ss s r s t
play

ss - PowerPoint PPT Presentation

Sep 30, 2023 •466 likes •1.69k views

ss sr s t t r trs r

  1. ❚❤❡ s✉♣❡r✈✐s❡❞ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠s ❛❝❝❡ss t♦ ❛ ❞❛t❛s❡t ♦❢ ❡①❛♠♣❧❡s✱ ❡❛❝❤ ❛ss♦❝✐❛t❡❞ ✐♥ ❣❡♥❡r❛❧ t♦ ❛ t❛r❣❡t ♦r ❧❛❜❡❧ ✳ ▲❡❛r♥ ❢r♦♠ ❞❛t❛ ✈✐❛ st❛t✐st✐❝ ♠♦❞❡❧s ❚❛s❦ ✲ P❡r❢♦r♠❛♥❝❡ ✲ ❊①♣❡r✐❡♥❝❡ ❬❚▼✾✼❪ ❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s Pr♦✜❧✐♥❣ ❆tt❛❝❦s✳✳✳❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ❚❛r❣❡t ❈❧♦♥❡ ❞❡✈✐❝❡ ❞❡✈✐❝❡ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✺✴✹✷

  2. ▲❡❛r♥ ❢r♦♠ ❞❛t❛ ✈✐❛ st❛t✐st✐❝ ♠♦❞❡❧s ❚❛s❦ ✲ P❡r❢♦r♠❛♥❝❡ ✲ ❊①♣❡r✐❡♥❝❡ ❬❚▼✾✼❪ ❚❤❡ s✉♣❡r✈✐s❡❞ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠s ❛❝❝❡ss t♦ ❛ ❞❛t❛s❡t ♦❢ ❡①❛♠♣❧❡s✱ ❡❛❝❤ ❛ss♦❝✐❛t❡❞ ✐♥ ❣❡♥❡r❛❧ t♦ ❛ t❛r❣❡t ♦r ❧❛❜❡❧ ✳ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s Pr♦✜❧✐♥❣ ❆tt❛❝❦s✳✳✳❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ❚❛r❣❡t ❈❧♦♥❡ ❞❡✈✐❝❡ ❞❡✈✐❝❡ ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✺✴✹✷

  3. ❚❤❡ s✉♣❡r✈✐s❡❞ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠s ❛❝❝❡ss t♦ ❛ ❞❛t❛s❡t ♦❢ ❡①❛♠♣❧❡s✱ ❡❛❝❤ ❛ss♦❝✐❛t❡❞ ✐♥ ❣❡♥❡r❛❧ t♦ ❛ t❛r❣❡t ♦r ❧❛❜❡❧ ✳ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s Pr♦✜❧✐♥❣ ❆tt❛❝❦s✳✳✳❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ❚❛r❣❡t ❈❧♦♥❡ ❞❡✈✐❝❡ ❞❡✈✐❝❡ ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ▲❡❛r♥ ❢r♦♠ ❞❛t❛ ✈✐❛ st❛t✐st✐❝ ♠♦❞❡❧s ❚❛s❦ ✲ P❡r❢♦r♠❛♥❝❡ ✲ ❊①♣❡r✐❡♥❝❡ ❬❚▼✾✼❪ ❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✺✴✹✷

  4. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s Pr♦✜❧✐♥❣ ❆tt❛❝❦s✳✳✳❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ❚❛r❣❡t ❈❧♦♥❡ ❞❡✈✐❝❡ ❞❡✈✐❝❡ ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ▲❡❛r♥ ❢r♦♠ ❞❛t❛ ✈✐❛ st❛t✐st✐❝ ♠♦❞❡❧s ❚❛s❦ ✲ P❡r❢♦r♠❛♥❝❡ ✲ ❊①♣❡r✐❡♥❝❡ ❬❚▼✾✼❪ ❙✉♣❡r✈✐s❡❞ ▲❡❛r♥✐♥❣ ❚❤❡ s✉♣❡r✈✐s❡❞ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠s ❛❝❝❡ss t♦ ❛ ❞❛t❛s❡t ♦❢ ❡①❛♠♣❧❡s✱ ❡❛❝❤ ❛ss♦❝✐❛t❡❞ ✐♥ ❣❡♥❡r❛❧ t♦ ❛ t❛r❣❡t ♦r ❧❛❜❡❧ ✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✺✴✹✷

  5. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈❧❛ssr♦♦♠ ❙✐❞❡✲❈❤❛♥♥❡❧ ❆tt❛❝❦s ❈❧♦♥❡ ❞❡✈✐❝❡ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✻✴✹✷

  6. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈❧❛ssr♦♦♠ ❙✐❞❡✲❈❤❛♥♥❡❧ ❆tt❛❝❦s ❚❛r❣❡t ❞❡✈✐❝❡ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✻✴✹✷

  7. ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ❝❧❛ss✐✜❡rs ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ ❧✐t❡r❛t✉r❡✿ ❙❱▼ ✭❬❍♦s✰✶✶❀ ❍❩✶✷❪✮✱ ❘❋ ✭❬▲❇▼✶✹❀ ▲❇▼✶✺❪✮ ❆❞✈❛♥❝❡❞ ❆tt❛❝❦ ❛s ▼✉❧t✐♣❧❡ ❈❧❛ss✐✜❝❛t✐♦♥ Pr♦❜❧❡♠s ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈❧❛ss✐✜❝❛t✐♦♥ ❈❧❛ss✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠ ❆ss✐❣♥ t♦ ❛ ❞❛t✉♠ � X ❛ ❧❛❜❡❧ Z ❛♠♦♥❣ ❛ s❡t ♦❢ ♣♦ss✐❜❧❡ ❧❛❜❡❧s Z = { s ✶ , s ✷ , s ✸ } ✱ ♦r ♣r♦❜❛❜✐❧✐t✐❡s✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✼✴✹✷

  8. ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ❝❧❛ss✐✜❡rs ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ ❧✐t❡r❛t✉r❡✿ ❙❱▼ ✭❬❍♦s✰✶✶❀ ❍❩✶✷❪✮✱ ❘❋ ✭❬▲❇▼✶✹❀ ▲❇▼✶✺❪✮ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈❧❛ss✐✜❝❛t✐♦♥ ❈❧❛ss✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠ ❆ss✐❣♥ t♦ ❛ ❞❛t✉♠ � X ❛ ❧❛❜❡❧ Z ❛♠♦♥❣ ❛ s❡t ♦❢ ♣♦ss✐❜❧❡ ❧❛❜❡❧s Z = { s ✶ , s ✷ , s ✸ } ✱ ♦r ♣r♦❜❛❜✐❧✐t✐❡s✳ ❆❞✈❛♥❝❡❞ ❆tt❛❝❦ ❛s ▼✉❧t✐♣❧❡ ❈❧❛ss✐✜❝❛t✐♦♥ Pr♦❜❧❡♠s ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✼✴✹✷

  9. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈❧❛ss✐✜❝❛t✐♦♥ ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣ ❝❧❛ss✐✜❡rs ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ ❧✐t❡r❛t✉r❡✿ ❙❱▼ ✭❬❍♦s✰✶✶❀ ❍❩✶✷❪✮✱ ❘❋ ✭❬▲❇▼✶✹❀ ▲❇▼✶✺❪✮ ❈❧❛ss✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠ ❆ss✐❣♥ t♦ ❛ ❞❛t✉♠ � X ❛ ❧❛❜❡❧ Z ❛♠♦♥❣ ❛ s❡t ♦❢ ♣♦ss✐❜❧❡ ❧❛❜❡❧s Z = { s ✶ , s ✷ , s ✸ } ✱ ♦r ♣r♦❜❛❜✐❧✐t✐❡s✳ ❆❞✈❛♥❝❡❞ ❆tt❛❝❦ ❛s ▼✉❧t✐♣❧❡ ❈❧❛ss✐✜❝❛t✐♦♥ Pr♦❜❧❡♠s ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✼✴✹✷

  10. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ◆♦t❛t✐♦♥s ◆♦t❛t✐♦♥s ❛♥❞ ❣❡♥❡r❛❧✐t✐❡s ◮ ❙✐❞❡✲❝❤❛♥♥❡❧ tr❛❝❡s✿ r❡❛❧✐③❛t✐♦♥s ♦❢ ❛ r❛♥❞♦♠ ✈❡❝t♦r � X ∈ R D ◮ D ✐s t❤❡ ♥✉♠❜❡r ♦❢ t✐♠❡ s❛♠♣❧❡s ✭♦r ❢❡❛t✉r❡s✮ ◮ ❚❛r❣❡t✿ ❛ s❡♥s✐t✐✈❡ ✈❛r✐❛❜❧❡ Z = f ( ❡ , ❦ ) ✐♥ Z = { s ✶ , . . . , s |Z| } Pr♦✜❧✐♥❣ ❛tt❛❝❦ s❝❡♥❛r✐♦ ◮ ❧❛❜❡❧❧❡❞ tr❛❝❡s D tr❛✐♥ = ( � x i , e i , k i ) N i = ✶ ✱ ❛❝q✉✐r❡❞ ✉♥❞❡r ❦♥♦✇♥ s❡❝r❡ts ◮ ❛tt❛❝❦ tr❛❝❡s D ❛tt❛❝❦ = ( � x i , e i ) N a i = ✶ ❛❝q✉✐r❡❞ ✉♥❞❡r ✉♥❦♥♦✇♥ s❡❝r❡ts ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✽✴✹✷

  11. ♠❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ ❪ tr❛✐♥ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ ❪ tr❛✐♥ ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮ ❬❈❘❘✵✸❪ ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ ❆✲♣♦st❡r✐♦r✐ ♣r♦❜❛❜✐❧✐t② s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s ✱ ✶ ✶ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s Pr♦✜❧✐♥❣ ❆tt❛❝❦ Pr♦✜❧✐♥❣ ♣❤❛s❡ ◮ ❡st✐♠❛t❡ ◮ p � X | Z = z ❆tt❛❝❦ ♣❤❛s❡ ◮ ▲✐❦❡❧✐❤♦♦❞ s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p � ( � x i ) i = ✶ ,..., N a , ( f ( e i , k )) i = ✶ ,..., N a X | Z ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✾✴✹✷

  12. ♠❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ ❪ tr❛✐♥ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ ❪ tr❛✐♥ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮ ❬❈❘❘✵✸❪ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s Pr♦✜❧✐♥❣ ❆tt❛❝❦ Pr♦✜❧✐♥❣ ♣❤❛s❡ ◮ ❡st✐♠❛t❡ ◮ p � X | Z = z p � X p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ ◮ p Z | � x ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ X = � ❆tt❛❝❦ ♣❤❛s❡ ◮ ▲✐❦❡❧✐❤♦♦❞ s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p � ( � x i ) i = ✶ ,..., N a , ( f ( e i , k )) i = ✶ ,..., N a X | Z ◮ ❆✲♣♦st❡r✐♦r✐ ♣r♦❜❛❜✐❧✐t② s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p Z | � f ( e i , k ) i = ✶ ,..., N a , ( � x i ) i = ✶ ,..., N a ✱ X ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✾✴✹✷

  13. ♠❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ ❪ tr❛✐♥ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ ❪ tr❛✐♥ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮ ❬❈❘❘✵✸❪ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s Pr♦✜❧✐♥❣ ❆tt❛❝❦ Pr♦✜❧✐♥❣ ♣❤❛s❡ ◮ ❡st✐♠❛t❡ ◮ p � X | Z = z p � X p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ ◮ p Z | � x ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ X = � ❆tt❛❝❦ ♣❤❛s❡ ◮ ▲✐❦❡❧✐❤♦♦❞ s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p � ( � x i ) i = ✶ ,..., N a , ( f ( e i , k )) i = ✶ ,..., N a X | Z ◮ ❆✲♣♦st❡r✐♦r✐ ♣r♦❜❛❜✐❧✐t② s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p Z | � f ( e i , k ) i = ✶ ,..., N a , ( � x i ) i = ✶ ,..., N a ✱ X ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✾✴✹✷

