グ㏙ᏊタィᡭἲᶵᲔᏛ⩦䛻䜘䜛ゎ㔘ྍ⬟䝰䝕䝸䞁䜾රᗜ┴❧኱Ꮫ㧗ᗘ⏘ᴗ⛉Ꮫᢏ⾡◊✲ᡤ⸨஭ ᑗ┠ḟ••••••䝬䝔䝸䜰䝹䝈䞉䜲䞁䝣䜷䝬䝔䜱䜽䝇䠄MI䠅MI䛾┠ⓗ≀㉁⛉Ꮫ䛸ᶵᲔᏛ⩦䛾㛵ಀゎ㔘ྍ⬟䝰䝕䝸䞁䜾⥺ᆺ⊂❧グ㏙Ꮚ⏕ᡂ䠄LIDG䠅ἲ
LIDGἲ䛾ᛂ⏝౛䝬䝔䝸䜰䝹䝈䞉䜲䞁䝣䜷䝬䝔䜱䜽䝇䠄MI䠅䠄≀㉁⛉Ꮫ × AI䠅⤫ィᏛ䚸᝟ሗ⛉Ꮫ䚸䝟䝍䞊䞁ㄆ㆑䚸䝕䞊䝍䝃䜲䜶䞁䝇➼䛾ศ㔝䛷Ⓨ㐩䛧䛶䛝䛯ᶵᲔᏛ⩦䠄⤫ィⓗᏛ⩦䠅䛾ᡭἲ䜢≀㉁⛉Ꮫ䜈ᛂ⏝䛧䛯◊✲ᵝ䚻䛺ᶵᲔᏛ⩦ᡭἲ⤫ィᏛ⥺ᙧᅇᖐศᯒ᭱ᑠ஧஌ἲ䠄OLS䠅
୺ᡂศศᯒ䠄PCA䠅ィ⟬ᶵ⛉Ꮫ᝟ሗ⛉Ꮫ䝰䞁䝔䜹䝹䝻ἲ䠄MC䠅㑇ఏⓗ䜰䝹䝂䝸䝈䝮䠄GA䠅㑇ఏⓗ䝥䝻䜾䝷䝭䞁䜾䠄GP䠅㐍໬ⓗ䜰䝹䝂䝸䝈䝮䠄EA䠅⢏Ꮚ⩌᭱㐺໬䠄PSO䠅䝟䝍䞊䞁ㄆ㆑䝃䝫䞊䝖䝧䜽䝍䞊䝬䝅䞁䠄SVM䝙䝳䞊䝷䝹䝛䝑䝖䠄NN䠅䝕䜱䞊䝥䝷䞊䝙䞁䜾䠄DL䠅䝷䞁䝎䝮䝣䜷䝺䝇䝖䠄RF䠅䜰䞁䝃䞁䝤䝹Ꮫ⩦⤫ィⓗ௬ㄝ᳨ᐃỴᐃᮌ䠄DT䠅㉥ụ᝟ሗ㔞ᇶ‽䠄AIC䠅䝰䞁䝔䜹䝹䝻ᮌ᥈⣴䠄MCTS䠅䝧䜲䝈᥎ᐃᅽ⦰䝉䞁䝅䞁䜾䝇䝟䞊䝇䝰䝕䝸䞁䜾䝧䜲䝈᭱㐺໬
L1ṇ๎໬䠄LASSO䠅
L2ṇ๎໬䠄Ridge䠅䝧䜲䝈⤫ィMI䛾┠ⓗ1. ≀㉁᥈⣴:Ⰻ䛔≀ᛶ್䜢ᣢ䛴≀㉁䞉ᮦᩱ䛾Ⓨぢண 䝰䝕䝹䛾ᵓ⠏䛿ᚲ䛪䛧䜒ᚲせ䛷䛿䛺䛔
2. ≀ᛶண :ண 䝰䝕䝹䜢௬ᐃ䛧䚸ᮍ▱≀㉁䛾≀ᛶ䜢㧗⢭ᗘ䛻ண㠀⥺ᙧ䝰䝕䝹䠄Black box㛵ᩘ䠅䚸䛒䜛䛔䛿⥺ᙧ䝰䝕䝹
3. ἲ๎Ⓨぢ:≀ᛶⓎ⌧ᶵᵓ䛾ゎ᫂ᚓ䜙䜜䛯▱ぢ䛛䜙᪂䛯䛺ཎ⌮䚸ἲ๎䛾Ⓨぢ4. ≀ᛶ䝕䞊䝍䝧䞊䝇ᵓ⠏≀㉁⛉Ꮫ䛸ᶵᲔᏛ⩦䛸䛾㛵ಀ≀㉁⛉ᏛᶵᲔᏛ⩦EA䚸 BO䚸VS≀㉁᥈⣴≀ᛶண≀ᛶண

䠄Black box䠅䠄⥺ᙧ䝰䝕䝹䠅ᶵᵓゎ᫂䚸ἲ๎ⓎぢDL䚸RFLASSO䠛䠛䠛᭱㐺໬ၥ㢟ணၥ㢟䠄Black box䠅䝇䝟䞊䝇䝰䝕䝸䞁䜾䛺䛧౑䛘䜛⤫ィⓗᡭἲ䛿䛺䛔ї ≀㉁⛉Ꮫ⪅䛜స䜛䜉䛝ї ⥺ᆺ⊂❧グ㏙Ꮚ⏕ᡂ䠄LIDG䠅ἲ䛻䜘䜛ゎ㔘ྍ⬟䝰䝕䝸䞁䜾ゎ㔘ྍ⬟ᛶ䛿ᚲせ䛛䠛♫఍ⓗせㄳ:≀㉁᥈⣴ 䠚 ≀ᛶண䠄Black box䠅 䠚 ≀ᛶண䠄ゎ㔘ྍ⬟䝰䝕䝹䠅≀㉁᥈⣴䛻䛿ᚲ䛪䛧䜒≀ᛶண 䛿ᚲせ䛷䛿䛺䛔䠄EA䠅≀ᛶண 䛻䛿ᚲ䛪䛧䜒ゎ㔘ྍ⬟ᛶ䛿ᚲせ䛷䛿䛺䛔䠄DL䚸RF䠅䜎䛯䚸䝕䞊䝍⛉Ꮫ⪅䛾ከ䛟䛿ຠ⋡䛾Ⰻ䛔᭱㐺໬䜔䚸㧗㏿䞉㧗⢭ᗘண 䛻䛧䛛⯆࿡䛜䛺䛔䚹ゎ㔘ྍ⬟ᛶ䛸ண⢭ᗘ䛿䛒䜛⛬ᗘ䝖䝺䞊䝗䜸䝣䛾㛵ಀ

