ ࣝ ࢆ ࡅ ࡿ ࡇ ➼ ࡀ ◊ ✲ ࡉ ࢀ ࡚ ࠸ ࡿ ࠋ ࡇ ࡢ ኚ ࡢ 㐣 ⛬ ࡣ ࠊ ᩘ Ꮫ ⓗ グ
㏙ ࡍ ࡿ ࡇ ࡀ ࡛ ࡁ ࠊ ࡑ ࢀ ࡣ ࠊ ఱ ࢆ ⾜ ࠸ ࡓ ࠸ ࢆ ᫂ ♧ ࡍ ࡿ ࡇ ➼ ࡋ ࠸ ࠋ
ሗ ฎ ⌮ ࠾ ࡅ ࡿ ୖ ㏙ ࡢ ኚ ࡢ 㐣 ⛬ ࡣ ࠊ ほ ࢹ ࣮ ࢱ ࢆ ධ ຊ ࠊ ኚ ⤖ ᯝ ࢆ ฟ ຊ ࡍ ࡿ ᥎ ᐃ 㛵 ᩘ ࡋ ࡚ ⾲ ࡉ ࢀ ࠊ ࢹ ࣮ ࢱ ࡢ ᛶ ㉁ ࢆ ⾲ ⌧ ࡋ ࡓ ࣔ ࢹ ࣝ ࠊ ᥎ ᐃ 㛵 ᩘ ࡀ ࠺
࠶ ࢀ ࡤ ᮃ ࡲ ࡋ ࠸ ࡢ ࢆ ᣦ ᐃ ࡍ ࡿ ホ ౯ ᇶ ‽ ࢆ 」 ྜ ࡋ ࡓ ┠ ⓗ 㛵 ᩘ ࡢ ᭱ 㐺 ၥ 㢟 ࡢ ⤖ ᯝ ࡋ ࡚ グ ㏙ ࡉ ࢀ ࡿ ࠋ ࠼ ࡤ ࠊ ほ ࢹ ࣮ ࢱ ࡽ ࠊ ࡑ ࡇ ࡽ ┤ ᥋ ᚓ ࡽ ࢀ ࡞ ࠸ ࠶ ࡿ ᣦ ᶆ ್ ࢆ ồ ࡵ ࡿ ၥ 㢟 ࢆ ⪃ ࠼ ࡓ ࠊ ほ ࢹ ࣮ ࢱ ࡑ ࡢ ᣦ ᶆ ್ ࡑ ࢀ ࡒ ࢀ ࡢ ࡿ ⯙ ࠸ ࠊ ཬ ࡧ ࡑ ࢀ ࡽ ࡢ 㛵 ಀ ᛶ ࢆ グ ㏙ ࡍ ࡿ ࡢ ࡀ ࣔ ࢹ ࣝ ࡛ ࠶ ࡾ ࠊ ᥎ ᐃ 㛵 ᩘ ࡢ せ ồ ࢆ グ ㏙ ࡍ ࡿ ࡢ ࡀ ホ ౯ ᇶ ‽ ࡛ ࠶ ࡿ ࠋ
ࣔ ࢹ ࣝ ࡣ ࠊ ࢹ ࣮ ࢱ ࡢ ௬ ᐃ ࣭ ௬ ㄝ ࡛ ࠶ ࡾ ࠊ ࡑ ࡢ ᵓ ᡂ ࢆ ⪃ ࠼ ࡿ ࡇ ࢆ ࣔ ࢹ ࣜ ࣥ ࢢ
ࡪ ࠋ ୖ ㏙ ࡋ ࡓ ࢹ ࣮ ࢱ ࡣ ࠊ ⤌ ࡳ ㎸ ࡳ ࢭ ࣥ ࢧ ࣮ ࡸ ࢿ ࢵ ࢺ ࣡ ࣮ ࢡ ᖏ ᇦ ᖜ ࡢ ไ ⣙ ࠊ ே 㛫 ࡼ ࡿ ᭕ ࡞ ⾲ ⌧ ➼ ࡼ ࡗ ࡚ ࠊ ୍ ⯡ ☜ ࡛ ᵓ 㐀 ࡉ ࢀ ࡚ ࠸ ࡞ ࠸ ࢹ ࣮ ࢱ ࢆ ከ ࡃ ྵ ࡴ ࠋ ࡇ ࢀ ࡽ ࡢ ࢹ ࣮ ࢱ ࡽ ᭷ ⏝ ࡞ ሗ ࢆ ᢳ ฟ ࡍ ࡿ ࡣ ࠊ 㐺 ษ ࡞ ࣔ ࢹ ࣜ ࣥ ࢢ ࢆ ⾜
࠺ ࡇ ࡀ 㔜 せ ࡛ ࠶ ࡿ ࠋ ࠼ ࡤ ࠊ ᩥ Ꮠ ࡢ ⨶ ิ ࡛ ࠶ ࡿ ᩥ ❶ ࢆ ༢ ㄒ ิ ࡛ グ ㏙ ࡍ ࡿ ࡇ ࠊ
⏬ ⣲ ್ ࡢ 㞟 ྜ ࡛ ࠶ ࡿ ⏬ ീ ࢆ ≉ ᚩ ⓗ ࡞ ࣃ ࢱ ࣮ ࣥ ࡢ 㞟 ྜ ࡛ グ ㏙ ࡍ ࡿ ࡇ ࠊ ࡀ ࡇ ࢀ ┦ ᙜ ࡍ ࡿ ࠋ ࡇ ࢀ ࡽ ࡢ ฎ ⌮ ࡀ ࠺ ࡲ ࡃ ാ ࡅ ࡤ ࠊ ࡑ ࡢ ᚋ ࡢ ࢹ ࣮ ࢱ ࡢ ゎ 㔘 ࡣ ᱁ ẁ ᐜ ᫆ ࡞