  14. ♠❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ ❪ tr❛✐♥ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ ❪ tr❛✐♥ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮ ❬❈❘❘✵✸❪ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s X ∈ R D � Pr♦✜❧✐♥❣ ❆tt❛❝❦ ❈✉rs❡ ♦❢ ❞✐♠❡♥s✐♦♥❛❧✐t②✦ Pr♦✜❧✐♥❣ ♣❤❛s❡ ◮ ❡st✐♠❛t❡ ◮ p � X p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ X | Z = z p � ◮ p Z | � x ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ X = � ❆tt❛❝❦ ♣❤❛s❡ ◮ ▲✐❦❡❧✐❤♦♦❞ s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p � ( � x i ) i = ✶ ,..., N a , ( f ( e i , k )) i = ✶ ,..., N a X | Z ◮ ❆✲♣♦st❡r✐♦r✐ ♣r♦❜❛❜✐❧✐t② s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p Z | � f ( e i , k ) i = ✶ ,..., N a , ( � x i ) i = ✶ ,..., N a ✱ X ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✾✴✹✷

  15. ♠❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ ❪ tr❛✐♥ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ ❪ tr❛✐♥ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s X ∈ R D � Pr♦✜❧✐♥❣ ❆tt❛❝❦ ❈✉rs❡ ♦❢ ❞✐♠❡♥s✐♦♥❛❧✐t②✦ Pr♦✜❧✐♥❣ ♣❤❛s❡ ◮ ❡st✐♠❛t❡ ◮ p � X p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ X | Z = z p � ◮ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮ ❬❈❘❘✵✸❪ ◮ p Z | � x ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ X = � ❆tt❛❝❦ ♣❤❛s❡ ◮ ▲✐❦❡❧✐❤♦♦❞ s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p � ( � x i ) i = ✶ ,..., N a , ( f ( e i , k )) i = ✶ ,..., N a X | Z ◮ ❆✲♣♦st❡r✐♦r✐ ♣r♦❜❛❜✐❧✐t② s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p Z | � f ( e i , k ) i = ✶ ,..., N a , ( � x i ) i = ✶ ,..., N a ✱ X ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✾✴✹✷

  16. ♠❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ ❪ tr❛✐♥ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s X ∈ R D � Pr♦✜❧✐♥❣ ❆tt❛❝❦ ❈✉rs❡ ♦❢ ❞✐♠❡♥s✐♦♥❛❧✐t②✦ Pr♦✜❧✐♥❣ ♣❤❛s❡ → ǫ : R D → R C ❪ ◮ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ D tr❛✐♥ − ◮ ❡st✐♠❛t❡ ◮ p ǫ ( � X ) p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ X ) | Z = z p ǫ ( � ◮ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮ ❬❈❘❘✵✸❪ ◮ p Z | ǫ ( � x ) ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ X )= ǫ ( � ❆tt❛❝❦ ♣❤❛s❡ ◮ ▲✐❦❡❧✐❤♦♦❞ s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p ǫ ( � ( ǫ ( � x i )) i = ✶ ,..., N a , ( f ( e i , k )) i = ✶ ,..., N a X ) | Z ◮ ❆✲♣♦st❡r✐♦r✐ ♣r♦❜❛❜✐❧✐t② s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p Z | ǫ ( � f ( e i , k ) i = ✶ ,..., N a , ( ǫ ( � x i )) i = ✶ ,..., N a ✱ X ) ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✾✴✹✷

  17. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s X ∈ R D � Pr♦✜❧✐♥❣ ❆tt❛❝❦ ❈✉rs❡ ♦❢ ❞✐♠❡♥s✐♦♥❛❧✐t②✦ Pr♦✜❧✐♥❣ ♣❤❛s❡ → ρ : R D → R D ❪ ◮ ♠❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ D tr❛✐♥ − → ǫ : R D → R C ❪ ◮ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ D tr❛✐♥ − ◮ ❡st✐♠❛t❡ ◮ p ǫ ( ρ ( � X )) p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ X )) | Z = z p ǫ ( ρ ( � ◮ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮ ❬❈❘❘✵✸❪ ◮ p Z | ρ ( ǫ ( � x )) ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ X ))= ǫ ( ρ ( � ❆tt❛❝❦ ♣❤❛s❡ ◮ ▲✐❦❡❧✐❤♦♦❞ s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p ǫ ( ρ ( � ( ǫ ( ρ ( � x i ))) i = ✶ ,..., N a , ( f ( e i , k )) i = ✶ ,..., N a X )) | Z ◮ ❆✲♣♦st❡r✐♦r✐ ♣r♦❜❛❜✐❧✐t② s❝♦r❡ ❢♦r ❡❛❝❤ ❦❡② ❤②♣♦t❤❡s✐s k � � d k = p Z | ǫ ( ρ ( � f ( e i , k ) i = ✶ ,..., N a , ( ǫ ( ρ ( � x i ))) i = ✶ ,..., N a ✱ X )) ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✾✴✹✷

  18. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼❛♥❞❛t♦r② ❉✐♠❡♥s✐♦♥❛❧✐t② ❘❡❞✉❝t✐♦♥ ❆ ✈❛st ❞♦♠❛✐♥ ❋❡❛t✉r❡s ✭P♦✐♥ts ♦❢ ■♥t❡r❡sts ✲ ❋❡❛t✉r❡ ❡①tr❛❝t✐♦♥ P♦■✮ s❡❧❡❝t✐♦♥ ◮ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ◮ ❙❖❉ ❬❈❘❘✵✸❪ ❆♥❛❧②s✐s ✭P❈❆✮ ❬❆r❝✰✵✻❀ ❇❍❲✶✷❪ ◮ ❙❖❙❚ ❬❇❉P✶✵❪ ◮ ▲✐♥❡❛r ❉✐s❝r✐♠✐♥❛♥t ❆♥❛❧②s✐s ◮ ❙◆❘ ❬▼❖P✵✽❪✴ ◆■❈❱ ✭▲❉❆✮ ❬❙❆✵✽❀ ❇r✉✰✶✺❪ ❬❇❤❛✰✶✹❪ ◮ Pr♦❥❡❝t✐♦♥ P✉rs✉✐ts ✭PP✮ ◮ t ✲t❡st✱ F ✲t❡st✱✳✳✳ ❬●▲❘P✵✻❀ ❬❉✉r✰✶✺❪ ❈❑✶✹❪ ❋✐❣✉r❡✿ ❙◆❘ ❝♦♠♣✉t❡❞ ♦♥ s②♥❝❤r♦♥✐③❡❞ tr❛❝❡s✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✵✴✹✷

  19. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ▼✐s❛❧✐❣♥✐♥❣ ❈♦✉♥t❡r♠❡❛s✉r❡s ◮ ❘❛♥❞♦♠ ❉❡❧❛②s✱ ❈❧♦❝❦ ❏✐tt❡r✐♥❣✱ ✳✳✳ ◮ ■♥ t❤❡♦r②✿ ✐♥s✉✣❝✐❡♥t t♦ ♣r♦✈✐❞❡ s❡❝✉r✐t②✱ s✐♥❝❡ ✐♥❢♦r♠❛t✐♦♥ st✐❧❧ ❧❡❛❦ ✭s♦♠❡✇❤❡r❡✮ ◮ ■♥ ♣r❛❝t✐❝❡✿ ♦♥❡ ♦❢ t❤❡ ♠❛✐♥ ✐ss✉❡s ❢♦r ❡✈❛❧✉❛t♦rs ❋✐❣✉r❡✿ ❙◆❘ ❝♦♠♣✉t❡❞ ♦♥ ❞❡s②♥❝❤r♦♥✐③❡❞ tr❛❝❡s✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✶✴✹✷

  20. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼❛♥❛❣❡ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ▼✐s❛❧✐❣♥✐♥❣ ❈♦✉♥t❡r♠❡❛s✉r❡s ◮ ❘❛♥❞♦♠ ❉❡❧❛②s✱ ❈❧♦❝❦ ❏✐tt❡r✐♥❣✱ ✳✳✳ ◮ ■♥ t❤❡♦r②✿ ✐♥s✉✣❝✐❡♥t t♦ ♣r♦✈✐❞❡ s❡❝✉r✐t②✱ s✐♥❝❡ ✐♥❢♦r♠❛t✐♦♥ st✐❧❧ ❧❡❛❦ ✭s♦♠❡✇❤❡r❡✮ ◮ ■♥ ♣r❛❝t✐❝❡✿ ♦♥❡ ♦❢ t❤❡ ♠❛✐♥ ✐ss✉❡s ❢♦r ❡✈❛❧✉❛t♦rs ❘❡❛❧✐❣♥♠❡♥t ▼❛♥❞❛t♦r② r❡❛❧✐❣♥♠❡♥t ♣r❡♣r♦❝❡ss✐♥❣ ◮ ♥♦t ❛ ✇✐❞❡ ❧✐t❡r❛t✉r❡ ◮ ✐♥ ♣r❛❝t✐❝❡✿ ❡✈❛❧✉❛t✐♦♥ ❧❛❜s ❤♦♠❡✲♠❛❞❡ r❡❛❧✐❣♥♠❡♥t t❡❝❤♥✐q✉❡s ◮ s✐❣♥❛❧ ❞❡❢♦r♠❛t✐♦♥s ♦r ♣❛tt❡r♥ ❡①tr❛❝t✐♦♥ ❜❛s❡❞ ♦♥ ♣r✐♦r ✉♥✈❡r✐✜❡❞ ❛ss✉♠♣t✐♦♥s ◮ ❘✐s❦s✿ ◮ ❞❡❢♦r♠❛t✐♦♥s → ✐♥❢♦r♠❛t✐♦♥ ❞❡❣r❛❞❛t✐♦♥ ◮ ♣❛tt❡r♥ ❡①tr❛❝t✐♦♥ → ✐♥❢♦r♠❛t✐♦♥ ❧♦ss ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✶✴✹✷

  21. ❜② ♠❡❛♥s ♦❢ ❛ ♥❡✉r❛❧ ♥❡t✇♦r❦ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚❤✐s t❛❧❦ Pr♦✜❧✐♥❣ ♣❤❛s❡ → ρ : R D → R D ❪ ◮ ♠❛♥❛❣❡ ❞❡✲s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ D tr❛✐♥ − → ǫ : R D → R C ❪ ◮ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ D tr❛✐♥ − ◮ ❡st✐♠❛t❡ ◮ p ǫ ( ρ ( � X )) | Z = z ✱ p ǫ ( ρ ( � X )) ✱ p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ ◮ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮❬❈❘❘✵✸❪ ◮ p Z | ǫ ( ρ ( � x ) ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ ❚❤✐s t❛❧❦ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦✿ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ ✭❞❡❛❧ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ✰ ❡①tr❛❝t✐♦♥ ❢❡❛t✉r❡ ✰ ❛♣♣r♦①✐♠❛t❡ ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✷✴✹✷