80%䛧䛛ᙜ䛯䜙䛺䛔ゎ㔘䞉ㄝ᫂ྍ⬟䛺䝰䝕䝹䛸䚸99%ᙜ䛯䜛䝤䝷䝑䜽䝪䝑䜽䝇㛵ᩘ䛷䛿䚸䛹䛱䜙䛜౯್䛜㧗䛔䛛䠛ゎ㔘ྍ⬟ᛶ䛾ព⩏䞉 ᶵᵓゎ᫂䚸≀⌮ἲ๎Ⓨぢ䛻䛴䛺䛜䜛ྍ⬟ᛶ䛜䛒䜛䠄Ꮫ⾡ⓗ䛻᪂䛯䛺ᴫᛕ䛾Ⓨぢ䠅䞉 ධຊ䠄グ㏙Ꮚ䠅䛸ฟຊ䠄≀ᛶ್䠅䛸䛾㛵ಀ䛜䜟䛛䜛䝤䝷䝑䜽䞉䝪䝑䜽䝇㛵ᩘ䛷䛿ධຊ䛸ฟຊ䛸䛾㛫䛾㛵ಀ䛜୙᫂ї䛹䛾䜘䛖䛺ධຊ䛜Ⰻ䛔ฟຊ䜢ᣢ䛴䛛䠄ண䜑䠅䜟䛛䜙䛺䛔ї䜎䛯䚸䛭䛾㛵ᩘ䛾㐺⏝⠊ᅖ䛜䜟䛛䜙䛺䛔୍᪉䚸ゎ㔘ྍ⬟䛺䝰䝕䝹䛷䛒䜜䜀䚸䛹䛾䝟䝷䝯䞊䝍䜢䛹䜜䛰䛡ୖ䛢䜜䜀≀ᛶ್䛜䛹䜜䛰䛡ୖ䛜䜛䛛䚸䛸䛔䛖䛣䛸䛜䜟䛛䜛䚹їⰋ䛔≀㉁ೃ⿵䛾ぢᙜ䛜䛴䛟ї䝰䝕䝹䛾㐺⏝⠊ᅖ䛜䜟䛛䜛䠄ྍ⬟ᛶ䛜䛒䜛䠅ї㝈⏺್䛜䜟䛛䜛ї䛭䛾㝈⏺್䜢㉸䛘䜛䛯䜑䛾䝠䞁䝖䛜ᚓ䜙䜜䜛䠄ྍ⬟ᛶ䛜䛒䜛䠅ゎ㔘ྍ⬟䛺䝰䝕䝹䛸䛿䠛
1. ༢⣧䛺ᙧ䛷䛒䜛
2. ⤒㦂䜔┤ឤ䛻ッ䛘䜛ᙧ
3. ண ⢭ᗘ䛜䛭䛣䛭䛣㧗䛔ࢇ૜= ࢉ࢕࢔࢙࢚.
૛ࢀ䜘䛳䛶䚸ゎ㔘ྍ⬟䝰䝕䝹䠄䛩䛺䜟䛱䚸≀⌮ⓗព࿡䜢ᢳฟྍ⬟䛺䝰䝕䝹䠅䜢ᚓ䜛䛯䜑䛻䛿䚸䝰䝕䝹䛾ᵓ⠏ẁ㝵䛷䛂ண ⢭ᗘ䛃䛰䛡䛷䛺䛟䚸
1. ༢⣧䛥
2. ᩚྜᛶ䛻䜒༑ศ㓄៖䛩䜛ᚲせ䛜䛒䜛䚹䝰䝕䝹䛾䛂༢⣧䛥䛃䛸䛂ᩚྜᛶ䛃䛾ᐃ⩏䛂༢⣧䛥䛃䞉 ㄝ᫂ኚᩘ䛜ᑡᩘ䠄䝇䝟䞊䝇䠅䛷䛒䜛䞉 ㄝ᫂ኚᩘ䛾ᙧ䛜༢⣧౯್䛜㧗䛔䛸ุ᩿࢞࢏࢞࢏ ,,࢞࢐䛂ᩚྜᛶ䛃䞉 ≀⌮ⓗᩚྜᛶ䠄≀⌮ⓗḟඖ䚸ᑐ⛠ᛶ䠅䞉 ஦๓▱㆑䚸⤒㦂䛸䛾ᩚྜᛶ|࢞࢏ െ ࢞࢐ |࢞࢏ + ࢞࢐

䛣䜜䜙䛿㏻ᖖ䛾ᶵᲔᏛ⩦䛷䛿↓ど䛥䜜䜛䛜䚸LIDGἲ䛷䛿⪃៖ྍ⬟⥺ᙧ䝰䝕䝹䛸㠀⥺ᙧ䝰䝕䝹⥺ᙧ䝰䝕䝹:䞉 ィ⟬䝁䝇䝖ప䛔䞉 㐣㐺ྜ䛧䛻䛟䛔䠄low variance䠅䠄䝃䞁䝥䝹✵㛫䛾ኚ໬䛻㕌ឤ䠅䞉 䝅䞁䝥䝹䛺䝰䝕䝹䛜ᚓ䜙䜜䜛ї ≀⌮ⓗព࿡䜢ᢳฟ䛷䛝䜛㠀⥺ᙧ䝰䝕䝹:䞉 ィ⟬䝁䝇䝖㧗䛔䞉 㐣㐺ྜ䛧䜔䛩䛔䠄high variance䠅䠄䝃䞁䝥䝹✵㛫䛾ኚ໬䛻ᩄឤ䠅䞉 Ṥ䛹䝤䝷䝑䜽䝪䝑䜽䝇䛺䝰䝕䝹䛜ᚓ䜙䜜䜛ї ≀⌮ⓗព࿡䛾ᢳฟ䛿ᅔ㞴䞉 ⾲⌧ຊ䛜ప䛔䠄high bias䠅䞉 ⾲⌧ຊ䛜㧗䛔䠄low bias䠅⾲⌧ຊ䛸䝅䞁䝥䝹䛥䛸䛾㛫䛾䝖䝺䞊䝗䜸䝣䜢䛹䛾䜘䛖䛻ゎỴ䛩䜛䛛䠛ї グ㏙Ꮚ䜢᪂䛯䛻⏕ᡂ䛧䚸䛭䛾୰䛛䜙Ⰻ䛔グ㏙Ꮚ䛾䜏䜢㑅䜆ゎ㔘ྍ⬟䝰䝕䝸䞁䜾䛾ᇶᮏ᪉㔪⥺ᙧᅇᖐ ᤼ グ㏙Ꮚ⏕ᡂ ᤼ 䝰䝕䝹㑅ᢥ⥺ᙧᅇᖐศᯒ
1. ⥺ᙧ䝰䝕䝹䛾௬ᐃࢿ: ㄗᕪ㡯 (䜺䜴䝇ศᕸ)࢟ = ࢄࢼ + ࢿ┠ⓗኚᩘ䠄ᚑᒓኚᩘ䠅෡ ᥎ᐃ್࢟:෡ࢼ: ᅇᖐಀᩘ෡
෡ = ࢄࢼ࢟௚䛾≀ᛶ್(≉ᚩ㔞/ㄝ᫂ኚᩘ/グ㏙Ꮚ)