ࡿ ࠋ ♧ ࡋ ࡓ ⮬ ↛ ゝ ㄒ ࡸ ⏬ ീ ࡢ ฎ ⌮ ࡛ ࡣ ࠊ ᢳ ฟ ࡉ ࢀ ࡓ ༢ ㄒ ิ ࡽ ᩥ ❶ ࡢ ࢺ ࣆ ࢵ ࢡ
ࢆ ゎ 㔘 ࡋ ࡓ ࡾ ࠊ ᒁ ᡤ ⓗ ࡞ ⏬ ീ ࣃ ࢱ ࣮ ࣥ ࡢ 㞟 ྜ ࡽ ⏬ ീ య ࡢ ព ࢆ ゎ 㔘 ࡋ ࡓ ࡾ ࡍ
ࡿ ࠋ
ホ ౯ ᇶ ‽ ࡣ ࠊఱ ࡽ ࡢ 㔞 ࡢ ᭱ ᑠ ࠊࡶ ࡋ ࡃ ࡣ ᭱ ࡛ ࠶ ࡿ ሙ ྜ ࡀ ୍ ⯡ ⓗ ࡛ ࠶ ࡿ ࠋ
᭱ ࡶ ᡂ ຌ ࡋ ࡚ ࠾ ࡾ ࠊ⏝ ࠸ ࡽ ࢀ ࡿ ࡇ ࡀ ከ ࠸ ࡶ ࡢ ࡣ ࠊ ㄗ ᕪ 㛵 ࡍ ࡿ ࡶ ࡢ ࡛ ࠶ ࡿ ࠋ ᥎ ᐃ 㛵 ᩘ ᇶ ࡙ ࠸ ࡓ ᥎ ᐃ ⤖ ᯝ ࡑ ࡢ ṇ ゎ ࡍ ࡿ ್ ࡢ 㛫 ࡢ ㄗ ᕪ ࡢ ࢧ ࣥ ࣉ ࣝ ᖹ ᆒ ࢆ ᭱ ᑠ ࡍ ࡿ ᪉ ἲ ࡣ ࠊ ≉ ᭱ ᑠ ἲ ࡤ ࢀ ࠊ ከ ࡃ ࡢ ᛂ ⏝ ࠾ ࠸ ࡚ ᡂ ຌ ࢆ
ࡵ ࡚ ࠸ ࡿ ࠋ ࡲ ࡓ ࠊ ୖ ㏙ ࡢ ㄗ ᕪ 㝈 ࡽ ࡎ ᥎ ᐃ ್ ࡢ ㄗ ᕪ ࢆ ẕ 㞟 ᅋ ࠾ ࠸ ࡚ ᖹ ᆒ ࡋ ࡓ ࡶ ࡢ ࡣ ࠊ ỗ ㄗ ᕪ ࡤ ࢀ ࠊ ண 㔜 ࡁ ࢆ ⨨ ࡃ ᶵ Ე Ꮫ ⩦ ➼ ࡢ ศ 㔝 ࡛ ࡣ ࠊ ࡇ ࡢ
᭱ ᑠ ࢆ ホ ౯ ᇶ ‽ ࡍ ࡿ ࡇ ࡀ ከ ࠸ ࠋ
ࡇ ࡇ ࡛ ࠊ ࣔ ࢹ ࣝ ホ ౯ ᇶ ‽ ࡣ ᐦ ᥋ 㛵 㐃 ࡋ ࡚ ࠸ ࡿ ࡓ ࡵ ࠊ ࣔ ࢹ ࣜ ࣥ ࢢ ࡣ ࠊ ᥇ ⏝ ࡍ
No.1
ࡿ ホ ౯ ᇶ ‽ ᇶ ࡙ ࡁ ࠊ ࡑ ࢀ ࡀ ィ ⟬ ྍ ⬟ ࡞ ⠊ ᅖ ࡛ ࠊ ၥ 㢟 ࡢ グ ㏙ ᚲ せ ༑ ศ ࡞ 」 㞧 ᗘ
࡛ タ ィ ࡉ ࢀ ࡿ ᚲ せ ࡀ ࠶ ࡿ ࠋ ୖ ㏙ ࡢ ࡼ ࠺ ࠊ ࣔ ࢹ ࣝ ࡣ ࡼ ࡾ ṇ ☜ ࢹ ࣮ ࢱ ࡢ ᛶ ㉁ ࢆ グ
㏙ ࡍ ࡿ ࡇ ࢆ ồ ࡵ ࡽ ࢀ ࡿ ࡀ ࠊ ࣔ ࢹ ࣝ ホ ౯ ᇶ ‽ ࡢ ┦ ᛶ ࡼ ࡗ ࡚ ࡣ ࠊ ᭱ 㐺 ࡀ ィ ⟬ ᅔ 㞴 ࡞ ࡿ ሙ ྜ ࡀ ࠶ ࡿ ࠋ ࡑ ࡢ ࡓ ࡵ ࠊ ホ ౯ ᇶ ‽ ࡼ ࡗ ࡚ ࡣ ࠊ ࡑ ࢀ ࢆ ィ ⟬ ྍ ⬟ ࡍ ࡿ ࡓ ࡵ ࠊ ࣔ ࢹ ࣝ ࡢ ᪉ ไ ⣙ ࢆ ࡅ ࡿ ሙ ྜ ࡶ ࠶ ࡿ ࠋ ࠼ ࡤ ࠊ ࠶ ࡽ ࡺ ࡿ ၥ 㢟 㐺 ⏝ ྍ