  22. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚❤✐s t❛❧❦ Pr♦✜❧✐♥❣ ♣❤❛s❡ → ρ : R D → R D ❪ ◮ ♠❛♥❛❣❡ ❞❡✲s②♥❝❤r♦♥✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❬ D tr❛✐♥ − ❉❊❊P ▲❊❆❘◆■◆● → ǫ : R D → R C ❪ ◮ ♠❛♥❞❛t♦r② ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ❬ D tr❛✐♥ − ◮ ❡st✐♠❛t❡ ◮ p ǫ ( ρ ( � X )) | Z = z ✱ p ǫ ( ρ ( � X )) ✱ p Z ✭❣❡♥❡r❛t✐✈❡ ♠♦❞❡❧✮ ◮ ●❛✉ss✐❛♥ ❤②♣♦t❤❡s✐s ✭ ❚❡♠♣❧❛t❡ ❆tt❛❝❦ ✮❬❈❘❘✵✸❪ ◮ p Z | � X ✭❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ ❜② ♠❡❛♥s ♦❢ ❛ ♥❡✉r❛❧ ♥❡t✇♦r❦ ˆ p ( � x , W ) ≈ p Z | � X = � x ❚❤✐s t❛❧❦ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦✿ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ ✭❞❡❛❧ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ✰ ❡①tr❛❝t✐♦♥ ❢❡❛t✉r❡ ✰ ❛♣♣r♦①✐♠❛t❡ ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✷✴✹✷

  23. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥t❡♥ts ✶✳ ❈♦♥t❡①t ❛♥❞ ❙t❛t❡ ♦❢ t❤❡ ❆rt ✷✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛❣❛✐♥st ▼✐s❛❧✐❣♥♠❡♥t ✷✳✶ ◆❡✉r❛❧ ◆❡t✇♦r❦ ❈❧❛ss✐✜❡rs ✷✳✷ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ✷✳✸ ❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ✸✳ ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ✹✳ ❈♦♥❝❧✉s✐♦♥s ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✸✴✹✷

  24. ❯♥✐✈❡rs❛❧ ❛♣♣r♦①✐♠❛t✐♦♥ t❤❡♦r❡♠ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ■♥ ❙❈❆ ❧✐tt❡r❛t✉r❡ ❬▼❍▼✶✸❀ ▼❩✶✸❀ ▼▼❚✶✺❀ ▼❉▼✶✻❪ ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ✭▼▲P✮ p ( � ˆ x , W ) = s ◦ λ n ◦ σ n − ✶ ◦ λ n − ✶ ◦ · · · ◦ λ ✶ ( � x ) = � y ≈ p Z | � X = � x λ i ❧✐♥❡❛r ❢✉♥❝t✐♦♥s ✭❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥s ♦❢ t✐♠❡ s❛♠♣❧❡s✮ ❞❡♣❡♥❞✐♥❣ ♦♥ s♦♠❡ tr❛✐♥❛❜❧❡ ✇❡✐❣❤ts W σ i ♥♦♥✲❧✐♥❡❛r ❢✉♥❝t✐♦♥s s ♥♦r♠❛❧✐③✐♥❣ s♦❢t♠❛① ❢✉♥❝t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✹✴✹✷ ❋✐❣✉r❡✿ ▲✐♥❡❛r ❧❛②❡r ✐♥ ❛♥ ▼▲P ✭ ❋✉❧❧② ❈♦♥♥❡❝t❡❞ ▲❛②❡r ✮

  25. ❯♥✐✈❡rs❛❧ ❛♣♣r♦①✐♠❛t✐♦♥ t❤❡♦r❡♠ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ■♥ ❙❈❆ ❧✐tt❡r❛t✉r❡ ❬▼❍▼✶✸❀ ▼❩✶✸❀ ▼▼❚✶✺❀ ▼❉▼✶✻❪ ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ✭▼▲P✮ p ( � ˆ x , W ) = s ◦ λ n ◦ σ n − ✶ ◦ λ n − ✶ ◦ · · · ◦ λ ✶ ( � x ) = � y ≈ p Z | � X = � x λ i ❧✐♥❡❛r ❢✉♥❝t✐♦♥s ✭❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥s ♦❢ t✐♠❡ s❛♠♣❧❡s✮ ❞❡♣❡♥❞✐♥❣ ♦♥ s♦♠❡ tr❛✐♥❛❜❧❡ ✇❡✐❣❤ts W σ i ♥♦♥✲❧✐♥❡❛r ❢✉♥❝t✐♦♥s s ♥♦r♠❛❧✐③✐♥❣ s♦❢t♠❛① ❢✉♥❝t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✹✴✹✷ ❋✐❣✉r❡✿ ▲✐♥❡❛r ❧❛②❡r ✐♥ ❛♥ ▼▲P ✭ ❋✉❧❧② ❈♦♥♥❡❝t❡❞ ▲❛②❡r ✮

  26. ❯♥✐✈❡rs❛❧ ❛♣♣r♦①✐♠❛t✐♦♥ t❤❡♦r❡♠ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ■♥ ❙❈❆ ❧✐tt❡r❛t✉r❡ ❬▼❍▼✶✸❀ ▼❩✶✸❀ ▼▼❚✶✺❀ ▼❉▼✶✻❪ ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ✭▼▲P✮ p ( � ˆ x , W ) = s ◦ λ n ◦ σ n − ✶ ◦ λ n − ✶ ◦ · · · ◦ λ ✶ ( � x ) = � y ≈ p Z | � X = � x λ i ❧✐♥❡❛r ❢✉♥❝t✐♦♥s ✭❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥s ♦❢ t✐♠❡ s❛♠♣❧❡s✮ ❞❡♣❡♥❞✐♥❣ ♦♥ s♦♠❡ tr❛✐♥❛❜❧❡ ✇❡✐❣❤ts W σ i ♥♦♥✲❧✐♥❡❛r ❛❝t✐✈❛t✐♦♥ ❢✉♥❝t✐♦♥s s ♥♦r♠❛❧✐③✐♥❣ s♦❢t♠❛① ❢✉♥❝t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✹✴✹✷ ❋✐❣✉r❡✿ ▲✐♥❡❛r ❧❛②❡r ✐♥ ❛♥ ▼▲P ✭ ❋✉❧❧② ❈♦♥♥❡❝t❡❞ ▲❛②❡r ✮

  27. ❆r❝❤✐t❡❝t✉r❡ ❤②♣❡r✲♣❛r❛♠❡t❡rs ❯♥✐✈❡rs❛❧ ❛♣♣r♦①✐♠❛t✐♦♥ t❤❡♦r❡♠ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ■♥ ❙❈❆ ❧✐tt❡r❛t✉r❡ ❬▼❍▼✶✸❀ ▼❩✶✸❀ ▼▼❚✶✺❀ ▼❉▼✶✻❪ ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ✭▼▲P✮ p ( � ˆ x , W ) = s ◦ λ n ◦ σ n − ✶ ◦ λ n − ✶ ◦ · · · ◦ λ ✶ ( � x ) = � y ≈ p Z | � X = � x λ i ❧✐♥❡❛r ❢✉♥❝t✐♦♥s ✭❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥s ♦❢ t✐♠❡ s❛♠♣❧❡s✮ ❞❡♣❡♥❞✐♥❣ ♦♥ s♦♠❡ tr❛✐♥❛❜❧❡ ✇❡✐❣❤ts W σ i ♥♦♥✲❧✐♥❡❛r ❛❝t✐✈❛t✐♦♥ ❢✉♥❝t✐♦♥s s ♥♦r♠❛❧✐③✐♥❣ s♦❢t♠❛① ❢✉♥❝t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✹✴✹✷ ❋✐❣✉r❡✿ ▲✐♥❡❛r ❧❛②❡r ✐♥ ❛♥ ▼▲P ✭ ❋✉❧❧② ❈♦♥♥❡❝t❡❞ ▲❛②❡r ✮

  28. ❯♥✐✈❡rs❛❧ ❛♣♣r♦①✐♠❛t✐♦♥ t❤❡♦r❡♠ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ■♥ ❙❈❆ ❧✐tt❡r❛t✉r❡ ❬▼❍▼✶✸❀ ▼❩✶✸❀ ▼▼❚✶✺❀ ▼❉▼✶✻❪ ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ✭▼▲P✮ p ( � ˆ x , W ) = s ◦ λ n ◦ σ n − ✶ ◦ λ n − ✶ ◦ · · · ◦ λ ✶ ( � x ) = � y ≈ p Z | � X = � x λ i ❧✐♥❡❛r ❢✉♥❝t✐♦♥s ✭❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥s ♦❢ t✐♠❡ s❛♠♣❧❡s✮ ❞❡♣❡♥❞✐♥❣ ♦♥ s♦♠❡ tr❛✐♥❛❜❧❡ ✇❡✐❣❤ts W σ i ♥♦♥✲❧✐♥❡❛r ❛❝t✐✈❛t✐♦♥ ❢✉♥❝t✐♦♥s s ♥♦r♠❛❧✐③✐♥❣ s♦❢t♠❛① ❢✉♥❝t✐♦♥ ❆r❝❤✐t❡❝t✉r❡ ❤②♣❡r✲♣❛r❛♠❡t❡rs ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✹✴✹✷ ❋✐❣✉r❡✿ ▲✐♥❡❛r ❧❛②❡r ✐♥ ❛♥ ▼▲P ✭ ❋✉❧❧② ❈♦♥♥❡❝t❡❞ ▲❛②❡r ✮

  29. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ■♥ ❙❈❆ ❧✐tt❡r❛t✉r❡ ❬▼❍▼✶✸❀ ▼❩✶✸❀ ▼▼❚✶✺❀ ▼❉▼✶✻❪ ▼✉❧t✐✲▲❛②❡r P❡r❝❡♣tr♦♥ ✭▼▲P✮ p ( � ˆ x , W ) = s ◦ λ n ◦ σ n − ✶ ◦ λ n − ✶ ◦ · · · ◦ λ ✶ ( � x ) = � y ≈ p Z | � X = � x λ i ❧✐♥❡❛r ❢✉♥❝t✐♦♥s ✭❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥s ♦❢ t✐♠❡ s❛♠♣❧❡s✮ ❞❡♣❡♥❞✐♥❣ ♦♥ s♦♠❡ tr❛✐♥❛❜❧❡ ✇❡✐❣❤ts W σ i ♥♦♥✲❧✐♥❡❛r ❛❝t✐✈❛t✐♦♥ ❢✉♥❝t✐♦♥s s ♥♦r♠❛❧✐③✐♥❣ s♦❢t♠❛① ❢✉♥❝t✐♦♥ ❆r❝❤✐t❡❝t✉r❡ ❤②♣❡r✲♣❛r❛♠❡t❡rs ❯♥✐✈❡rs❛❧ ❛♣♣r♦①✐♠❛t✐♦♥ t❤❡♦r❡♠ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✹✴✹✷ ❋✐❣✉r❡✿ ▲✐♥❡❛r ❧❛②❡r ✐♥ ❛♥ ▼▲P ✭ ❋✉❧❧② ❈♦♥♥❡❝t❡❞ ▲❛②❡r ✮

  30. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛♥s❧❛t✐♦♥✲■♥✈❛r✐❛♥❝❡ Classification Classifier 0% 20% 40% 60% Horse Dog Cat ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✺✴✹✷

  31. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛♥s❧❛t✐♦♥✲■♥✈❛r✐❛♥❝❡ Classification Classifier 0% 20% 40% 60% Horse Dog Cat ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✺✴✹✷

  32. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛♥s❧❛t✐♦♥✲■♥✈❛r✐❛♥❝❡ Classification Classifier 0% 20% 40% 60% Horse Dog Cat ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✺✴✹✷

  33. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛♥s❧❛t✐♦♥✲■♥✈❛r✐❛♥❝❡ P(Z|X=x) Classifier 0% 50% 100% x Z=1 Z=0 ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✺✴✹✷