䝃䞁䝥䝹
1䝃䞁䝥䝹
2…
䝃䞁䝥䝹m

෡
2. 䛒䜛᮲௳䛾䜒䛸䛷ᅇᖐಀᩘ ࢼ 䜢ồ䜑䜛࢟ࢼ䞉 LASSO෡ࢼࡸ࡭ࡿࡿࡻ = ‫ܖܑܕ܏ܚ܉‬ࢼ…

࢞૚૚࢞૚૛

…

…

…

࢟࢓࢞࢓૚

࢞࢓૛…

࢟૛…

࢞૛૚…

࢞૛૛૛࢖૚࢟ െ ࢄࢼ ࢒ + ࣅ ࢼ ࢒૛૚࢞࢔࢞૚࢔
࢞૛࢔…

࢞࢓࢔ࢄ ࢓×࢔ :グ㏙Ꮚ⾜ิ䠄ィ⏬⾜ิ䠅࢔ࢼ ࢒ ‫ ؠ‬෍ ࢼ࢏ ࢖૛…

Lp 䝜䝹䝮䛾ᐃ⩏૛࢟ െ ࢄࢼ ࢒࢞૛࢟૚䞉 ᭱ᑠ஧஌ἲ䠄OLS䠅෡ࢼࡻࡸࡿ = ‫ܖܑܕ܏ܚ܉‬࢞૚࢏ୀ૚૚/࢖グ㏙Ꮚ⾜ิ䛸グ㏙Ꮚ䝧䜽䝖䝹䛾ᐃ⩏ィ⏬⾜ิ
グ㏙Ꮚ⾜ิ(࢓ × ࢔ + ૚)૚૚‫ڭ‬
ࢄ=૚‫ڭ‬૚࢞૚૚࢞૛૚‫ڭ‬࢞࢏૚‫ڭ‬࢞࢓૚

࢞૚૛࢞૛૛‫ڭ‬
࢞࢏૛‫ڭ‬࢞࢓૛

䝟䝍䞊䞁ㄆ㆑䛷䛾グ㏙Ꮚ䠄≉ᚩ䠅䝧䜽䝖䝹䛾ᐃ⩏࢞࢏, = [૚, ࢞࢏૚ , ࢞࢏૛ , … , ࢞࢏࢔ ]ࢀ

࢔ + ૚ ḟඖ≉ᚩ✵㛫ୖ䛾䝧䜽䝖䝹࢏ ␒┠䛾䝃䞁䝥䝹䛻ᑐ䛩䜛≉ᚩ㔞䛾㓄ิ
ࢄ = [࢞૚, , ࢞૛, , … , ࢞࢓, ]ࢀ
ࢀ࢟࢏ = ࢞࢏, ࢼ + ࢿ࢏

( ࢟࢏ = ࢼࢀ ࢞࢏, + ࢿ࢏ )

࢟ = ࢄࢼ + ࢿ࢔ 䛿㏻ᖖᅛᐃ࢓ 䛿ቑຍ䛩䜛ྍ⬟ᛶ䛜䛒䜛‫ڮ‬‫ڮ‬‫ڰ‬‫ڮ‬‫ڰ‬‫ڮ‬࢞,࢐࢞૚࢐࢞૛࢐‫ڭ‬࢞࢏࢐‫ڭ‬࢞࢓࢐‫ڮ‬‫ڮ‬‫ڰ‬‫ڮ‬‫ڰ‬‫ڮ‬࢞૚࢔࢞૛࢔‫ڭ‬࢞࢏࢔ ࢞࢏,‫ڭ‬࢞࢓࢔࢟ = ࢄࢼ + ࢿ䝇䝟䞊䝇䝰䝕䝸䞁䜾䛷䛾グ㏙Ꮚ䜉䛟䛸䜛䛾ᐃ⩏࢞,࢐ = [࢞૚࢐ , ࢞૛࢐ , … , ࢞࢓࢐ ]ࢀ࢓ ḟඖ䝃䞁䝥䝹✵㛫ୖ䛾䝧䜽䝖䝹࢐ ␒┠䛾グ㏙Ꮚ䛾ྛ䝃䞁䝥䝹䛷䛾್䛾㓄ิ
ࢄ = [૚, ࢞,૚ , ࢞,૛ , … , ࢞,࢔ ]࢔࢟ = ෍ ࢞,࢐ ࢼ࢐ + ࢿ࢐ୀ૙

࢟ = ࢄࢼ + ࢿ࢔ 䛿ቑຍ䛩䜛ྍ⬟ᛶ䛜䛒䜛࢓ 䛿㏻ᖖᅛᐃ

┠ⓗኚᩘグ㏙Ꮚ୕ゅᙧ䛾㠃✚

Height ࢎ20ಶ䛾ᵝ䚻䛺୕ゅᙧ䛾䝕䞊䝍グ㏙Ꮚ⏕ᡂ䛾౛Area ࡿBase ࢈ᗏ㎶䛸㧗䛥䜢グ㏙Ꮚ䛸䛧䛯⥺ᙧᅇᖐࡿ = ૙. ૚૚૟ૡ૚ ࢈ + ૙. ૚૜ૠૡ૙ ࢎ െ ૙. ૙૜ૡૠ૟࡭ࢊ࢐. ࡾ૛ = ૙. ૞૞૚૞ᗏ㎶䛸㧗䛥䛾✚䜢᪂䛧䛔グ㏙Ꮚ䛸䛧䛯⥺ᙧᅇᖐࡿ = ૙. ૝ૢૢૡ ࢈ࢎ െ ૛. ૜૜૜ × ૚૙ି૞࡭ࢊ࢐. ࡾ૛ = ૚. ૙૙૙૙グ㏙Ꮚ䛾ᩘ䛿୍䛴ᑡ䛺䛔䛾䛻᥎ᐃ⢭ᗘ䛿Ⰻ䛟䛺䛳䛶䛔䜛䚹グ㏙Ꮚ⏕ᡂ䛾ព⩏䛿䚸グ㏙Ꮚ䛾ᩘ䜢ቑຍ䛥䛫䜛䛣䛸䛷䛿䛺䛟䚸Ⰻ䛔グ㏙Ꮚ䜢స䜛䛣䛸䛷䛒䜛䚹䛣䛾䝰䝕䝹䛛䜙୕ゅᙧ䛾㠃✚䛾ἲ๎䠄බᘧ䠅䜢෌Ⓨぢ૚ࡿ = ࢈ࢎ૛