⬟ ࡞ ᴟ ࡵ ࡚ ⮬ ⏤ ᗘ ࡢ 㧗 ࠸ ࣔ ࢹ ࣝ ࢆ ᥇ ⏝ ࡋ ࡓ ࡍ ࡿ ࠋ ⮬ ⏤ ᗘ ࡣ ࣔ ࢹ ࣝ ࣃ ࣛ ࣓ ࣮ ࢱ ࡢ
ᩘ ࡰ ྠ ࡌ ࡛ ࠶ ࡿ ࡓ ࡵ ࠊ ⮬ ⏤ ᗘ ࡢ 㧗 ࠸ ࣔ ࢹ ࣝ ࡛ ࡣ ࠊ ᭱ 㐺 ࡉ ࢀ ࡿ ࡁ ࣃ ࣛ ࣓ ࣮ ࢱ ࡢ ᩘ ࡀ ᴟ ࡵ ࡚ ከ ࡃ ࡞ ࡿ ࠋ ୍ ⯡ ᭱ 㐺 ࡣ ࣃ ࣛ ࣓ ࣮ ࢱ ࡢ ⤌ ࡳ ྜ ࢃ ࡏ ࡢ ᩘ ౫ Ꮡ ࡋ
࡚ ィ ⟬ 㔞 ࡀ ቑ ࠼ ࡿ ࡓ ࡵ ࠊ ᴟ ➃ ⮬ ⏤ ᗘ ࡢ 㧗 ࠸ ࣔ ࢹ ࣝ ࡣ ᭱ 㐺 ࡀ ᅔ 㞴 ࡛ ࠶ ࡿ ࠋ ୍ ᪉
࡛ ࠊ ᴟ ➃ ⮬ ⏤ ᗘ ࡢ ప ࠸ ࣔ ࢹ ࣝ ࡀ ᚲ ࡎ ࡋ ࡶ Ⰻ ࠸ ヂ ࡛ ࡶ ࡞ ࠸ ࠋ ⮬ ⏤ ᗘ ࡢ ప ࠸ ࣔ ࢹ ࣝ ࡣ ၥ 㢟 ࡢ グ ㏙ ࢆ ṇ ☜ ⾜ ࠼ ࡎ ࠊ ௬ ᭱ 㐺 ࡀ ᡂ ຌ ࡋ ࡓ ࡋ ࡚ ࡶ ࠊ ⤖ ᯝ ࡀ ᡤ ᮃ ࡢ ᛶ
⬟ ࢆ ‶ ࡓ ࡉ ࡞ ࠸ ࡇ ࡀ ከ ࠸ ࠋ
ᮏ ㄽ ᩥ ࡛ ࡣ ࠊBayes ⓗ ࡞ ホ ౯ ᇶ ‽ ࢆ ⏝ ࠸ ࠊ ࡑ ࡢ ᇶ ‽ ࠾ ࠸ ࡚ ⌧ ᐇ ⓗ ࡞ ᥎ ᐃ ࣝ ࢦ ࣜ ࢬ ࣒ ࢆ ᑟ ฟ ࡍ ࡿ ࡓ ࡵ ࡢ ࠊ ☜ ⋡ ⓗ ࣔ ࢹ ࣜ ࣥ ࢢ 㛵 ࡍ ࡿ ◊ ✲ ࢆ ⾜ ࠺ ࠋBayes ⓗ ࡞ ホ ౯ ᇶ ‽ ᇶ ࡙ ࡁ ᭱ 㐺 ࡉ ࢀ ࡓ ᥎ ᐃ 㛵 ᩘ ࡣ ࠊ ୍ ⯡ Ᏻ ᐃ ࡞ ゎ ࡞ ࡿ ࡇ ࡀ ▱ ࡽ ࢀ
࡚ ࠸ ࡿ ࠋ ࡑ ࢀ ࡣ ࠊ ホ ౯ ᇶ ‽ ࠾ ࠸ ࡚ ࠊ ࡑ ࡢ ࣔ ࢹ ࣝ ࡢ ᐃ ࡉ ࢀ ࠺ ࡿ ☜ ⋡ ⓗ ࡞ ኚ ື ࡢ ᙳ 㡪 ࢆ ⪃ ៖ ࡋ ࡓ ᥎ ᐃ ࢆ ┠ ᣦ ࡍ ࡓ ࡵ ࡛ ࠶ ࡿ ࠋ ࡇ ࡢ ᛶ ㉁ ࢆ ⏝ ࡋ ࠊ ᮏ ㄽ ᩥ ࡛ ࡣ ࠊ ୍ ⯡
ࢹ ࣮ ࢱ ࡀ ㊊ ࡋ ࡸ ࡍ ࡃ ࠊ ゎ ࡀ Ᏻ ᐃ ࡞ ࡾ ࡸ ࡍ ࠸ ࠊ ᩍ ᖌ ࡞ ࡋ ᥎ ᐃ ࡸ 㞃 ࢀ ኚ ᩘ ᥎ ᐃ ࢆ ⾜ ࠺ ၥ 㢟 ࢆ ᢅ ࠺ ࠋ୍ ᪉ ࡛ ࠊ Bayes ᭱ 㐺 ࡞ ᥎ ᐃ ࡣ ィ ⟬ ࢥ ࢫ ࢺ ࡀ ࡁ ࠸ ࡇ ࡶ ▱