  34. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛♥s❧❛t✐♦♥✲■♥✈❛r✐❛♥❝❡ P(Z|X=x) Classifier 0% 50% 100% x Z=1 Z=0 ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✺✴✹✷

  35. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛♥s❧❛t✐♦♥✲■♥✈❛r✐❛♥❝❡ P(Z|X=x) Classifier 0% 50% 100% x Z=1 Z=0 ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✺✴✹✷

  36. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥✈♦❧✉t✐♦♥❛❧ ▲❛②❡rs Input Output 0 1 3 3 7 11 1 1 3 Length = 9 2 2 2 6 0 2 1 0 0 4 2 2 3 1 3 conv. filters of size 2 × 1 0 ❋✐❣✉r❡✿ ▲✐♥❡❛r ❧❛②❡r ✐♥ ❛♥ ▼▲P✳ Depth = 1 Depth= 3 ❋✐❣✉r❡✿ ❈♦♥✈♦❧✉t✐♦♥❛❧ ❧❛②❡r ✐♥ ❛ ❈◆◆✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✻✴✹✷

  37. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s P♦♦❧✐♥❣ ▲❛②❡rs Before Pooling 8 1 15 11 Input Output After Pooling 10 25 9 15 25 3 7 11 1 0 1 0 0 0 1 0 1 0 0 0 22 8 6 24 2 2 6 0 1 1 0 1 1 0 1 1 0 1 1 7 9 0 4 2 0 4 conv. filters of size 2 × 3 Depth= 4 Depth = 3 Depth= 4 1 ❋✐❣✉r❡✿ ❈♦♥✈♦❧✉t✐♦♥❛❧ ❧❛②❡r ✐♥ ❛ ❈◆◆✳ Depth= 4 ❋✐❣✉r❡✿ P♦♦❧✐♥❣ ❧❛②❡r ✐♥ ❛ ❈◆◆✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✼✴✹✷

  38. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆ ❦✐♥❞ ♦❢ ❈◆◆ ❛r❝❤✐t❡❝t✉r❡ Temporal Features Side-Channel Trace Abstract Features Scores FC + CONV+ Softmax ACT+ CONV+ POOL ACT+ POOL CONV+ ACT+ POOL 1 ❆r❝❤✐t❡❝t✉r❡ ✐♥s♣✐r❡❞ ❜② ❆❧❡①◆❡t ❬❑❙❍✶✷❪✱ ❱●● ❬❙❩✶✹❪✱ ❘❡s◆❡t ❬❍❡✰✶✻❪ ❞❡s✐❣♥ r✉❧❡s✿ ◮ ❘❡❞✉❝❡ t❡♠♣♦r❛❧ ❢❡❛t✉r❡s t♦ ♦♥❧② ♦♥❡ ◮ ▼❛✐♥t❛✐♥ t✐♠❡ ❝♦♠♣❧❡①✐t② ♦❢ ❡❛❝❤ ❧❛②❡r ✭♦♥❡✲❤❛❧❢ ♣♦♦❧✐♥❣ ✇❤❡♥ ♥✉♠❜❡r ♦❢ ❢❡❛t✉r❡ ♠❛♣s ✐s ❞♦✉❜❧❡❞✮ ❈❍❊❙ ✷✵✶✼ ✲ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ✇✐t❤ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❆❣❛✐♥st ❏✐tt❡r✲❇❛s❡❞ ❈♦✉♥t❡r♠❡❛s✉r❡s ✲ Pr♦✜❧✐♥❣ ❆tt❛❝❦s ❲✐t❤♦✉t Pr❡✲♣r♦❝❡ss✐♥❣✳ ❊✳ ❈❛❣❧✐ ✲ ❈✳ ❉✉♠❛s ✲ ❊✳ Pr♦✉✛ ◮ ✹ ❈♦♥✈ ✰ P♦♦❧ ❧❛②❡rs ◮ t❛♥❤ ❛❝t✐✈❛t✐♦♥s ◮ ❜❛t❝❤ ♥♦r♠❛❧✐s❛t✐♦♥ ❬■❙✶✺❪ ◮ ✶ ❢✉❧❧② ❝♦♥♥❡❝t❡❞ ❧❛②❡r ✰ s♦❢t♠❛① ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✽✴✹✷

  39. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛✐♥✐♥❣ ❛♥❞ ❱❛❧✐❞❛t✐♦♥ ✭✶✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✶✾✴✹✷

  40. Pr ✶ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦st ❢✉♥❝t✐♦♥ ✲ ❈r♦ss✲❡♥tr♦♣② ◮ ❜❛t❝❤ ♦❢ tr❛✐♥✐♥❣ ❞❛t❛ ( � x i , z i ) i ∈ I ✱ ♦✉t♣✉ts ♦❢ t❤❡ ❝✉rr❡♥t ♠♦❞❡❧ ( � y i ) i ∈ I ◮ ❧❛❜❡❧s z i = s j ❛r❡ ♦♥❡✲❤♦t ❡♥❝♦❞❡❞ ✿ � z i = � s j = ( ✵ , . . . , ✵ , ✶ , ✵ , . . . , ✵ ) ���� j ▲♦ss ❢✉♥❝t✐♦♥ |Z| L = − ✶ � � � z i [ t ] log � y i [ t ] ✭✶✮ | I | i ∈ I t = ✶ ▼❛①✐♠✉♠✲ ❛✲♣♦st❡r✐♦r✐ ♦r ❈r♦ss✲❡♥tr♦♣② y i ≈ Pr [ Z | � ◮ � X = � x i ] ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✵✴✹✷

  41. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦st ❢✉♥❝t✐♦♥ ✲ ❈r♦ss✲❡♥tr♦♣② ◮ ❜❛t❝❤ ♦❢ tr❛✐♥✐♥❣ ❞❛t❛ ( � x i , z i ) i ∈ I ✱ ♦✉t♣✉ts ♦❢ t❤❡ ❝✉rr❡♥t ♠♦❞❡❧ ( � y i ) i ∈ I ◮ ❧❛❜❡❧s z i = s j ❛r❡ ♦♥❡✲❤♦t ❡♥❝♦❞❡❞ ✿ � z i = � s j = ( ✵ , . . . , ✵ , ✶ , ✵ , . . . , ✵ ) ���� j ▲♦ss ❢✉♥❝t✐♦♥ |Z| L = − ✶ � � � z i [ t ] log � y i [ t ] ✭✶✮ | I | i ∈ I t = ✶ ▼❛①✐♠✉♠✲ ❛✲♣♦st❡r✐♦r✐ ♦r ❈r♦ss✲❡♥tr♦♣② y i ≈ Pr [ Z | � ◮ � X = � x i ] ◮ � z i ≈ Pr [ Z | Z = � s j ] y i ] = − � |Z| ◮ H ( � z i , � y i ) = H ( � z i ) + D KL ( � z i || � y i ) = E � z i [ − log � t = ✶ � z i [ t ] log � y i [ t ] ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✵✴✹✷

  42. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛✐♥✐♥❣ ❛♥❞ ❱❛❧✐❞❛t✐♦♥ ✭✷✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✶✴✹✷

  43. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛✐♥✐♥❣ ❛♥❞ ❱❛❧✐❞❛t✐♦♥ ✭✷✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✶✴✹✷

  44. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛✐♥✐♥❣ ❛♥❞ ❱❛❧✐❞❛t✐♦♥ ✭✷✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✶✴✹✷

  45. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛✐♥✐♥❣ ❛♥❞ ❱❛❧✐❞❛t✐♦♥ ✭✷✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✶✴✹✷

  46. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❖✈❡r✜tt✐♥❣ ❆❝❝✉r❛❝② ❈♦rr❡❝t ♣r❡❞✐❝t✐♦♥s ❚♦t❛❧ ♣r❡❞✐❝t✐♦♥s ❊✈❛❧✉❛t❡ ❛♥❞ ❝♦♠♣❛r❡ tr❛✐♥✐♥❣ ❛♥❞ ✈❛❧✐❞❛t✐♦♥ ❛❝❝✉r❛❝② ▲❡❛r♥ ❜② ❤❡❛rt ✭ ❖❱❊❘❋■❚❚■◆● ✮ Accuracy Training Validation Epoch ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✷✴✹✷

  47. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❖✈❡r✜tt✐♥❣ ❆❝❝✉r❛❝② ❈♦rr❡❝t ♣r❡❞✐❝t✐♦♥s ❚♦t❛❧ ♣r❡❞✐❝t✐♦♥s ❊✈❛❧✉❛t❡ ❛♥❞ ❝♦♠♣❛r❡ tr❛✐♥✐♥❣ ❛♥❞ ✈❛❧✐❞❛t✐♦♥ ❛❝❝✉r❛❝② ❯♥❞❡rst❛♥❞ s✐❣♥✐✜❝❛♥t ❢❡❛t✉r❡s ▲❡❛r♥ ❜② ❤❡❛rt ✭ ❖❱❊❘❋■❚❚■◆● ✮ Accuracy Accuracy Training Training Validation Validation Epoch Epoch ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✷✴✹✷

  48. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❖✈❡r✜tt✐♥❣ ❆❝❝✉r❛❝② ❈♦rr❡❝t ♣r❡❞✐❝t✐♦♥s ❚♦t❛❧ ♣r❡❞✐❝t✐♦♥s ❊✈❛❧✉❛t❡ ❛♥❞ ❝♦♠♣❛r❡ tr❛✐♥✐♥❣ ❛♥❞ ✈❛❧✐❞❛t✐♦♥ ❛❝❝✉r❛❝② ❲❤②❄ ▲❡❛r♥ ❜② ❤❡❛rt ✭ ❖❱❊❘❋■❚❚■◆● ✮ ❚♦♦ ❝♦♠♣❧❡① ♠♦❞❡❧ Accuracy ◆♦t ❡♥♦✉❣❤ tr❛✐♥✐♥❣ ❞❛t❛ Training ❙♦❧✉t✐♦♥❄ ❘❡❞✉❝❡ ♠♦❞❡❧ ❝❛♣❛❝✐t② ❘❡❣✉❧❛r✐③❛t✐♦♥ Validation ❉r♦♣♦✉t Epoch ❊❛r❧②✲❙t♦♣♣✐♥❣ ❉❛t❛ ❛✉❣♠❡♥t❛t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✷✴✹✷

  49. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❖✈❡r✜tt✐♥❣ ❆❝❝✉r❛❝② ❈♦rr❡❝t ♣r❡❞✐❝t✐♦♥s ❚♦t❛❧ ♣r❡❞✐❝t✐♦♥s ❊✈❛❧✉❛t❡ ❛♥❞ ❝♦♠♣❛r❡ tr❛✐♥✐♥❣ ❛♥❞ ✈❛❧✐❞❛t✐♦♥ ❛❝❝✉r❛❝② ❲❤②❄ ▲❡❛r♥ ❜② ❤❡❛rt ✭ ❖❱❊❘❋■❚❚■◆● ✮ ❚♦♦ ❝♦♠♣❧❡① ♠♦❞❡❧ Accuracy ◆♦t ❡♥♦✉❣❤ tr❛✐♥✐♥❣ ❞❛t❛ Training ❙♦❧✉t✐♦♥❄ ❘❡❞✉❝❡ ♠♦❞❡❧ ❝❛♣❛❝✐t② ❘❡❣✉❧❛r✐③❛t✐♦♥ Validation ❉r♦♣♦✉t Epoch ❊❛r❧②✲❙t♦♣♣✐♥❣ ❉❛t❛ ❛✉❣♠❡♥t❛t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✷✴✹✷