LIDG䛷䛾グ㏙Ꮚ⏕ᡂ1: ᇶᮏ₇⟬ᇶᮏ䠄ึᮇ䠅グ㏙Ꮚ:࢞૚ , ࢞૛ᇶᮏ₇⟬:࢞࢏ ‫ؠ‬࢞૚ , ࢞૛ ,ି૚࢞ି૚૚ , ࢞૛ ,࢞૚ି૚, ࢞૛ି૚,࢞૚ + ࢞૛ , ࢞૚ െ ࢞૛ ,࢞૚ + ࢞૛ ି૚ , ࢞૚ െ ࢞૛ ି૚ ,࢞૚ + ࢞૛ ି૚ , ࢞૚ െ ࢞૛ ି૚ ,࢞૚࢏ , ࢞૛࢏ , … , ࢞࢓࢏ି૚ି૚࢞ି૚‫ି࢞ ؠ‬૚࢏૚࢏ , ࢞૛࢏ , … , ࢞࢓࢏࢞࢏ ି૚ ‫ؠ‬ࢀࢀ࢞૚࢏ ି૚ , ࢞૛࢏ ି૚ , … , ࢞࢓࢏ ି૚

࢞࢏ + ࢞࢐ ‫ؠ‬ࢀ࢞૚࢏ + ࢞૚࢐ , … , ࢞࢓࢏ + ࢞࢓࢐ࢀ䜒䛱䜝䜣䚸䜒䛳䛸」㞧䛺ᇶᮏ₇⟬䠄ᖹ᪉᰿䜔ᣦᩘ䚸ᑐᩘ㛵ᩘ䛺䛹䠅䜢⪃䛘䛶䜒Ⰻ䛔䛜䚸ゎ㔘ᛶ䛾ほⅬ䛛䜙䚸䛣䛾᫬Ⅼ䛷䛒䜎䜚䛻䜒」㞧䛺ᙧ䜢⪃䛘䜛䛾䛿ዲ䜎䛧䛟䛺䛔䚹䛣䜜䛰䛡䛷䜒䚸䛒䜛⛬ᗘ䛾⾲⌧ຊྥୖ䛜ぢ㎸䜑䜛䚹LIDG䛷䛾グ㏙Ꮚ⏕ᡂ2: ┤✚䛻䜘䜛⏕ᡂ㸦ࢠ࢏ 䛿ᇶᮏ₇⟬䛷ᚓ䜙䜜䛯1ḟグ㏙Ꮚ䛸䛩䜛䚹 ࢞࢏ , ࢞࢐ , ૚/࢞࢏ , |࢞࢏ |,…䠅

1st order:

2nd order:

3rd order:

4th order: …
5th order: …

ࢠ૙ , ࢠ૚ , ࢠ૛ࢠ૛૙ , ࢠ૛૚ , ࢠ૛૛ ,ࢠ૙ ࢠ૚ , ࢠ૙ ࢠ૛ , ࢠ૚ ࢠ૛ࢠ૜૙ , ࢠ૜૚ , ࢠ૜૛ ,ࢠ૛૙ ࢠ૚ , ࢠ૛૙ ࢠ૛ , ࢠ૛૚ ࢠ૛ ,ࢠ૙ ࢠ૛૚ , ࢠ૙ ࢠ૛૛ , ࢠ૚ ࢠ૛૛ ,ࢠ૙ ࢠ૚ ࢠ૛૜ࡴ૝ = ૚૞૜ࡴ૞ = ૛૚૜ࡴ૚ = ૜૜ࡴ૛ = ૟૜ࡴ૜ = ૚૙ࢠ࢏ ࢠ࢐ ‫ࢠ ؠ‬૚࢏ ࢠ૚࢐ , ࢠ૛࢏ ࢠ૛࢐ , … , ࢠ࢓࢏ ࢠ࢓࢐䛣䛾䜘䛖䛻䛧䛶䚸グ㏙Ꮚ䜢ᚲせ䛺䛰䛡ẁ㝵ⓗ䛻䝅䝇䝔䝬䝔䜱䝑䜽䛻⏕ᡂ䛷䛝䜛䚹グ㏙Ꮚ䛾」㞧䛥䜒ẁ㝵ⓗ䛻ቑຍ䛥䛫䜛䛣䛸䛜䛷䛝䜛䚹䠄䜒䛱䜝䜣䛣䜜䜙䛾グ㏙Ꮚ䛾㛫䛻䛿ᚋ㏙䛩䜛ከ㔜ඹ⥺ᛶ䛜⏕䛨䜛ྍ⬟ᛶ䛜䛒䜛䠅ࢀከ㔜ඹ⥺ᛶඹ⥺ᛶ‽ඹ⥺ᛶከ㔜ඹ⥺ᛶ‽ከ㔜ඹ⥺ᛶ࢞ ࢏ = ࢉ࢐ ࢞ ࢐ + ࢉ ૙࢞ ࢏ ~ ࢉ࢐ ࢞ ࢐ + ࢉ૙࢞ ࢏ = ࢉ࢐ ࢞ ࢐ + ࢉ࢑ ࢞ ࢑ + ‫ ڮ‬+ ࢉ ૙࢞ ࢏ ~ ࢉ࢐ ࢞ ࢐ + ࢉ࢑ ࢞ ࢑ + ‫ ڮ‬+ ࢉ૙グ㏙Ꮚ⏕ᡂ䜢⾜䛖䛸䚸ᐜ᫆䛻䛣䛾䜘䛖䛺㛵ಀᘧ䛜⏕ᡂ䛥䜜䛶䛧䜎䛖䚹ఱᨾ䚸ከ㔜ඹ⥺ᛶ䜢᳨ฟ䞉㝖ཤ䛧䛺䛡䜜䜀䛺䜙䛺䛔䛾䛛䠛䠄ఱᨾ䚸グ㏙Ꮚ✵㛫䜢⥺ᙧ⊂❧໬䛧䛺䛡䜜䜀䛺䜙䛺䛔䛛䠛䠅䞉 ᅇᖐಀᩘ䛾ቑ኱䚸Ⓨᩓ䞉 䝃䞁䝥䝹✵㛫䛾ኚ໬䛻ᑐ䛩䜛䝰䝕䝹䛾୙Ᏻᐃᛶ䠄ỗ໬ᛶ⬟䛾పୗ䠅䞉 䝰䝕䝹㑅ᢥ䛾୙Ᏻᐃᛶ᭱ᑠ஧஌ἲ (OLS)ࢄ = ࢞૚ , ࢞૛ , ࢞૜ , … , ࢞࢔෡ࢼ‫ܖܑܕ܏ܚ܉ = ܁ۺ۽‬ࣔࡸ ࢼࣔࢼࢼ࢟ െ ࢄࢼ ࢒ࡸ ࢼ ‫ ࢟ ؠ‬െ ࢄࢼ ࢒૛= െ ࢄࢀ ࢟ െ ࢄࢀ ࢄࢼ = ૙ି૚෡ࢼ‫࢟ ࢀࢄ ࢄ ࢀࢄ = ܁ۺ۽‬૛૛ି૚ࢄࢀ ࢄ=૛ο‫ࢄ ࢀࢄ ܜ܍܌‬ణ䛧䚸ࢄࢀ ࢄ 䛿ṇ๎⾜ิ䛷䛒䜛䛸䛩䜛䚹䛴䜎䜚䚸 ࢄࢀ ࢄ 䛿㏫⾜ิ䜢ᣢ䛴䛸䛩䜛䚹‫ ് ࢄ ࢀࢄ ܜ܍܌‬૙ї 䛣䜜䛿䛴䜎䜚䚸 ࢞૚ , ࢞૛ , ࢞૜ , … , ࢞࢔ 䛜⥺ᆺ⊂❧䛷䛒䜛䛸䛔䛖䛣䛸䚹ṇ๎໬䛾3䛴䛾䜰䝥䝻䞊䝏ࢄ = ࢞૚ , ࢞૛ , ࢞૜ , … , ࢞࢔ 䛻䛚䛔䛶䚸࢞૚ , ࢞૛ , ࢞૜ , … , ࢞࢔ 䛜⥺ᙧ⊂❧䛷䛺䛡䜜䜀䠛
1. ⨩๎㡯䜢ᑟධ䛧ṇ๎໬䛧䛶䚸⦆࿴ၥ㢟䜢ゎ䛟(Ridge, LASSO)
2. ᇶᗏኚ᥮䛻䜘䜚䚸┤஺ᇶᗏ䜢స䜛 (PCR, PLS)
3. ከ㔜ඹ⥺ᛶ㛵ಀ䜢඲䛶ぢ䛴䛡䛶㝖ཤ䛧䚸⥺ᆺ⊂❧໬䛥䛫䜛(LIDG)ከ㔜ඹ⥺ᛶ࢞ ࢏ = ࢉ૚ ࢞ ૚ + ࢉ ૛ ࢞ ૛ + ‫ ڮ‬+ ࢉ ࢔ ࢞ ࢔