ࡽ ࢀ ࡚ ࠾ ࡾ ࠊࡑ ࢀ ࢆ ⾜ ࠼ ࡿ ࣔ ࢹ ࣝ ࡢ ࢡ ࣛ ࢫ ࡣ 㝈 ᐃ ࡉ ࢀ ࡿ ࡇ ࡀ ከ ࠸ ࠋᮏ ㄽ ᩥ ࡛ ࡣ ࠊ Bayes ᭱ 㐺 ࡞ ᥎ ᐃ ࡀ ⌧ ᐇ ⓗ ࡞ ィ ⟬ 㛫 ࡛ ⾜ ࠼ ࡿ ⠊ ᅖ ࡛ ࠊ 㐺 ษ ࡞ 」 㞧 ᗘ ࢆ ᣢ ࡘ ☜ ⋡
ࣔ ࢹ ࣝ ࢆ ࠊ ࠸ ࡃ ࡘ ࡢ ᛂ ⏝ ྜ ࢃ ࡏ ࡚ ๓ ▱ ㆑ ࢆ ά ⏝ ࡋ ࡚ タ ィ ࣭ ᥦ ࡍ ࡿ ࠋ Bayes ᭱ 㐺 ࡞ ᥎ ᐃ ࢆ ⾜ ࠺ ሙ ྜ ࠊ ᚋ ศ ᕸ ࡀ ᚲ せ ࡞ ࡿ ࡓ ࡵ ࠊ ල య ⓗ ࡞ ࣔ ࢹ ࣜ ࣥ ࢢ
࡛ ࡣ ࠊ ᚋ ศ ᕸ ࡢ ᑟ ฟ ᚲ せ ࡞ ほ ࣔ ࢹ ࣝ ࠊ ๓ ศ ᕸ ࢆ タ ィ ࡍ ࡿ ࠋ ᮏ ㄽ ᩥ ࡢ ᵓ ᡂ ࢆ ௨ ୗ ♧ ࡍ ࠋ
㸯 ❶ ࡛ ࡣ ࠊ ◊ ✲ ࡢ ⫼ ᬒ ࠊ ព ⩏ ࢆ ㏙ ࠊ ᮏ ㄽ ᩥ ࡢ ᑟ ධ ࢆ ⾜ ࠺ ࠋ
㸰 ❶ ࡛ ࡣ ࠊᮏ ㄽ ᩥ ࡛ ᢅ ࠺ Bayes᭱ 㐺 ࡞ ᥎ ᐃ ᇶ ࡙ ࡃ ࣝ ࢦ ࣜ ࢬ ࣒ ࡢ ᯟ ⤌ ࡳ ࢆ ♧ ࡍ ࠋ࠸ ࡃ ࡘ ࡢ Bayes ⓗ ࡞ ホ ౯ ᇶ ‽ ࢆ ᑟ ධ ࡋ ࠊࡑ ࢀ ࡒ ࢀ ᑐ ࡋ ࡚ ࠊ ࠺ ࠸ ࡗ ࡓ ᥎ ᐃ 㛵 ᩘ ࡀ ᭱ 㐺 ࡢ ⤖ ᯝ ࡋ ࡚ ᑟ ฟ ࡉ ࢀ ࡿ ࢆ ㄝ ᫂ ࡍ ࡿ ࠋ ࡑ ࡢ 㝿 ࠊ ྛ ᥎ ᐃ 㛵 ᩘ ࠾ ࡅ ࡿ ຠ ⋡ ⓗ ࡞ ィ ⟬ ࣝ ࢦ ࣜ ࢬ ࣒ ࡋ ࡚ ࠊMarkov chain Monte Carlo ἲ ࠊ ኚ ศ Bayes ἲ 㛵 ࡍ ࡿ ࣞ ࣅ ࣗ ࣮ ࢆ ⾜ ࠸ ࠊ ල య ⓗ ࡞ ࣝ ࢦ ࣜ ࢬ ࣒ ࡢ ᑟ ฟ ࢆ ⾜ ࠺ ࠋ ᭦ ࠊ ኚ ศ Bayes ἲ ࡘ ࠸ ࡚ ࡢ ㏆ ఝ ᡭ ἲ ࢆ ᥦ ࣭ ᑟ ධ ࡍ ࡿ ࠋ
㸱 ❶ ࡛ ࡣ ࠊ ල య ࡋ ࡚ ࠊ ㏻ ὶ ᥎ ᐃ ၥ 㢟 ࢆ ᢅ ࠺ ࠋ ㏻ ࡣ ࠊ ᡃ ࠎ ࡢ ⏕ ά ࣭ ⤒ ῭ ࡢ ᇶ ┙ ࡞ ࡿ ᴟ ࡵ ࡚ 㔜 せ ࡞ せ ⣲ ࡛ ࠶ ࡿ ࠋ ㏻ ὶ ࡣ ࠊ ㏻ ࢆ ⾲ ࡍ ᇶ ᮏ ⓗ ࡞ 㔞 ࡛ ࠶ ࡿ
No.2
㏻ ὶ 㔞 ㏻ ᐦ ᗘ ࠊ ㏻ ㏿ ᗘ ࡽ ᵓ ᡂ ࡉ ࢀ ࡿ ࠋ ࡇ ࢀ ࡽ ࡢ ࠺ ࡕ ࢀ 㸰 ࡘ ࡀ ồ ࡲ