  50. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❆rt✐✜❝✐❛❧❧② ❣❡♥❡r❛t❡ ♥❡✇ tr❛✐♥✐♥❣ ❞❛t❛ ❜② ❞❡❢♦r♠✐♥❣ t❤♦s❡ ♣r❡✈✐♦✉s❧② ❛❝q✉✐r❡❞✱ ❆♣♣❧②✐♥❣ tr❛♥s❢♦r♠❛t✐♦♥s t❤❛t ♣r❡s❡r✈❡ t❤❡ ❧❛❜❡❧ Z ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✸✴✹✷

  51. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❈♦✉♥t❡r♠❡❛s✉r❡ ❊♠✉❧❛t✐♦♥ ■❞❡❛ ❊♠✉❧❛t❡ t❤❡ ❡✛❡❝ts ♦❢ ♠✐s❛❧✐❣♥✐♥❣ ❝♦✉♥t❡r♠❡❛s✉r❡s t♦ ❣❡♥❡r❛t❡ ♥❡✇ tr❛❝❡s ❙❍■❋❚■◆● ❆❉❉✲❘❊▼❖❱❊ 𝑈 ∗ − 𝑈 𝑈 ∗ − 𝑈 2 𝐸′ 2 Original trace Shifting Window Deforming trace via AR technique t Time Samples Augmented trace 𝐸 0 ❋✐❣✉r❡✿ SH T ❋✐❣✉r❡✿ AR R P❛r❛♠❡t❡r T ✿ ♯ ♦❢ ♣♦ss✐❜❧❡ ♣♦s✐t✐♦♥s P❛r❛♠❡t❡r R ✿ ♯ ♦❢ ❛❞❞❡❞ ❛♥❞ r❡♠♦✈❡❞ ♣♦✐♥ts ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ❛r❡ ❛♣♣❧✐❡❞ ♦♥❧✐♥❡ ❞✉r✐♥❣ tr❛✐♥✐♥❣ ♣❤❛s❡✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✹✴✹✷

  52. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛✐♥✐♥❣ ✇✐t❤ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✺✴✹✷

  53. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚r❛✐♥✐♥❣ ✇✐t❤ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✺✴✹✷

  54. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ◮ ❘❛♥❞♦♠ ❞❡❧❛②s ✭s♦❢t✇❛r❡ ❝♦✉♥t❡r♠❡❛s✉r❡✮ ◮ ❆rt✐✜❝✐❛❧ ❏✐tt❡r ✭s✐♠✉❧❛t❡❞ ❤❛r❞✇❛r❡ ❝♦✉♥t❡r♠❡❛s✉r❡✮ ◮ ❘❡❛❧ ❏✐tt❡r ✭❤❛r❞✇❛r❡ ❝♦✉♥t❡r♠❡❛s✉r❡✮ ❑❡r❛s ✶✳✷✳✶ ❧✐❜r❛r② ✇✐t❤ ❚❡♥s♦r✢♦✇ ❜❛❝❦❡♥❞ ❬❈❤♦✰✶✺❪ ✭♦♣❡♥ s♦✉r❝❡✱ t♦❞❛② ✷✳✷✳✹✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✻✴✹✷

  55. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ◮ ❘❛♥❞♦♠ ❞❡❧❛②s ✭s♦❢t✇❛r❡ ❝♦✉♥t❡r♠❡❛s✉r❡✮ ◮ ❆rt✐✜❝✐❛❧ ❏✐tt❡r ✭s✐♠✉❧❛t❡❞ ❤❛r❞✇❛r❡ ❝♦✉♥t❡r♠❡❛s✉r❡✮ ◮ ❘❡❛❧ ❏✐tt❡r ✭❤❛r❞✇❛r❡ ❝♦✉♥t❡r♠❡❛s✉r❡✮ ❑❡r❛s ✶✳✷✳✶ ❧✐❜r❛r② ✇✐t❤ ❚❡♥s♦r✢♦✇ ❜❛❝❦❡♥❞ ❬❈❤♦✰✶✺❪ ✭♦♣❡♥ s♦✉r❝❡✱ t♦❞❛② ✷✳✷✳✹✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✻✴✹✷

  56. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❘❛♥❞♦♠ ❞❡❧❛②s 0.5 0 Power Consumption −0.5 0 1000 2000 3000 4000 0.5 0 −0.5 0 1000 2000 3000 4000 0.5 0 −0.5 0 1000 2000 3000 4000 Time samples ✭❛✮ ❖♥❡ ❧❡❛❦✐♥❣ ♦♣❡r❛t✐♦♥ ❙❡t✉♣ ◮ ❚❛r❣❡t ❈❤✐♣✿ ❆t♠❡❣❛✸✷✽P ◮ ❚❛r❣❡t ❱❛r✐❛❜❧❡✿ Z = ❍❲ ( ❙❜♦① ( P ⊕ K )) ◮ ❆❝q✉✐s✐t✐♦♥✿ t❤r♦✉❣❤ ❈❤✐♣❲❤✐s♣❡r❡r❬❖❈✶✹❪ ♣❧❛t❢♦r♠✱ ≈ ✹ , ✵✵✵ t✐♠❡ s❛♠♣❧❡s ◮ ❈♦✉♥t❡r♠❡❛s✉r❡✿ ❘❛♥❞♦♠ ❉❡❧❛②s ✲ ✐♥s❡rt✐♦♥ ♦❢ r ♥♦♣ ♦♣❡r❛t✐♦♥s✱ r ∈ [ ✵ , ✶✷✼ ] ✉♥✐❢♦r♠ r❛♥❞♦♠ ◮ ✶ , ✵✵✵ tr❛✐♥✐♥❣ tr❛❝❡s ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✼✴✹✷

  57. ❆tt❛❝❦ ❙❍ ✵ ❙❍ ✶✵✵ ❙❍ ✺✵✵ ❆❝❝✉r❛❝② ✷✼✳✵✪ ✶ ✵✵✵ ✸✶✳✽✪ ✶✵✶ ✼✽✪ ✼ ❚❛❜❧❡✿ ♥✉♠❜❡r ♦❢ ❛tt❛❝❦ tr❛❝❡s t♦ ❤❛✈❡ ●❊ ✶✳ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❘❛♥❞♦♠ ❞❡❧❛②s ❉❛t❛ ❛✉❣♠❡♥t❛t✐♦♥ ✈s ♦✈❡r✜tt✐♥❣ ❚r❛✐♥✐♥❣ 1.0 1.0 0.9 0.9 0.8 0.8 0.8 0.7 0.7 0.6 training accuracy training accuracy 0.6 0.6 0.5 validation accuracy validation accuracy 0.5 0.4 0.4 0.4 training accuracy 0.3 0.2 0.3 validation accuracy 0.2 0.2 0 20 40 60 80 100 120 0 20 40 60 80 100 120 140 0 50 100 150 200 250 300 Epoch Epoch Epoch 200 225 105 200 0 0 0 2 3 0 0 0 0 175 0 0 2 2 1 0 0 0 0 0 4 0 0 1 0 0 0 0 0 0 0 90 0 1 4 10 7 1 1 0 0 0 0 0 4 20 0 0 0 0 1 0 15 4 2 1 1 1 0 0 1 1 175 150 0 0 0 24 75 0 0 0 0 0 1 18 58 14 8 0 0 0 0 2 80 14 2 1 0 0 0 2 2 2 75 150 125 0 0 26 114 52 36 2 0 0 0 0 0 67 163 0 0 0 0 3 3 0 0 15 200 14 0 1 0 0 3 True label True label True label 125 60 0 0 0 89 203 0 0 0 0 0 0 14 97 76 99 6 0 0 0 0 1 34 229 28 0 0 0 4 4 4 100 100 0 0 3 44 60 102 9 0 0 0 0 0 72 146 0 0 0 0 5 5 0 2 0 1 27 174 14 0 0 5 45 75 0 0 0 25 70 0 0 0 0 0 0 1 7 26 54 7 0 0 0 0 0 0 4 18 65 8 0 6 6 6 75 30 0 0 0 1 6 22 4 0 0 0 0 0 0 1 2 13 17 0 7 0 0 0 11 22 0 0 0 0 50 7 7 50 0 0 0 0 4 0 0 0 0 0 0 0 0 1 3 0 0 0 0 0 0 0 0 0 1 3 0 8 8 8 15 25 25 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Predicted label Predicted label Predicted label 0 0 0 ❙❍ ✵ ❙❍ ✶✵✵ ❙❍ ✺✵✵ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✽✴✹✷

  58. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❘❛♥❞♦♠ ❞❡❧❛②s ❉❛t❛ ❛✉❣♠❡♥t❛t✐♦♥ ✈s ♦✈❡r✜tt✐♥❣ ❚r❛✐♥✐♥❣ 1.0 1.0 0.9 0.9 0.8 0.8 0.8 0.7 0.7 0.6 training accuracy training accuracy 0.6 0.6 0.5 validation accuracy validation accuracy 0.5 0.4 0.4 0.4 training accuracy 0.3 0.2 0.3 validation accuracy 0.2 0.2 0 20 40 60 80 100 120 0 20 40 60 80 100 120 140 0 50 100 150 200 250 300 Epoch Epoch Epoch ❙❍ ✵ ❙❍ ✶✵✵ ❙❍ ✺✵✵ ❆tt❛❝❦ ❙❍ ✵ ❙❍ ✶✵✵ ❙❍ ✺✵✵ N ⋆ ❆❝❝✉r❛❝② ✷✼✳✵✪ > ✶ , ✵✵✵ ✸✶✳✽✪ ✶✵✶ ✼✽✪ ✼ ❚❛❜❧❡✿ N ⋆ = ♥✉♠❜❡r ♦❢ ❛tt❛❝❦ tr❛❝❡s t♦ ❤❛✈❡ ●❊ = ✶✳ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✽✴✹✷

  59. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❘❛♥❞♦♠ ❉❡❧❛②s ✲ ❚✇♦ ▲❡❛❦✐♥❣ ❖♣❡r❛t✐♦♥s 0.5 0 Power consumption −0.5 0 1000 2000 3000 4000 0.5 0 −0.5 0 1000 2000 3000 4000 0.5 0 −0.5 0 1000 2000 3000 4000 Time samples ❚✇♦ ❧❡❛❦✐♥❣ ♦♣❡r❛t✐♦♥s ❋✐rst ♦♣❡r❛t✐♦♥ ✲ ❚❡st ❛❝❝✿ ✼✻ . ✽ % ✱ N ⋆ = ✼ ❙❡❝♦♥❞ ♦♣❡r❛t✐♦♥ ✲ ❚❡st ❛❝❝✿ ✽✷ . ✺ % ✱ N ⋆ = ✻ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✷✾✴✹✷