૙ = ࢄࢉ䛴䜎䜚䚸ከ㔜ඹ⥺ᛶ䛜Ꮡᅾ䛩䜛䛸䛔䛖䛣䛸䛿䚸ࢄࢉ = ૙ 䛜㠀⮬᫂䛺ゎ䜢ᣢ䛴䛸䛔䛖䛣䛸䚹ї 䜘䛳䛶䚸ከ㔜ඹ⥺ᛶ䜢᳨ฟ䛩䜛䛯䜑䛻䛿䚸䛭䛾㠀⮬᫂ゎ䠄䛾䝉䝑䝖䠅䜢ぢ䛴䛡䜜䜀Ⰻ䛔䚹ࢄࢉ = ૙ 䛜㠀⮬᫂䛺ゎ䜢ᣢ䛴᮲௳:1. ຎỴᐃ⣔䚸༶䛱 ࢓ < ࢔ 䛾䛸䛝
2. 䝷䞁䜽䛜ⴠ䛱䛶䛔䜛䛸䛝䚸༶䛱 ‫࢓(ܖܑܕ < ࢘ ؠ ࢄ ܓܖ܉ܚ‬, ࢔)࢓࢔૚ ૙ ૙ ૙ ࢇ૙ ૚ ૙ ૙ ࢈૙ ૙ ૚ ૙ ࢉ૙ ૙ ૙ ૚ ࢊ࢓૚૙૙૙૙૙࢔૙૚૙૙૙૙૙ ࢇ૙ ࢈૚ ࢉ૙ ૙૙ ૙૙ ૙㠀⮬᫂ゎ䛾ᩘ䛿௨ୗ䛷୚䛘䜙䜜䜛࢔െ࢘䛣䜜䛜グ㏙Ꮚ㛫䛾ከ㔜ඹ⥺ᛶ㛵ಀ䛾ᩘ㒊ศ✵㛫䝸䝇䝖㑅ᢥἲ䛻䜘䜛ከ㔜ඹ⥺ᛶ䛾㝖ཤ㝵ẁ⾜ิἲ䛛䜙௨ୗ䛾ከ㔜ඹ⥺ᛶ䛜ᚓ䜙䜜䛯䛸䛩䜛࢞࢑ = ࢉ࢑࢏ ࢞࢏ + ࢉ࢑࢐ ࢞࢐

࢞࢒ = ࢉ࢒࢏ ࢞࢏ + ࢉ࢒࢐ ࢞࢐࢓࢞ ࢓ = ࢉ࢓࢏ ࢞ ࢏ + ࢉ࢐ ࢞ ࢐䝸䝇䝖⾲♧࢞࢑ , ࢞࢒ , ࢞࢓ , ࢞࢏ , ࢞࢐Temporary basisࢃ = ‫ ࢏࢞{(ܖ܉ܘܛ‬, ࢞࢐ , ࢞࢑ , ࢞࢒ , ࢞࢓ })ࢄᇱ = [࢞࢏ , ࢞࢐ , ࢞࢑ , ࢞࢒ , ࢞࢓ ]‫ࢄ ܓܖ܉ܚ = ࢃ ܕܑ܌‬ᇱ = ૛䛣䛾⥺ᙧໟ ‫ ࢏࢞{(ܖ܉ܘܛ‬, ࢞࢐ , ࢞࢑ , ࢞࢒ , ࢞࢓ })䛾ᇶᗏ䛾ᩘ䠄ḟඖ䠅䛿 2 䛧䛛䛺䛔䜘䛳䛶䚸ୖ䛾䝸䝇䝖䛛䜙ዲ䛝䛺グ㏙Ꮚ䜢 2 䛴㑅䜆䜘䛖䛻䛩䜛䚹
select ࢞࢏ , ࢞࢐ and remove ࢞࢑ , ࢞࢒ , ࢞࢓orselect ࢞࢏ , ࢞࢑ and remove ࢞࢐ , ࢞࢒ , ࢞࢓orselect ࢞࢒ , ࢞࢓ and remove ࢞࢏ , ࢞࢐ , ࢞࢑…