ࢀ ࡤ ṧ ࡾ ࡢ 㸯 ࡘ ࡣ ୍ ព ᐃ ࡲ ࡿ ࠋ ᮏ ❶ ࡛ ࡣ ࠊ ࢧ ࣥ ࣉ ࣜ ࣥ ࢢ ࣞ ࣮ ࢺ ࡸ ⏬ ㉁ ࠊ ⏬ ゅ ࡢ ᝏ ࠸ ࢘ ࢙ ࣈ ࢝ ࣓ ࣛ ⏬ ീ ࡽ ㏻ ᐦ ᗘ ㏻ ㏿ ᗘ ࢆ ࡑ ࢀ ࡒ ࢀ ᩍ ᖌ ࡞ ࡋ ࡢ タ ᐃ ࡛ ᥎ ᐃ ࡍ ࡿ ၥ 㢟 ࢆ ᢅ ࠺ ࠋ ᚑ ᮶ ἲ ࠾ ࡅ ࡿ ๓ ᥦ ᮲ ௳ ࡛ ࠶ ࡗ ࡓ 㧗 ࠸ ࢧ ࣥ ࣉ ࣜ ࣥ ࢢ ࣞ ࣮ ࢺ ࡸ ⏬
㉁ ࠊ ⏬ ゅ ࢆ せ ồ ࡏ ࡎ ࠊ ே ᡭ ࡼ ࡿ ࣛ ࣋ ࣝ ࡅ ࢆ ⾜ ࡗ ࡓ ᩍ ᖌ ࢹ ࣮ ࢱ ࢆ ࡶ ⏝ ࠸ ࡞ ࠸ ࡇ
ࡽ ࠊ ୍ ⯡ ᥎ ᐃ ࡣ Ᏻ ᐃ ࡞ ࡾ ࡸ ࡍ ࠸ ࡀ ࠊ 㸰 ❶ ࡢ ᯟ ⤌ ࡳ ᇶ ࡙ ࡁ ࠊBayes ᭱ 㐺 ࡞ ᥎ ᐃ ࢆ ⾜ ࠺ ࡇ ࡛ ࡇ ࢀ ࢆ ゎ Ỵ ࡍ ࡿ ࠋ ᥦ ἲ ࡣ ᚑ ᮶ ἲ ẚ ࡚ 㧗 ᗘ ࡞ ࣥ ࣇ ࣛ
ࡸ ࢥ ࢫ ࢺ ࡢ 㧗 ࠸ ᩍ ᖌ ࢹ ࣮ ࢱ ࢆ ᚲ せ ࡋ ࡞ ࠸ ࡓ ࡵ ࠊ ᑟ ධ ࢥ ࢫ ࢺ ࡢ ప ࠸ ᪉ ἲ ࡞ ࡿ ࠋ ᐇ ࢹ ࣮ ࢱ ࢆ ⏝ ࠸ ࡓ ᐇ 㦂 ࠾ ࠸ ࡚ ࠊ ࢧ ࣥ ࣉ ࣜ ࣥ ࢢ ࣞ ࣮ ࢺ ࡸ ⏬ ㉁ ࠊ ⏬ ゅ ࡢ ᝏ ࠸ ᮲ ௳ ࡛
ࡶ ࠊ ᥦ ἲ ࡀ Ⰻ ዲ ㏻ ὶ ᥎ ᐃ ࢆ ⾜ ࠼ ࡿ ࡇ ࢆ ☜ ࡵ ࡓ ࠋ
㸲 ❶ ࡛ ࡣ ࠊ ู ࡢ ࡋ ࡚ ࠊ ⏬ ീ ㉸ ゎ ീ ၥ 㢟 ࢆ ᢅ ࠺ ࠋ ⏬ ീ ฎ ⌮ ࡢ ◊ ✲ ࠾ ࠸ ࡚ ࠊ
ຎ ࡋ ࡓ ほ ⏬ ീ ࡽ ࡑ ࡢ ཎ ⏬ ീ ࢆ ᥎ ᐃ ࣭ ඖ ࡍ ࡿ ࡇ ࡣ ࠊ 㠀 ᖖ ᇶ ᮏ ⓗ ࡘ 㔜 せ ࡞ ၥ 㢟 ࡛ ࠶ ࡿ ࠋ ᮏ ❶ ࡛ ࡣ ࠊ ≉ ⨨ ࢬ ࣞ ࠊ ࣎ ࢣ ࠊ ゎ ീ ᗘ ࡢ ప ୗ ➼ ࡢ ⥺ ᙧ ຎ ኚ
ࢆ ཷ ࡅ ࡓ ほ ⏬ ീ ࡽ ඖ ⏬ ീ ࡢ ඖ ࢆ ⾜ ࡞ ࠺ ㉸ ゎ ീ ၥ 㢟 ࢆ ᢅ ࠺ ࠋ ᚑ ᮶ ἲ ࡼ ࡾ ࡶ
ຎ ኚ ࢆ 㐺 ษ ⾲ ⌧ ࡛ ࡁ ࡿ ほ ࣔ ࢹ ࣝ ࢆ ᥦ ࡋ ࠊ ⏬ ീ ࡢ ๓ ศ ᕸ ࡋ ࡚ ࠊ ⏬ ീ ࡢ ࡽ ࡉ 㐃 ⥆ ᛶ ࢆ ྠ ⾲ ⌧ ࡛ ࡁ ࡿ 」 ᒙGauss-Markov☜ ⋡ ሙ ࡑ ࡢ ὴ ⏕