  60. ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  61. ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  62. ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ◮ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  63. ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ◮ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ◮ ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  64. ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ◮ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ◮ ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ◮ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  65. ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ◮ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ◮ ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ◮ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ P(Z|X=x) Estjmator F( . ; θ) 0% 20% 40% 60% 80% 100% x Z=0 Z=1 ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  66. ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ◮ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ◮ ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ◮ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ P(Z|X=x) Estjmator F( . ; θ) 0% 20% 40% 60% 80% 100% x Z=0 Z=1 ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  67. ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ◮ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ◮ ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ◮ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ P(Z|X=x) Estjmator F( . ; θ) 0% 20% 40% 60% 80% 100% x Z=0 Z=1 ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  68. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥❝❧✉s✐♦♥s ❛❜♦✉t ❈◆◆ ◮ ❈◆◆s ♣r♦✈✐❞❡ ❛♥ ✐♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤ t♦ ❝♦♥str✉❝t ❛ ❞✐s❝r✐♠✐♥❛t✐✈❡ ♠♦❞❡❧ ❢r♦♠ ♠✐s❛❧✐❣♥❡❞ ❞❛t❛ ◮ ❈◆◆ ♠♦❞❡❧s ♠❛② ❤❛✈❡ ❤✐❣❤ ❝❛♣❛❝✐t② ❛♥❞ r❡q✉✐r❡ ♣❧❡♥t② ♦❢ ❞❛t❛ t♦ ❜❡ tr❛✐♥❡❞ ◮ ❙✐❞❡✲❈❤❛♥♥❡❧✲❛❞❛♣t❡❞ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡s ◮ ❊✛❡❝t✐✈❡♥❡ss✴❡✣❝✐❡♥❝② ♦❢ t❤❡ ❈◆◆✰❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ❛♣♣r♦❛❝❤ ❡①♣❡r✐♠❡♥t❛❧❧② ✈❡r✐✜❡❞ ◮ ❚♦❞❛② ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛tt❛❝❦s s②st❡♠❛t✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ✐♥ ❙✐❞❡✲❈❤❛♥♥❡❧ t❡sts ❢♦r ❡♠❜❡❞❞❡❞ ❝r②♣t♦❣r❛♣❤② ❡✈❛❧✉❛t✐♦♥ ❆♠♦♥❣ ♥❡✇ ♣r♦❜❧❡♠❛t✐❝s✳✳✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ♣r♦✈✐❞❡s ❜❧❛❝❦✲❜♦① ♠♦❞❡❧s✿ P(Z|X=x) Estjmator F( . ; θ) 0% 20% 40% 60% 80% 100% x Z=0 Z=1 ▲❛❝❦ ♦❢ ♣♦st❡r✐♦r ❦♥♦✇❧❡❞❣❡✿ ❤♦✇ ❞✐❞ t❤❡ ♠♦❞❡❧ ❧❡❛r♥❄ ▲❛❝❦ ♦❢ tr✉st✿ ✇❤❡r❡ ❞✐❞ t❤❡ ♠♦❞❡❧ ❣❡t t❤❡ ✐♥❢♦r♠❛t✐♦♥❄ ◆♦ ❤✐♥ts t♦ ❝♦rr❡❝t ✈✉❧♥❡r❛❜✐❧✐t② ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✵✴✹✷

  69. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❈♦♥t❡♥ts ✶✳ ❈♦♥t❡①t ❛♥❞ ❙t❛t❡ ♦❢ t❤❡ ❆rt ✷✳ ❉❡❡♣ ▲❡❛r♥✐♥❣ ❛❣❛✐♥st ▼✐s❛❧✐❣♥♠❡♥t ✷✳✶ ◆❡✉r❛❧ ◆❡t✇♦r❦ ❈❧❛ss✐✜❡rs ✷✳✷ ❉❛t❛ ❆✉❣♠❡♥t❛t✐♦♥ ✷✳✸ ❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ✸✳ ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ✹✳ ❈♦♥❝❧✉s✐♦♥s ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✶✴✹✷

  70. ❛❜❧❡ t♦ ❞❡t❡❝t P♦✐♥ts ♦❢ ■♥t❡r❡st ✭P♦■s✮ ❛s ❧♦♥❣ ❛s t❤❡ ♠♦❞❡❧ ❤❛s ❧❡❛r♥❡❞ s♦♠❡t❤✐♥❣ ❛❧r❡❛❞② ♣r♦♣♦s❡❞ ✐♥ ■♠❛❣❡ ❘❡❝♦❣♥✐t✐♦♥ ❬❙❱❩✶✸❀ ❙♣r✰✶✹❪ st❛rts t♦ ❜❡ ✉s❡❞ ✐♥ ❙❈❆ ❬❚✐♠✶✾❀ ❍●●✶✾❪ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ▲✳▼❛s✉r❡ ❡t ❛❧✳ ✱ ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ❢♦r ●❡♥❡r❛❧ ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ✐♥ Pr♦✜❧✐♥❣ ❆tt❛❝❦s ✱ ❈❖❙❆❉❊ ✷✵✶✾ ✭❉❛r♠st❛❞t✱ ✺t❤ ❆♣r✐❧ ✷✵✶✾✮ ◮ ♣r♦♣♦s❡s ❛ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ❜❛s❡❞ ♦♥ ❛ tr❛✐♥❡❞ ❈◆◆ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✷✴✹✷

  71. ❛❧r❡❛❞② ♣r♦♣♦s❡❞ ✐♥ ■♠❛❣❡ ❘❡❝♦❣♥✐t✐♦♥ ❬❙❱❩✶✸❀ ❙♣r✰✶✹❪ st❛rts t♦ ❜❡ ✉s❡❞ ✐♥ ❙❈❆ ❬❚✐♠✶✾❀ ❍●●✶✾❪ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ▲✳▼❛s✉r❡ ❡t ❛❧✳ ✱ ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ❢♦r ●❡♥❡r❛❧ ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ✐♥ Pr♦✜❧✐♥❣ ❆tt❛❝❦s ✱ ❈❖❙❆❉❊ ✷✵✶✾ ✭❉❛r♠st❛❞t✱ ✺t❤ ❆♣r✐❧ ✷✵✶✾✮ ◮ ♣r♦♣♦s❡s ❛ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ❜❛s❡❞ ♦♥ ❛ tr❛✐♥❡❞ ❈◆◆ ◮ ❛❜❧❡ t♦ ❞❡t❡❝t P♦✐♥ts ♦❢ ■♥t❡r❡st ✭P♦■s✮ ❛s ❧♦♥❣ ❛s t❤❡ ♠♦❞❡❧ ❤❛s ❧❡❛r♥❡❞ s♦♠❡t❤✐♥❣ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✷✴✹✷

  72. st❛rts t♦ ❜❡ ✉s❡❞ ✐♥ ❙❈❆ ❬❚✐♠✶✾❀ ❍●●✶✾❪ ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ▲✳▼❛s✉r❡ ❡t ❛❧✳ ✱ ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ❢♦r ●❡♥❡r❛❧ ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ✐♥ Pr♦✜❧✐♥❣ ❆tt❛❝❦s ✱ ❈❖❙❆❉❊ ✷✵✶✾ ✭❉❛r♠st❛❞t✱ ✺t❤ ❆♣r✐❧ ✷✵✶✾✮ ◮ ♣r♦♣♦s❡s ❛ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ❜❛s❡❞ ♦♥ ❛ tr❛✐♥❡❞ ❈◆◆ ◮ ❛❜❧❡ t♦ ❞❡t❡❝t P♦✐♥ts ♦❢ ■♥t❡r❡st ✭P♦■s✮ ❛s ❧♦♥❣ ❛s t❤❡ ♠♦❞❡❧ ❤❛s ❧❡❛r♥❡❞ s♦♠❡t❤✐♥❣ ◮ ❛❧r❡❛❞② ♣r♦♣♦s❡❞ ✐♥ ■♠❛❣❡ ❘❡❝♦❣♥✐t✐♦♥ ❬❙❱❩✶✸❀ ❙♣r✰✶✹❪ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✷✴✹✷

  73. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ▲✳▼❛s✉r❡ ❡t ❛❧✳ ✱ ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ❢♦r ●❡♥❡r❛❧ ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ✐♥ Pr♦✜❧✐♥❣ ❆tt❛❝❦s ✱ ❈❖❙❆❉❊ ✷✵✶✾ ✭❉❛r♠st❛❞t✱ ✺t❤ ❆♣r✐❧ ✷✵✶✾✮ ◮ ♣r♦♣♦s❡s ❛ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ❜❛s❡❞ ♦♥ ❛ tr❛✐♥❡❞ ❈◆◆ ◮ ❛❜❧❡ t♦ ❞❡t❡❝t P♦✐♥ts ♦❢ ■♥t❡r❡st ✭P♦■s✮ ❛s ❧♦♥❣ ❛s t❤❡ ♠♦❞❡❧ ❤❛s ❧❡❛r♥❡❞ s♦♠❡t❤✐♥❣ ◮ ❛❧r❡❛❞② ♣r♦♣♦s❡❞ ✐♥ ■♠❛❣❡ ❘❡❝♦❣♥✐t✐♦♥ ❬❙❱❩✶✸❀ ❙♣r✰✶✹❪ ◮ st❛rts t♦ ❜❡ ✉s❡❞ ✐♥ ❙❈❆ ❬❚✐♠✶✾❀ ❍●●✶✾❪ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✷✴✹✷

  74. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♥ ✐❞❡❛❧ ❝❛s❡ ■❞❡❛❧ ❝❛s❡✿ ✇❡ ❦♥♦✇ F ∗ = Pr [ Z | ❳ ] ✭ ✐✳❡✳ F ∗ : R D → P ( Z ) ⊂ [ ✵ , ✶ ] |Z| ✮ ❆♥ ❡①♣❧❛♥❛t✐♦♥ ❆♥ ❡①❛♠♣❧❡ ◮ ❆ss✉♠❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❧❡❛❦❛❣❡ ✐s ✈❡r② ❧♦❝❛❧✐③❡❞ ✭❢❡✇ P♦■s✮ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✸✴✹✷

  75. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♥ ✐❞❡❛❧ ❝❛s❡ ■❞❡❛❧ ❝❛s❡✿ ✇❡ ❦♥♦✇ F ∗ = Pr [ Z | ❳ ] ✭ ✐✳❡✳ F ∗ : R D → P ( Z ) ⊂ [ ✵ , ✶ ] |Z| ✮ ❆♥ ❡①❛♠♣❧❡ ❆♥ ❡①♣❧❛♥❛t✐♦♥ ◮ ❆ss✉♠❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❧❡❛❦❛❣❡ ✐s ✈❡r② ❧♦❝❛❧✐③❡❞ ✭❢❡✇ P♦■s✮ ◮ ❈♦♥s✐❞❡r ❛ ♥❡✇ tr❛❝❡ ❛♥❞ ✐ts ❧❛❜❡❧ � x , z ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✸✴✹✷

  76. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♥ ✐❞❡❛❧ ❝❛s❡ ■❞❡❛❧ ❝❛s❡✿ ✇❡ ❦♥♦✇ F ∗ = Pr [ Z | ❳ ] ✭ ✐✳❡✳ F ∗ : R D → P ( Z ) ⊂ [ ✵ , ✶ ] |Z| ✮ ❆♥ ❡①❛♠♣❧❡ ❆♥ ❡①♣❧❛♥❛t✐♦♥ ◮ ❆ss✉♠❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❧❡❛❦❛❣❡ ✐s ✈❡r② ❧♦❝❛❧✐③❡❞ ✭❢❡✇ P♦■s✮ ◮ t ✵ ♥♦♥ ✐♥❢♦r♠❛t✐✈❡✿ x [ t ✵ ] �→ � x [ t ✵ ] + ǫ ♥♦t s❡♥s✐t✐✈❡ � ◮ ■♥ ♦t❤❡r ✇♦r❞s✱ t ✵ ♥♦♥ ✐♥❢♦r♠❛t✐✈❡ x [ t ✵ ] F ∗ ( � ∂ → x )[ z ] ≈ ✵ ∂� ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✸✴✹✷