ึᮇグ㏙Ꮚ✵㛫䛜ᣢ䛴䛔䛛䛺䜛᝟ሗ䠄ᅇᖐ⢭ᗘ䠅䜒ⴠ䛸䛥䛪䛻グ㏙Ꮚ䛾ᩘ䜢ῶ䜙䛩䛣䛸䛜䛷䛝䜛䚹LIDG methodඛ⾜◊✲䛾⤂௓
LIDG䛾㐺⏝౛䚸ඛ⾜◊✲䛸䛾ẚ㍑

ඛ⾜◊✲
L. M. Ghiringhelli, et al., PRL 114, 105503 (2015)
1. 䛒䜛ᑡᩘ䛾ึᮇグ㏙Ꮚ䛻ᑐ䛧䚸ᅄ๎₇⟬䜔࿴䜔ᕪ䛾⤯ᑐ್䜔ᣦᩘ䛺䛹䚸䛒䜙䜖䜛₇⟬䜢᪋䛧䛶㧗ḟඖグ㏙Ꮚ✵㛫䜢స䜛
2. 䛭䛾ᚋLASSO䠄least absolute shrinkage and selection operator䠅䛸࿧䜀䜜䜛⨩๎㡯௜䛝䛾⥺ᙧᅇᖐ䛻䜘䛳䛶ᑡᩘ䛾グ㏙Ꮚ䛻⤠䜚㎸䜐䛣䜜䛻䜘䜚䚸⾲⌧ຊ䚸ỗ໬ᛶ⬟䛜㧗䛟䚸ୟ䛴䚸ẚ㍑ⓗ䝅䞁䝥䝹䛺ᅇᖐ䝰䝕䝹䜢ᢳฟ䛩䜛䛣䛸䛻ᡂຌઢࡱ ‫ ࡿࡾ ࡮࡭ࡱ ؠ‬െ ࡱ࡭࡮ ࢆ࡮= ૙. ૚૙ૡࡱ࡭ ࡮ െ ࡵࡼ ࡮࢘૛࢖ ࡭+ ૚. ૠૢ|࢙࢘ ࡭ െ ࢘࢖ ࡮ ||࢘࢖ ࡮ െ ࢙࢘ ࡮ |+ ૜. ૠ૟૟െ ૙. ૙૛૟ૠࢋ࢞࢖(࢙࢘ ࡭ )ࢋ࢞࢖(࢘ࢊ ࡭ )ඛ⾜◊✲䛾ၥ㢟Ⅼ

1. ᚓ䜙䜜䛯ᅇᖐᘧ䛜䜎䛰」㞧
ศẕ䛻ᣦᩘ㛵ᩘ䛜ྵ䜎䜜䛶䛔䛯䜚䛧䛶䚸┤䛠䛻䛿≀⌮ⓗព࿡䜢ᢳฟ䛩䜛䛣䛸䛜䛷䛝䛺䛔
2. LASSO䛻䜘䜛䝰䝕䝹㑅ᢥ䛻䛚䛔䛶䛿䚸グ㏙Ꮚ䛾㛫䛻ᙉ䛔┦㛵䛜䛒䜛ሙྜ䚸䛹䛾グ㏙Ꮚ䛜㑅䜀䜜䜛䛛䝁䞁䝖䝻䞊䝹䛷䛝䛺䛔
3. 䠄グ㏙Ꮚ⏕ᡂ䛾㒊ศ䛜䝅䝇䝔䝬䝔䜱䝑䜽䛷䛺䛔䠅Previous work

Our approach

Sample space setting

Sample space setting࢓ ~ ૚૙૙࢓ ~ ૚૙૙Calculation of ࢟

Calculation of ࢟

Prep. basic descriptors
ࢄ(૙) = [૚, ࢞૚ , ࢞૛ , … , ࢞࢔ ]Prep. basic descriptors
ࢄ(૙) = [૚, ࢞૚ , ࢞૛ , … , ࢞࢔ ]Descriptor generationࢄLinearly independent
descriptor generation (LIDG)

LASSOExhaustive search
MP solver
BO, MCTS, GA
LASSO, L0
Backward selection

࢔ ~ ૚૙

࢔ ~ ૚૙૙૙
࢔ ~ ૚૙

L. M. Ghiringhelli, et al., PRL 114, 105503 (2015)࢔ ~ ૚૙
࢔ < ࢓

࢔ ~ ૚૙Linearly independent descriptor generation method
Sample space setting࢓ ~ ૚૙૙

Calculation of ࢟

Prep. basic descriptors
ࢄ(૙) = [૚, ࢞૚ , ࢞૛ , … , ࢞࢔ ]Linearly independentize (LI)OLS

࢔ ~ ૚૙2nd order DG࢔ < ࢓OLS

Exhaustive search
MP solver
BO, MCTS, GA
LASSO, L0
Backward selection

࢔ ~ ૚૙LI

3rd order DGLI
䞉䞉䞉

LIDG

1st order DG࢔ ~ ૜૙࢔ ~ ૛૙

࢔ ~ ૞૙࢔ ~ ૜૙࢔ ~ ૚૙૙࢔ ~ ૝૙㐺⏝౛┠ⓗኚᩘ: 2ඖ༙ᑟయ䠄82ಶ䠅䛾RSᵓ㐀䛸ZBᵓ㐀䛾䜶䝛䝹䜼䞊ᕪᑐ⛠໬グ㏙Ꮚ䠄Aඖ⣲䚸Bඖ⣲䛾ཎᏊ༙ᚄ䠅οࡱ(࡭, ࡮) = οࡱ(࡮, ࡭)ᅇᖐ⤖ᯝඛ⾜◊✲䛾䝰䝕䝹

Y. Kanda, H. Fujii, and T. Oguchi, STAM 20, 1178 (2019).

ඛ⾜◊✲䛸䛾ẚ㍑䚸LIDGἲ䛾ඃ఩ᛶ䞉 グ㏙Ꮚ䜢ẁ㝵ⓗ䛻ቑຍ䛥䛫䜛䛣䛸䛜䛷䛝䜛䚹䜎䛯䚸グ㏙Ꮚ䜢ẁ㝵ⓗ䛻」㞧䛺䜒䛾䛻䛩䜛䛣䛸䛜䛷䛝䜛䚹䞉 グ㏙Ꮚ䜢ᚲせ䛺ᩘ䛰䛡⏕ᡂ䛩䜛䛣䛸䛜䛷䛝䜛䚹䠄ᚋ䛾䝰䝕䝹㑅ᢥ䛜ᴦ䛻䛺䜛䠅䞉 グ㏙Ꮚ㑅ᢥ䛻◊✲⪅䛾▱㆑䞉⤒㦂䜢䛒䜛⛬ᗘᑟධ䛩䜛䛣䛸䛜䛷䛝䜛䚹䠄㒊ศ✵㛫䝸䝇䝖䠅䞉 ከ㔜ඹ⥺ᛶ䜔ᙉ䛔‽ከ㔜ඹ⥺ᛶ䛜ྲྀ䜚㝖䛛䜜䛶䛔䜛䛾䛷䚸ї ᅇᖐಀᩘ䛜↓⏝䛻኱䛝䛟䛺䜙䛪䚸᭷ព䛺ᅇᖐศᯒ䜢⾜䛖䛣䛸䛜䛷䛝䜛ї Ᏻᐃ䛧䛯䝰䝕䝹㑅ᢥ䛜ྍ⬟䠄᭱䜒༢⣧䛺ᚋ㏥㑅ᢥἲ䜒䚸LASSO䜒ྠᵝ䛾䝰䝕䝹䜢㑅ᢥ䛩䜛䠅䞉 ᏶඲䛺ከ㔜ඹ⥺ᛶ㛵ಀ䛜ᚓ䜙䜜䜛䛾䛷䚸䛭䜜䜢౑䛳䛶䚸᭱⤊ⓗ䛻ᚓ䜙䜜䛯䝰䝕䝹䛾ᘧኚᙧ䜢⾜䛖䛣䛸䛜䛷䛝䜛䚹Example
Calculation

Experiment

AkaiKKR (KKR-CPA)LDA (MJW)
Crystal structure: BCC
Lattice constant = 2.86 䊅Scalar relativistic
BZ quality = 10 (nk=256)
edelta = 0.0001
ewidth = 1.2
Complex energy mesh = 85
L max = 3
H. Saito: Physics and Applications of Invar Alloys,Maruzen, Tokyo, (1978), 18.