ࣔ ࢹ ࣝ ࢆ ⏝ ࠸ ࡿ ࠋ ㉸ ゎ ീ ᥎ ᐃ ࡣ ࠊ ほ ࢹ ࣮ ࢱ ࡀ ༑ ศ ࡞ ሙ ྜ ࠊ ゎ ࡀ ୍ ព ᐃ ࡲ ࡽ
࡞ ࠸ Ⰻ タ ᐃ ၥ 㢟 ࡞ ࡿ ࡇ ࡀ ࠶ ࡿ ࡀ ࠊ 㸰 ❶ ࡢ ᯟ ⤌ ࡳ ᇶ ࡙ ࡁ ࠊBayes ᭱ 㐺 ࡞ ᥎ ᐃ ࢆ ⾜ ࠺ ࡇ ࡛ ࡇ ࢀ ࢆ ゎ Ỵ ࡍ ࡿ ࠋ ᐇ 㦂 ࠾ ࠸ ࡚ ࡣ ࠊ ᥦ ἲ ࡀ ᪤ Ꮡ ἲ ࡼ ࡾ ࡶ 㧗 ⢭ ᗘ
᥎ ᐃ ࢆ ⾜ ࠼ ࡿ ࡇ ࢆ ☜ ࡵ ࡓ ࠋ
㸳 ❶ ࡛ ࡣ ࠊ ධ ຊ 㑅 ᢥ ⓗ ᅇ ᖐ ࢆ ᢅ ࠺ ࠋ ᅇ ᖐ ࡣ ࠊ ሗ ฎ ⌮ ࠾ ࡅ ࡿ ᇶ ᮏ ⓗ ࡞ ၥ 㢟 タ ᐃ ࡛ ࠶ ࡾ ࠊ ධ ຊ 㐃 ⥆ ್ ࡢ ฟ ຊ ࡢ 㛫 ࡢ 㛵 ᩘ ࢆ Ꮫ ⩦ ࡍ ࡿ ࠋ ほ ࢹ ࣮ ࢱ ࡽ 㐃 ⥆ ್
ࢆ ண ࡍ ࡿ ၥ 㢟 ୍ ⯡ ᛂ ⏝ ࡛ ࡁ ࡿ 㠀 ᖖ 㔜 せ ࡞ ၥ 㢟 ࡛ ࠶ ࡿ ࠋ ᮏ ❶ ࡛ ࡣ ࠊ ≉ Ꮫ ⩦ ࢹ ࣮ ࢱ ࠾ ࠸ ࡚ ࠊ ᩍ ᖌ ࢹ ࣮ ࢱ ࡀ ほ ࢹ ࣮ ࢱ ࡢ ୍ 㒊 ࡢ 㡿 ᇦ ࡢ ࡳ ᇶ ࡙ ࠸ ࡚ ࡉ ࢀ ࡚
࠸ ࡿ ≧ ἣ ࠾ ࡅ ࡿ ᅇ ᖐ ࢆ ᢅ ࠺ ࠋ ධ ຊ ࡛ ࠶ ࡿ ほ ࢹ ࣮ ࢱ ࡢ ୍ 㒊 ࢆ 㞃 ࢀ ኚ ᩘ ࣔ ࢹ ࣜ ࣥ ࢢ ࡼ ࡗ ࡚ 㑅 ᢥ ⓗ ᩍ ᖌ ࢹ ࣮ ࢱ ᑐ ᛂ ࡅ ࡿ ࡇ ࡛ ࠊ ࡇ ࡢ ၥ 㢟 タ ᐃ ࢆ 㐺 ษ ᢅ ࠺
ࣔ ࢹ ࣝ ࢆ ᥦ ࡍ ࡿ ࠋ 㞃 ࢀ ኚ ᩘ ࢆ ⏝ ࡋ ࡓ ࣔ ࢹ ࣜ ࣥ ࢢ ࡣ ࠊ ᥎ ᐃ ࡍ ࡿ ࣃ ࣛ ࣓ ࣮ ࢱ ࡢ ᩘ ࡀ ከ ࡃ ࡞ ࡿ ࡓ ࡵ ࠊ ほ ࢹ ࣮ ࢱ ࡀ ༑ ศ ࡞ ሙ ྜ ࠊ ゎ ࡀ Ᏻ ᐃ ࡞ ࡿ ࡇ ࡀ ࠶ ࡿ ࡀ ࠊ 㸰 ❶ ࡢ ᯟ ⤌ ࡳ ᇶ ࡙ ࡁ ࠊBayes ᭱ 㐺 ࡞ ᥎ ᐃ ࢆ ⾜ ࠺ ࡇ ࡛ ࡇ ࢀ ࢆ ゎ Ỵ ࡍ ࡿ ࠋ ᐇ 㦂
࠾ ࠸ ࡚ ࠊ ᪤ Ꮡ ἲ ẚ ࡚ ᥦ ἲ ࡀ ࡼ ࡾ 㧗 ⢭ ᗘ ࡞ ᥎ ᐃ ࢆ ⾜ ࠼ ࡿ ࡇ ࢆ ☜ ࡵ ࡓ ࠋ 㸴 ❶ ࡛ ࡣ ࠊ ᮏ ㄽ ᩥ ࡢ ࡲ ࡵ ࢆ ⾜ ࠸ ࠊ ᚋ ࡢ ᒎ ᮃ ࢆ ㏙ ࡿ ࠋ
No.3
㹌㹭
᪩
᪩✄⏣Ꮫ ༤ኈ㸦ᕤᏛ㸧 Ꮫ⏦ㄳ ◊✲ᴗ⦼᭩
Ặྡ ᮌ Ꮥ⾜ ༳
㸦 ᖺ ᭶ ⌧ᅾ㸧
