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Page 1: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 2: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 3: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 4: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 5: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 6: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 7: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

M = conv( Y ) where Y = { , , … }

Page 8: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 9: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 10: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 11: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 12: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 13: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 14: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 15: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 16: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

Page 17: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

Page 18: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

Page 19: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

Page 20: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

μ⊤

Page 21: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

〈x, p〉p ∈ Δ

〈 η, μ〉μ ∈M

μ

p* = e i i = (x )

Page 22: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 23: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

〈x, p〉p ∈ Δ

〈x, p〉+ H(p )p ∈ Δ

〈 η, μ〉μ ∈M

〈 η, μ〉+ H(μ )μ ∈M

μ⊤

p* = exp(x ) / Z

Page 24: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 25: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

〈x, p〉p ∈ Δ

〈x, p〉+ H(p )p ∈ Δ

〈 η, μ〉μ ∈M

〈 η, μ〉+ H(μ )μ ∈M

μ⊤

Page 26: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

〈x, p〉p ∈ Δ

〈x, p〉+ H(p )p ∈ Δ

〈 η, μ〉μ ∈M

〈 η, μ〉+ H(μ )μ ∈M

〈x, p〉– ½ ‖Ap ‖2

p ∈ Δ

〈 η, μ〉– ½ ‖μ ‖2

μ ∈M

μ⊤

Page 27: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

∂ μ *∂ η

〈 η, μ〉– ½ ‖μ ‖2

μ ∈M

Page 28: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 29: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
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Page 34: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
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Page 37: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
Page 38: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM

LA (η, μ ) = 〈 η, μ〉– ½ ‖μ ‖2 }–〈 η, μ〉+ ½ ‖μ ‖2

μ ∈M

LA (η, μ ) = 〈 η, μ〉– ½ ‖μ ‖2 + ρ(μ, μ ) }–〈 η, μ〉+ ½ ‖μ ‖2

μ ∈M

ρ

_ _

_

_ _

_

_

Page 39: PowerPoint Presentationvene.ro/talks/sparsemap-icml18-talk.pdf · 2020. 10. 15. · PowerPoint Presentation Author: Vlad Niculae Created Date: 7/11/2018 11:58:33 AM
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