Everyone may image that there is a simple model on the back of this curve
We try to find the simple model by using LIDG method
Target property (࢓ = ૢૢ):Magnetic moment of binary alloy ࡭૚ି࢞ ࡮࢞ࡹ(࡭, ࡮, ࢞)Initial descriptors (࢔ = ૠ):Concentration, ࢞Magnetic moment of pure bulk, ࡹࡼ ࡭ , ࡹࡼ ࡮
The number of valence electrons, ࢆ ࡭ , ࢆ(࡮)
Magnetic moment of impurity atom, ࡹࡵ ࡭, ࡮ࡹࡵ ࡮, ࡭The results of OLS with 1st, 2nd, and 3rd order descriptors
1st order (8)ࡾ૛ = ૙. ૢ૙૟ࡽ૛ = ૙. ૡૡૠUp to 2nd order (17)ࡾ૛ = ૙. ૢ૟ૢࡽ૛ = ૙. ૢ૞૙Up to 3rd order (24)ࡾ૛ = ૙. ૢૢ૟ࡽ૛ = ૙. ૢૢ૚Obtained model by backward selectionࡹ ࡭, ࡮, ࢞ ~ ૚ െ ࢞ ࡹࡼ ࡭ + ࢞ࡹࡼ ࡮+࢞(૚ െ ࢞) െ૝. ૙૜ + ૙. ૛ૡࢆ ࡭ + ૙. ૟૛ࡹࡵ ࡮, ࡭ + ૙. ૛૙ ࡹࡼ ࡭ + ࡹࡵ ࡭, ࡮An interpretation
by analogy with the regular solution approximation for binary compound systemഥ ࡭, ࡮, ࢞ + οࡹ ࡭, ࡮, ࢞
ࡹ ࡭, ࡮, ࢞ = ࡹഥ ࡭, ࡮, ࢞ ‫ ؠ‬૚ െ ࢞ ࡹࡼ ࡭ + ࢞ࡹࡼ ࡮ࡹοࡹ ࡭, ࡮, ࢞ ‫(࢞ ؠ‬૚ െ ࢞)ષ(࡭, ࡮)Averaged magnetic moment term(linear to ࢞)

Mixing (excessive) magnetic moment term generated by alloyingષ ࡭, ࡮ = െ૝. ૙૜ + ૙. ૛ૡࢆ ࡭ + ૙. ૟૛ࡹࡵ ࡮, ࡭ + ૙. ૛૙ ࡹࡼ ࡭ + ࡹࡵ ࡭, ࡮Interaction parameter (does not depend on ࢞)Summary• We propose RREF method for detecting MCL• The subspace list is useful for breaking the detected MCL relationships• This is a new approach to solve MCL problem in linear regression analysis• By combining these methods, LIDG method was proposed• LIDG method was applied to analyze SPCs and we could obtain a simple(interpretable) model with high generalization capability.

Use of symmetry in target property
If we can find symmetries,
1.
2.

we can increase samples which are symmetrically equivalent.
we can construct descriptors to satisfy the above regulations in advance

Magnetic moment of alloys expected to have a symmetry like,ࡹ(࡭, ࡮, ࢞) = ࡹ(࡮, ࡭, ૚ െ ࢞)ࡹ(࡭, ࡮, ࢞࡭ , ࢞࡮ ) = ࡹ(࡮, ࡭, ࢞࡮ , ࢞࡭ )࡭, ࡮, ࢞࡭ , ࢞࡮: identifiers (primary key)(not descriptor)ࡱࡹ ࡭, ࡮, ࢞࡭ , ࢞࡮ = ࡹ ࡭, ࡮, ࢞࡭ , ࢞࡮࣌ࡹ(࡭, ࡮, ࢞࡭ , ࢞࡮ ) = ࡹ(࡮, ࡭, ࢞࡮ , ࢞࡭ ) = ࡹ ࡭, ࡮, ࢞࡭ , ࢞࡮Symmetrization operator (projection operator):
ࡿ= ࡱ+࣌

Symmetrization of descriptors
Symmetrization operator:
ࡿ= ࡱ+࣌ࡿࡹࡼ ࡭ = ࡹࡼ ࡭ + ࡹࡼ ࡮ࡿࡹࡼ ࡮ = ࡹࡼ ࡮ + ࡹࡼ ࡭
ࡿ࢞࡭ = ࢞࡭ + ࢞࡮ࡿ࢞࡮ = ࢞࡮ + ࢞࡭ࡿࡹࡵ ࡭, ࡮ = ࡹࡵ ࡭, ࡮ + ࡹࡵ ࡮, ࡭ࡿࡹࡵ ࡮, ࡭ = ࡹࡵ ࡮, ࡭ + ࡹࡵ ࡭, ࡮ࡿ࢞࡭ ࡹࡼ ࡭ = ࢞࡭ ࡹࡼ ࡭ + ࢞࡮ ࡹࡼ ࡮

If we use these symmetrical descriptors,
we can get a more reasonable model.

The number of multicollinearities
Linear span:ࢃ = ‫࢞{(ܖ܉ܘܛ‬૚ , ࢞૛ , ࢞૜ , … , ࢞࢔ })Design matrix:ࢄ = ࢞૚ , ࢞૛ , ࢞૜ , … , ࢞࢔

The number of non-trivial solutions of ࢄࢉ = ૙means the number of extra basis in span ࢃ࢔ െ ‫)ࢃ(ܕܑ܌‬‫࢘ ؠ )ࢄ(ܓܖ܉ܚ = )ࢃ(ܕܑ܌‬then, the number of non-trivial (independent) solutions is given by ࢔ െ ࢘
independent one set of solution

RREF method
Make row reduced echelon form (rref) of ࢄ by basic operations.
ࡾࢄࡽ = ࢄ࢘࢘ࢋࢌ

ࡾ(࢓ × ࢓): row basic transformation operator (regular)ࡽ(࢔ × ࢔): column basic transformation operator (regular and orthogonal)(here suppose that it just change the order of columns)