✀㢮ู 㢟ྡ㸪 Ⓨ⾲࣭Ⓨ⾜ᥖ㍕ㄅྡ㸪 Ⓨ⾲࣭Ⓨ⾜ᖺ᭶㸪 㐃ྡ⪅㸦⏦ㄳ⪅ྵࡴ㸧 ㄽᩥ㸦ᰝㄞ
᭷ࡾ㸧
○ Takayuki Katsuki, Tetsuro Morimura, Masato Inoue, “Traffic Velocity Estimation From Vehicle Count Sequences”, IEEE Transactions on Intelligence Transportation Systems, to appear, 2016.
○ Takayuki Katsuki, Akira Torii, Masato Inoue, “Posterior Mean Super-resolution with a Causal Gaussian Markov Random Field Prior”, IEEE Transactions on Image Processing 21(7), pp.
3182—3193, IEEE, 2012.
Tsuyoshi Idé, Takayuki Katsuki, Tetsuro Morimura, Robert Morris, “City-Wide Traffic Flow Estimation From a Limited Number of Low-Quality Cameras”, IEEE Transactions on Intelligence Transportation Systems, to appear, 2016
㹌㹭
᪩
᪩✄⏣Ꮫ ༤ኈ㸦ᕤᏛ㸧 Ꮫ⏦ㄳ ◊✲ᴗ⦼᭩
✀㢮ู 㢟ྡ㸪 Ⓨ⾲࣭Ⓨ⾜ᥖ㍕ㄅྡ㸪 Ⓨ⾲࣭Ⓨ⾜ᖺ᭶㸪 㐃ྡ⪅㸦⏦ㄳ⪅ྵࡴ㸧 ᅜ 㝿 ㆟
ண✏㸦ᰝㄞ
᭷ࡾ㸧
○ Takayuki Katsuki, Masato Inoue, “Bayesian Regression Selecting Valuable Subset from Mixed Bag Training Data”, In Proceedings of the 23rd International Conference on Pattern Recognition (ICPR2016), to appear, 2016.