  77. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♥ ✐❞❡❛❧ ❝❛s❡ ■❞❡❛❧ ❝❛s❡✿ ✇❡ ❦♥♦✇ F ∗ = Pr [ Z | ❳ ] ✭ ✐✳❡✳ F ∗ : R D → P ( Z ) ⊂ [ ✵ , ✶ ] |Z| ✮ ❆♥ ❡①❛♠♣❧❡ ❆♥ ❡①♣❧❛♥❛t✐♦♥ ◮ ❆ss✉♠❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❧❡❛❦❛❣❡ ✐s ✈❡r② ❧♦❝❛❧✐③❡❞ ✭❢❡✇ P♦■s✮ ◮ t ✵ ♥♦♥ ✐♥❢♦r♠❛t✐✈❡✿ x [ t ✵ ] �→ � x [ t ✵ ] + ǫ ♥♦t s❡♥s✐t✐✈❡ � ◮ ■♥ ♦t❤❡r ✇♦r❞s✱ t ✵ ♥♦♥ ✐♥❢♦r♠❛t✐✈❡ x [ t ✵ ] F ∗ ( � ∂ → x )[ z ] ≈ ✵ ∂� ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✸✴✹✷

  78. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♥ ✐❞❡❛❧ ❝❛s❡ ■❞❡❛❧ ❝❛s❡✿ ✇❡ ❦♥♦✇ F ∗ = Pr [ Z | ❳ ] ✭ ✐✳❡✳ F ∗ : R D → P ( Z ) ⊂ [ ✵ , ✶ ] |Z| ✮ ❆♥ ❡①❛♠♣❧❡ ❆♥ ❡①♣❧❛♥❛t✐♦♥ ◮ ❆ss✉♠❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❧❡❛❦❛❣❡ ✐s ✈❡r② ❧♦❝❛❧✐③❡❞ ✭❢❡✇ P♦■s✮ ◮ t ✶ ✐♥❢♦r♠❛t✐✈❡✿ � x [ t ✶ ] �→ � x [ t ✶ ] + ǫ ✐s ❧✐❦❡❧② t♦ ❛✛❡❝t t❤❡ ♦♣t✐♠❛❧ ♠♦❞❡❧✬s ❞❡❝✐s✐♦♥ ◮ t ✶ ✐♥❢♦r♠❛t✐✈❡ � � � x [ t ✶ ] F ∗ ( � � ∂ → x )[ z ] � > ✵ � ∂� ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✸✴✹✷

  79. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♥ ✐❞❡❛❧ ❝❛s❡ ■❞❡❛❧ ❝❛s❡✿ ✇❡ ❦♥♦✇ F ∗ = Pr [ Z | ❳ ] ✭ ✐✳❡✳ F ∗ : R D → P ( Z ) ⊂ [ ✵ , ✶ ] |Z| ✮ ❆♥ ❡①❛♠♣❧❡ ❆♥ ❡①♣❧❛♥❛t✐♦♥ ◮ ❆ss✉♠❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❧❡❛❦❛❣❡ ✐s ✈❡r② ❧♦❝❛❧✐③❡❞ ✭❢❡✇ P♦■s✮ ◮ t ✶ ✐♥❢♦r♠❛t✐✈❡✿ � x [ t ✶ ] �→ � x [ t ✶ ] + ǫ ✐s ❧✐❦❡❧② t♦ ❛✛❡❝t t❤❡ ♦♣t✐♠❛❧ ♠♦❞❡❧✬s ❞❡❝✐s✐♦♥ ◮ t ✶ ✐♥❢♦r♠❛t✐✈❡ � � � x [ t ✶ ] F ∗ ( � ∂ � → x )[ z ] � > ✵ � ∂� ❈♦♥s❡q✉❡♥❝❡s x F ∗ ( � ■❢ t ✐s ❛ P♦■✱ t❤❡♥ ✐t s❤♦✉❧❞ ❜❡ s❡❡♥ ✐♥ t❤❡ ❣r❛❞✐❡♥ts ∇ � x )[ z ] ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✸✴✹✷

  80. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♥ ✐❞❡❛❧ ❝❛s❡ ■❞❡❛❧ ❝❛s❡✿ ✇❡ ❦♥♦✇ F ∗ = Pr [ Z | ❳ ] ✭ ✐✳❡✳ F ∗ : R D → P ( Z ) ⊂ [ ✵ , ✶ ] |Z| ✮ ❆♥ ❡①❛♠♣❧❡ ❆♥ ❡①♣❧❛♥❛t✐♦♥ ◮ ❆ss✉♠❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❧❡❛❦❛❣❡ ✐s ✈❡r② ❧♦❝❛❧✐③❡❞ ✭❢❡✇ P♦■s✮ ◮ t ✶ ✐♥❢♦r♠❛t✐✈❡✿ � x [ t ✶ ] �→ � x [ t ✶ ] + ǫ ✐s ❧✐❦❡❧② t♦ ❛✛❡❝t t❤❡ ♦♣t✐♠❛❧ ♠♦❞❡❧✬s ❞❡❝✐s✐♦♥ ◮ t ✶ ✐♥❢♦r♠❛t✐✈❡ � � � x [ t ✶ ] F ∗ ( � ∂ � → x )[ z ] � > ✵ � ∂� ❈♦♥s❡q✉❡♥❝❡s x F ∗ ( � ■❢ t ✐s ❛ P♦■✱ t❤❡♥ ✐t s❤♦✉❧❞ ❜❡ s❡❡♥ ✐♥ t❤❡ ❣r❛❞✐❡♥ts ∇ � x )[ z ] ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✸✴✹✷

  81. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♣♣❧✐❝❛t✐♦♥ ♦♥ ❡①♣❡r✐♠❡♥t❛❧ ❞❛t❛ ❉❡s❝r✐♣t✐♦♥ ❆❙❈❆❉ ❞❛t❛s❡t ❬Pr♦✰✶✽❪✿ ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴❆◆❙❙■✲❋❘✴❆❙❈❆❉ ✺✵ , ✵✵✵ tr❛❝❡s✱ ❡❛❝❤ ♦❢ ✼✵✵ ♣♦✐♥ts ❙♦✉r❝❡ ❝♦❞❡s ♦❢ s❡❝✉r❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥s ♦❢ ❆❊❙✶✷✽ ❢♦r ♣✉❜❧✐❝ ✽✲❜✐t ❛r❝❤✐t❡❝t✉r❡s ✭ ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴❆◆❙❙■✲❋❘✴s❡❝❆❊❙✲❆❚♠❡❣❛✽✺✶✺ ✮ ❈♦rr❡s♣♦♥❞s t♦ t❤❡ ✜rst ❆❊❙ r♦✉♥❞ ❚❤r❡❡ ❝❛s❡s st✉❞✐❡❞✿ ✶✳ ◆♦ ❝♦✉♥t❡r♠❡❛s✉r❡ ✿ s②♥❝❤r♦♥✐③❡❞ tr❛❝❡s✱ ♥♦ ♠❛s❦✐♥❣ ✷✳ ❆rt✐✜❝✐❛❧ r❛♥❞♦♠ s❤✐❢t ✸✳ ❙②♥❝❤r♦♥✐③❡❞ tr❛❝❡s✱ ❜♦♦❧❡❛♥ ♠❛s❦✐♥❣ ✭✉♥❦♥♦✇♥ ♠❛s❦s✮ ❚r❛✐♥❡❞ ♠♦❞❡❧ ❈◆◆ ✇✐t❤ ❛ ❱●●✲❧✐❦❡ ❛r❝❤✐t❡❝t✉r❡ ●r✐❞ s❡❛r❝❤ ♦❢ ❤②♣❡r♣❛r❛♠❡t❡rs ❇❡st ♠♦❞❡❧✿ ♠✐♥✐♠❛❧ tr❛❝❡ ♥✉♠❜❡r ✇❤❡♥ t❤❡ ❣✉❡ss✐♥❣ ❡♥tr♦♣② r❡❛❝❤❡s ✷ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✹✴✹✷

  82. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❋✐rst ❡①♣❡r✐♠❡♥t✿ ♥♦ ❝♦✉♥t❡r♠❡❛s✉r❡ ❆✈❡r❛❣❡ ♥✉♠❜❡r ♦❢ tr❛❝❡s t♦ r❡❝♦✈❡r t❤❡ s❡❝r❡t ❦❡②✿ ✸ SNR for Z = SBox ( p [3] ⊕ k [3]) ⊕ r out Gradient averaged on a 5-fold cross validation Synchronized traces No masking, no desynchronization 0 . 8 0 . 06 0 . 7 0 . 05 0 . 6 0 . 04 0 . 5 Gradient SNR 0 . 4 0 . 03 0 . 3 0 . 02 0 . 2 0 . 01 0 . 1 0 . 00 0 . 0 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 Time (samples) Time (samples) ❋✐❣✉r❡✿ ❙◆❘ ❋✐❣✉r❡✿ ●r❛❞✐❡♥t ❱✐s✉❛❧✐③❛t✐♦♥ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✺✴✹✷

  83. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❙❡❝♦♥❞ ❡①♣❡r✐♠❡♥t✿ ✇✐t❤ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ❆✈❡r❛❣❡ ♥✉♠❜❡r ♦❢ tr❛❝❡s t♦ r❡❝♦✈❡r t❤❡ s❡❝r❡t ❦❡②✿ ✸✳✻ Loss function gradient (average) No masking, random shift (100) SNR on ASCAD with random shift (100) 0 . 006 0.00625 0 . 005 0.00600 0 . 004 0.00575 Gradient SNR 0.00550 0 . 003 0.00525 0 . 002 0.00500 0.00475 0 . 001 0 100 200 300 400 500 600 700 0 . 000 Time(samples) 0 100 200 300 400 500 600 700 Time (samples) ❋✐❣✉r❡✿ ◆♦ P♦■ ❡♠♣❤❛s✐③❡❞ ❋✐❣✉r❡✿ ❇❛♥❞ ♦❢ ♣❡❛❦s ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✻✴✹✷

  84. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❙❡❝♦♥❞ ❡①♣❡r✐♠❡♥t✿ ✇✐t❤ ❞❡s②♥❝❤r♦♥✐③❛t✐♦♥ ❆✈❡r❛❣❡ ♥✉♠❜❡r ♦❢ tr❛❝❡s t♦ r❡❝♦✈❡r t❤❡ s❡❝r❡t ❦❡②✿ ✸✳✻ SNR on ASCAD with random shift (100) 0.00625 0.00600 0.00575 SNR 0.00550 0.00525 0.00500 0.00475 0 100 200 300 400 500 600 700 Time(samples) ❋✐❣✉r❡✿ ◆♦ P♦■ ❡♠♣❤❛s✐③❡❞ ❋✐❣✉r❡✿ ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ❢♦r ❡❛❝❤ tr❛❝❡ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✻✴✹✷

  85. ❈❧❛ss✐❢②✐♥❣ ❙✐❞❡✲❈❤❛♥♥❡❧ ❉❡s②♥❝❤r♦♥✐③❡❞ ❙✐❣♥❛❧s ✇✐t❤ ❈♦♥✈♦❧✉t✐♦♥❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❚❤✐r❞ ❡①♣❡r✐♠❡♥t✿ ✇✐t❤ ♠❛s❦✐♥❣ ❆✈❡r❛❣❡ ♥✉♠❜❡r ♦❢ tr❛❝❡s t♦ r❡❝♦✈❡r t❤❡ s❡❝r❡t ❦❡②✿ ≈ ✶✵✵ Loss function gradient (average) Signal-to-Noise Ratios ASCAD database With masking, no shift 0 . 8 r out 0 . 0005 Z ⊕ r out 0 . 7 0 . 6 0 . 0004 0 . 5 Gradient 0 . 0003 SNR 0 . 4 0 . 3 0 . 0002 0 . 2 0 . 0001 0 . 1 0 . 0000 0 . 0 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 Time (samples) Time (samples) ❋✐❣✉r❡✿ ❘❡q✉✐r❡s ❦♥♦✇❧❡❞❣❡ ♦❢ t❤❡ ♠❛s❦s ❋✐❣✉r❡✿ ◆♦ ❦♥♦✇❧❡❞❣❡ r❡q✉✐r❡❞ ✶✻✴✵✹✴✷✵✶✾✱ ❲❘❆❈✬❍ ✷✵✶✾ | ❊❧❡♦♥♦r❛ ❈❛❣❧✐ | ✸✼✴✹✷