૚૙ࢄ࢘࢘ࢋࢌ = ૙૙૙૙૙૚૙૙૙૙૙૙૚૙૙૙ࢇ૚ࢇ૛ࢇ૜૙૙૙

࢔െ࢘= ૟െ૜ = ૜࢈૚࢈૛࢈૜૙૙૙ࢄ࢘࢘ࢋࢌ ࢉ૚ , ࢉ૛ , ࢉ૜ = [૙, ૙, ૙]ࢊ૚ࢊ૛ࢊ૜૙૙
૙The simplest solutions:െࢇ૚െࢇ૛[ࢉ૚ , ࢉ૛ , ࢉ૜ ] = െࢇ૜૚૙૙૚૙૙૙૙૙૙૚૙૙૙૙૙ ࢇ૚૙ ࢇ૛૚ ࢇ૜૙ ૙૙ ૙૙ ૙࢈૚࢈૛࢈૜૙૙૙െ࢈૚െ࢈૛െ࢈૜૙૚૙െࢊ૚െࢊ૛െࢊ૜૙૙૚ࢊ૚ െࢇ૚ࢊ૛ െࢇ૛ࢊ૜ െࢇ૜ = ૙૚૙૙૙૙૙

RREF methodThe solutions of ࢄ࢘࢘ࢋࢌ ࢉ = ૙ are the solutions of ࢄࢉ = ૙ ?
ࡾࢄࡽ = ࢄ࢘࢘ࢋࢌ

ࢄ = ࡾି૚ ࢄ࢘࢘ࢋࢌ ࡽࢀࢄ࢘࢘ࢋࢌ ࢉ = ૙ࡾି૚ ࢄ࢘࢘ࢋࢌ ࢉ = ૙ࡾି૚ ࢄ࢘࢘ࢋࢌ ࡽࢀ ࡽࢉ = ૙
ࢄࡽࢉ = ૙We only have to remember the order change
How to obtain ࡽࢄࡽ = ࢞૚ , ࢞૛ , ࢞૜ , ࢞૝ ࡽ = ࢞૜ , ࢞૚ , ࢞૛ , ࢞૝૚૙૙૙૙૚૙૙૙૙
૚૙૙૙૙
૙
ࡽ=૙૚
૚૙૙૙
ࡽ=૚૙

૚૙૙૙૚
૙૙૙

૙
૚
૙
૙

૙
૚૙
૙

૙
૙
૙
૚

૙
૙
૙
૚

Raw data

Descriptors
MP: Magnetic moment of pure bulk A
Z: # of valence electrons

MI(A,B):
Magnetic moment of impurity A (B)in bulk B (A)ᨺᑕග䜢฼⏝䛧䛯䝬䝔䝸䜰䝹䝈䞉䜲䞁䝣䜷䝬䝔䜱䜽䝇ィ 䜲䞁䝣䜷䝬䝔䜱䜽䝇ᨺᑕග䜲䞁䝣䜷䝬䝔䜱䜽䝇≀㉁䞉ᮦᩱ⛉Ꮫ䛾┠ᶆ≀㉁䠄䜔䚸䛭䛾సᡂ᮲௳䠅┠ⓗ≀ᛶ್䝃䞁䝥䝹≀㉁䛛䜙䚸┠ⓗ䛸䛺䜛≀ᛶ್䜢㧗㏿䞉㧗⢭ᗘ䠄ᡤᮃ䛾≀ᛶ್䜢ᣢ䛴≀㉁䛾᥈⣴䛾㧗ຠ⋡໬䠅ᐃ䚸ணᨺᑕගᐇ㦂䚸DFTィ⟬䛾ᙺ๭ᐇ㦂䛾䠄᫬㛫䚸㈝⏝䠅䝁䝇䝖䝎䜴䞁䝯䜹䝙䝈䝮䛾ゎ᫂䠄௬ㄝ䚸䝇䝖䞊䝸䞊䛾᳨ド䠅䠄䛯䛰䛧䚸䝇䝨䜽䝖䝹┠ⓗ≀ᛶ್ 䛜᪤▱䛾ሙྜ䠅ᨺᑕග䜲䞁䝣䜷䝬䝔䜱䜽䝇≀㉁┠ⓗ≀ᛶ್ᐇ㦂䛻䜘䜛㧗㏿䞉㧗⢭ᗘᐃ䛜ᅔ㞴䛺ሙྜDFTィ⟬≀㉁㟁Ꮚ≧ែ┠ⓗ≀ᛶ್≀㉁䝇䝨䜽䝖䝹┠ⓗ≀ᛶ್ᨺᑕගၥ㢟Ⅼ䠖
1. 䛹䛖䛔䛖≀㉁䠄䛾≧ែ䠅䜢ぢ䛶䛔䜛䛛୙☜䛛䛺ሙྜ䛜䛒䜛
2. 䝇䝨䜽䝖䝹䚸DFTィ⟬䛾⤖ᯝ䛾ゎ㔘䛜㞴䛧䛔ሙྜ䛜䛒䜛
3. 䝇䝨䜽䝖䝹ྲྀᚓ䚸DFTィ⟬䛾䝁䝇䝖䛜㧗䛔ሙྜ䛜䛒䜛ᨺᑕග䜲䞁䝣䜷䝬䝔䜱䜽䝇ᶵᲔᏛ⩦䛷䜔䜚䛯䛔䛣䛸䠖 䝇䝨䜽䝖䝹ゎᯒჾ䚸ண䠄ᐇ㦂䞉ィ⟬䠅䝇䝨䜽䝖䝹ゎᯒჾண ჾჾ䛾ᵓ⠏1. ≀㉁䛾ᵓ㐀2. 㟁Ꮚ≧ែ3. ≀ᛶ್䞉䝇䝨䜽䝖䝹ゎ㔘ᛶ䛾ྥୖ䠄㓟໬ᩘ䚸㓄఩ᩘ䚸ᒁᡤ㟁Ꮚ≧ែ䠅䞉㐣ཤ䛾䝕䞊䝍䛛䜙᭱㐺䛺ᐇ㦂䛾ᥦ᱌䠄L➃䠛K➃䠛XAS䠛XPS䠛䠅䞉䝴䞊䝄䞊䛾฼౽ᛶ䛾ྥୖ䞉᪂ศ㔝㛤ᣅ
RIXS-MCD䛾ゎ㔘䚸XAS䝇䝨䜽䝖䝹➼䛾㧗䜶䝛䝹䜼䞊㡿ᇦ䛾ゎ㔘䠄Co K➃䠅௒䜎䛷↓ど䛧䛶䛔䛯㒊ศ䛛䜙ఱ䜙䛛䛾ព࿡䛜ᢳฟ䛥䜜䜛䛛䜒䛧䜜䛺䛔䚹䛭䛾௚䠄ᐇ㦂䞉ィ⟬䠅䝇䝨䜽䝖䝹䝕䞊䝍䝧䞊䝇ᵓ⠏䝕䞊䝍⿵᏶䚸䝜䜲䝈㝖ཤ䛻䜘䜛⢭ᗘྥୖ

NVIDIA, arXiv:1803.04189v3 [cs.CV] 29 Oct 2018