○ Takayuki Katsuki, Tesuro Morimura, Tsuyoshi Idé, “Unsupervised Object Counting without Object Recognition”, In Proceedings of the 23rd International Conference on Pattern Recognition (ICPR2016), to appear, 2016.
○ Takayuki Katsuki, Masato Inoue, “Posterior Mean Super-Resolution with a Compound Gaussian Markov Random Field Prior”, In Proceedings of the 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2012), pp. 841—844, 2012.
Satoshi Hara, Takayuki Katsuki, Hiroki Yanagisawa, Takafumi Ono, Ryo Okamoto, Shigeki Takeuchi, “Consistent and Efficient Nonparametric Different-Feature Selection”, In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS2017), to appear, 2017.
Daisuke Sato, Tetsuro Morimura, Takayuki Katsuki, Yosuke Toyota, Tsuneo Kato, Hironobu Takagi, “Automated Help System for Novice Older Users from Touchscreen Gestures”, In Proceedings of the 23rd International Conference on Pattern Recognition (ICPR2016), to appear, 2016.
Kumiko Maeda, Tetsuro Morimura, Takayuki Katsuki, Masayoshi Teraguchi, “Frugal signal control using low resolution web-camera and traffic flow estimation”, In Proceedings of the 2014 Winter Simulation Conference, pp. 2082—2091, 2014.
Takayuki Osogami, Takayuki Katsuki, “A Hierarchical Bayesian Choice Model with Visibility”, In Proceedings of the 22nd International Conference on Pattern Recognition, pp. 3618—3623, 2014.
Vikas Joshi, Nithya Rajamani, Takayuki Katsuki, Naveen Prathapaneni, LV Subramaniam,
“Information fusion based learning for frugal traffic state sensing”, In Proceedings of the 23rd international joint conference on Artificial Intelligence, pp. 2826—2832, 2013.
Tsuyoshi Idé, Takayuki Katsuki, Tetsuro Morimura, Robert Morris, “Monitoring Entire-City Traffic using Low-Resolution Web Cameras”, In Proceedings of the 20th ITS World Congress,
#3143, 2013.
㹌㹭
᪩
᪩✄⏣Ꮫ ༤ኈ㸦ᕤᏛ㸧 Ꮫ⏦ㄳ ◊✲ᴗ⦼᭩
✀㢮ู 㢟ྡ㸪 Ⓨ⾲࣭Ⓨ⾜ᥖ㍕ㄅྡ㸪 Ⓨ⾲࣭Ⓨ⾜ᖺ᭶㸪 㐃ྡ⪅㸦⏦ㄳ⪅ྵࡴ㸧
◊✲㸦ᰝ ㄞ࡞ࡋ㸧
ᮌ Ꮥ⾜, ᳃ᮧ ဴ㑻, “పࣇ࣮࣒࣮ࣞࣞࢺ⣔ิ⏬ീࡽࡢBayes㏻㏿ᗘ᥎ᐃ”, ➨16 ᅇሗㄽⓗᏛ⩦⌮ㄽ࣮࣡ࢡࢩࣙࢵࣉ(IBIS2013), 2013.
㣤⏣⣫ኈ㸪ᮌᏕ⾜㸪ᜍ⚄㈗⾜㸪୰ᕝ ⿱ᚿ, “࣋ࢬ᥎ᐃࢆ⏝࠸ࡓᣦᩘᛀ༷ᆺ⮬ᕫᅇᖐࣔ
ࢹࣝࡼࡿࢺࣞࣥࢻ, Ꮨ⠇ᛶࢆྵࡴࢹ࣮ࢱࡢண ”, ➨ 92 ᅇᩘ⌮ࣔࢹࣝၥ㢟ゎỴ (MPS)◊✲Ⓨ⾲, 2013.
ᮌᏕ⾜, ᳃ᮧဴ㑻, ᡭ ๛, “ప⏬㉁࡞ᐃⅬ⏬ീࡽࡢᩍᖌ࡞ࡋ㌴୧ྎᩘ᥎ᐃ”, ➨ 15 ᅇሗㄽⓗᏛ⩦⌮ㄽ࣮࣡ࢡࢩࣙࢵࣉ(IBIS2012), 2012.
ᮌ Ꮥ⾜, ୖ ┿㒓, “ΰྜࣔࢹࣝࡋ࡚ࡢ」ᒙGauss-Markov ☜⋡ሙࡼࡿ⏬ീࡢಟ
㡿ᇦศ”, 㟁Ꮚሗ㏻ಙᏛᢏ⾡◊✲ሗ࿌, 111(275), IBISML2011-75, pp. 223-230, 2011.
ᮌ Ꮥ⾜, 㫽ᒃ ⱥ, ୖ ┿㒓, “」ᒙMarkov☜⋡ሙ⥺ᙧຎኚᑐࡍࡿBayes㉸ゎ
ീ”, 㟁Ꮚሗ㏻ಙᏛᢏ⾡◊✲ሗ࿌, 110(83), NC2010-10, pp. 63-68, 2010.