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Search engines A search engine tries to bridge this gap Assumption: the required User

Search engines A search engine tries to bridge this gap Assumption: the required User

Query Sugges*ons Debapriyo Majumdar Information Retrieval Spring 2015 Indian Statistical Institute Kolkata Search engines A search engine tries to bridge this gap Assumption: the required User needs some information

441 views • 25 slides
MULTIMEDIA RETRIEVAL Electronic album, Personalised electronic journals Education and Training

MULTIMEDIA RETRIEVAL Electronic album, Personalised electronic journals Education and Training

3/4/2008 Multimedia? Text, images, drawings(graphics), animation, video, sound(speech) PCs, DVDs, games, digital TV, Web surfing etc. Applications of Multimedia Home Video on demand, Interactive TV MULTIMEDIA RETRIEVAL Electronic

575 views • 18 slides
Making Applications Mobile using containers Ottawa Linux Symposium, July 2006 Cedric Le Goater

Making Applications Mobile using containers Ottawa Linux Symposium, July 2006 Cedric Le Goater

Making Applications Mobile using containers Ottawa Linux Symposium, July 2006 Cedric Le Goater <clg@fr.ibm.com> Daniel Lezcano <dlezcano@fr.ibm.com> Clement Calmels <clement.calmels@fr.ibm.com> Dave Hansen

620 views • 29 slides
Workshop 1: The Erasmus Mundus brand name (EMBN) ( ) Prof. Boas Erez Prof. Philippe

Workshop 1: The Erasmus Mundus brand name (EMBN) ( ) Prof. Boas Erez Prof. Philippe

Workshop 1: The Erasmus Mundus brand name (EMBN) ( ) Prof. Boas Erez Prof. Philippe Gourbesville Prof. Philippe Gourbesville EM iDEA Conference, Lund 30/03/2012 1 Context Context - EMBN as third type of EMMC (2010) yp -

285 views • 14 slides
Image Segmentation Perceptual and Sensory Augmented Computing Luc Van Gool, ETH Zurich With

Image Segmentation Perceptual and Sensory Augmented Computing Luc Van Gool, ETH Zurich With

Image Segmentation Perceptual and Sensory Augmented Computing Luc Van Gool, ETH Zurich With important contributions by Vittorio Ferrari, Un. of Edinburgh Computer Vision WS 0/09 Slide credits: K. Grauman, B. Leibe, S. Lazebnik, S. Seitz, Y

1.7k views • 130 slides
1 2 3 4 5 6 The Graphics Processing Unit is controlled by the CPU through a direct interface

1 2 3 4 5 6 The Graphics Processing Unit is controlled by the CPU through a direct interface

1 2 3 4 5 6 The Graphics Processing Unit is controlled by the CPU through a direct interface of memory-mapped IO registers, and indirectly by parsing commands that the CPU has placed in memory. The display interface and blitter (block image

524 views • 25 slides
What Does Quality Mean? Operational meanings: CISC 323: Intro to Software Software does

What Does Quality Mean? Operational meanings: CISC 323: Intro to Software Software does

260 views • 22 slides
Discrete Time Markov Chains Discrete-Time Markov Chains Books - Introduction to Stochastic

Discrete Time Markov Chains Discrete-Time Markov Chains Books - Introduction to Stochastic

Markov Processes and Applications Markov Processes and Applications Discrete-Time Markov Chains D k h Continuous Time Markov Chains Continuous-Time Markov Chains Applications Applications Queuing theory Performance

977 views • 41 slides
Attacking AUTOSAR using Software and Hardware Attacks Pascal al Nasahl Graz University of

Attacking AUTOSAR using Software and Hardware Attacks Pascal al Nasahl Graz University of

Attacking AUTOSAR using Software and Hardware Attacks Pascal al Nasahl Graz University of Technology Niek Timmer mers Riscure 1 Introduction 2 Introduction Niek Timmers Principal Security Analyst @ Riscure 3 Introduction

1.34k views • 115 slides
Malware: Viruses, Worms, Rootkits, Botnets Spring 2015

Malware: Viruses, Worms, Rootkits, Botnets Spring 2015

CSE 484 / CSE M 584: Computer Security and Privacy Malware: Viruses, Worms, Rootkits, Botnets Spring 2015 Franziska (Franzi) Roesner

403 views • 37 slides
Direct Self-Consistent Field Computations on GPU Clusters Guochun Shi, Ivan Ufimtsev, Volodymyr

Direct Self-Consistent Field Computations on GPU Clusters Guochun Shi, Ivan Ufimtsev, Volodymyr

Direct Self-Consistent Field Computations on GPU Clusters Guochun Shi, Ivan Ufimtsev, Volodymyr Kindratenko Todd Martinez National Center for Supercomputing Department of Chemistry Applications Stanford University University of Illinois at

1.23k views • 26 slides
Linearizability, revisited Radha Jagadeesan Gustavo Petri Corin Pitcher James Riely

Linearizability, revisited Radha Jagadeesan Gustavo Petri Corin Pitcher James Riely

Linearizability, revisited Radha Jagadeesan Gustavo Petri Corin Pitcher James Riely DePaul University Purdue University ESOP 2010, FOSSACS 2012, TLDI 2012, ESOP 2013 Linearizability, revisited ESOP 2010, FOSSACS 2012,

1.24k views • 70 slides
The Soot framework for Java program analysis: a retrospective Patrick Lam, Eric Bodden, Ond

The Soot framework for Java program analysis: a retrospective Patrick Lam, Eric Bodden, Ond

The Soot framework for Java program analysis: a retrospective Patrick Lam, Eric Bodden, Ond rej Lhot ak, and Laurie Hendren October 2011 This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License . Soot a

867 views • 38 slides
3 John Series Lesson #020 October 19, 2003 Dean Bible Ministries www.deanbibleministries.org

3 John Series Lesson #020 October 19, 2003 Dean Bible Ministries www.deanbibleministries.org

3 John Series Lesson #020 October 19, 2003 Dean Bible Ministries www.deanbibleministries.org Dr. Robert L. Dean, Jr. Missions technically refers to a form of cross cultural evangelism where designated individuals are set apart by a local

417 views • 18 slides
Registrant List UCSF OCME Page 1 of 6 Name City, State Acosta R Maritza Masters Sausalito,

Registrant List UCSF OCME Page 1 of 6 Name City, State Acosta R Maritza Masters Sausalito,

University of California San Francisco 7/27/2015 MDM16M02: Essentials of Primary Care Registrant List UCSF OCME Page 1 of 6 Name City, State Acosta R Maritza Masters Sausalito, CA 1 2 Ajudia Ketan Md Placerville, CA Akinsanya

784 views • 6 slides
Localization: Algorithms and System Applications of Location Information Location aware

Localization: Algorithms and System Applications of Location Information Location aware

Localization: Algorithms and System Applications of Location Information Location aware information services e.g., E911, location-based search, target advertisement, tour guide, inventory management, traffic monitoring, disaster

912 views • 44 slides
Welcome to Advisens Transaction Insurance Insights Conference Welcoming Remarks Rebecca Bole

Welcome to Advisens Transaction Insurance Insights Conference Welcoming Remarks Rebecca Bole

Welcome to Advisens Transaction Insurance Insights Conference Welcoming Remarks Rebecca Bole EVP & Editor-in-Chief Advisen Leading the way to smarter and more efficient risk and insurance communities, Advisen delivers: The right

778 views • 48 slides
The End of the Tour Johnnie Odom Systems Integration Theres a girl with a crown and a

The End of the Tour Johnnie Odom Systems Integration Theres a girl with a crown and a

The End of the Tour Johnnie Odom Systems Integration Theres a girl with a crown and a scepter . and she says that the scene isnt what its been and shes thinking of going home. They Might Be Giants, The End of

461 views • 8 slides
Best Business Practices for Farmers Lessons from 15 Successful Farmers Market Farmers in

Best Business Practices for Farmers Lessons from 15 Successful Farmers Market Farmers in

Best Business Practices for Farmers Lessons from 15 Successful Farmers Market Farmers in Bri8sh Columbia Webinar Presenta,on Emily Hansen, Wallapak Polasub and Caroline Chiu Ins8tute for Sustainable Food Systems August 28 th , 2017 Image:

562 views • 52 slides
NASTAD Prevention an and Car are TA Meetin ing: Advancin ing Heal alth Equit ity Wednesd

NASTAD Prevention an and Car are TA Meetin ing: Advancin ing Heal alth Equit ity Wednesd

K ORRYN G AINES R ICARDO T ENORIIO C HRISTIAN V ARGAS I RECAS V ALENTINE D ARRION B ARNHILL J OHNNIE J. H ARRIS C HRISTOPHER R EDDING J OSE G ONZALES R ENDON R ICCO D EVANTE H OLDEN M ALCOLM L OREN H ICKSON D E M ARCO N EWMAN G REGORY F RAZIER P

863 views • 26 slides
PHYSICS DEPARTMENT NEWS AND EVENTS Welcome to the ACFI ! ATLAS Theory

PHYSICS DEPARTMENT NEWS AND EVENTS Welcome to the ACFI ! ATLAS Theory

PHYSICS DEPARTMENT NEWS AND EVENTS Welcome to the ACFI ! ATLAS Theory LIGO EXO PHYSICS DEPARTMENT NEWS AND EVENTS Our mission: We seek answers to key open ques0ons about

635 views • 17 slides
Semiclassics Workshop Welcome Amherst Center for Fundamental Interactions University of

Semiclassics Workshop Welcome Amherst Center for Fundamental Interactions University of

Semiclassics Workshop Welcome Amherst Center for Fundamental Interactions University of Massachusetts Amherst Many thanks to UMass and the ACFI for hosting this workshop! John Donoghue Michael Ramsey-Musolf Ingrid Pollard Mary Ann Ryan

298 views • 9 slides
Evaluating the use of Geant4 through LArSoft in the LArIAT simulation Hans Wenzel LArSoft

Evaluating the use of Geant4 through LArSoft in the LArIAT simulation Hans Wenzel LArSoft

Evaluating the use of Geant4 through LArSoft in the LArIAT simulation Hans Wenzel LArSoft Coordination Meeting October 6 th 2015 Charge Begin a two week (FTE effort not real 3me) project evalua3ng

145 views • 13 slides
T w o W e e k S p r i n g S a l e ! SAVE EVEN MORE SAVE EVEN MORE O N O N T

T w o W e e k S p r i n g S a l e ! SAVE EVEN MORE SAVE EVEN MORE O N O N T

Prices Good 3-29 thru 4-11-20 www.captainliquor.com T w o W e e k S p r i n g S a l e ! SAVE EVEN MORE SAVE EVEN MORE O N O N T E T E E B A E B A N - R N - R L - I L - I M A I M A I 4 2 $ 2 $

211 views • 8 slides

More recommend