Do Less, Get More: Streaming Submodular Maximization with Subsampling - - PowerPoint PPT Presentation

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Do Less, Get More: Streaming Submodular Maximization with Subsampling - - PowerPoint PPT Presentation

Jun 16, 2023 244 likes •376 views

Do Less, Get More: Streaming Submodular Maximization with Subsampling Moran Feldman 1 Amin Karbasi 2 Ehsan Kazemi 2 1 Open University of Israel and 2 Yale University Data Summarization Large set of images Videos Sensor data fMRI parcellation

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SLIDE 1

Do Less, Get More: Streaming Submodular Maximization with Subsampling

Ehsan Kazemi2 Moran Feldman1 Amin Karbasi2

1Open University of Israel and 2Yale University

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SLIDE 2

2

Data Summarization

Videos Large set of images Sensor data fMRI parcellation

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SLIDE 3

Submodularity

3

}) }) ({

f

({

— f

}) ({

f

({

— f

})

≥

Diminishing returns property for set functions.

V =

} {

∀ A ⊆ B ⊆ V and x ∉ B f (A ∪ {x}) - f (A) ≥ f (B ∪ {x}) - f (B)

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SLIDE 4

Submodularity

3

}) }) ({

f

({

— f

}) ({

f

({

— f

})

≥

Diminishing returns property for set functions.

V =

} {

∀ A ⊆ B ⊆ V and x ∉ B f (A ∪ {x}) - f (A) ≥ f (B ∪ {x}) - f (B)

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SLIDE 5

Streaming Algorithms

  • Many practical scenarios we need to use streaming

algorithms:

  • the data arrives at a very fast pace
  • there is only time to read the data once
  • random access to the entire data is not possible and
  • nly a small fraction of the data can be loaded to the

main memory

4

Summary Surveillance camera

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SLIDE 6

Streaming Algorithms

  • Many practical scenarios we need to use streaming

algorithms:

  • the data arrives at a very fast pace
  • there is only time to read the data once
  • random access to the entire data is not possible and
  • nly a small fraction of the data can be loaded to the

main memory

4

Summary Surveillance camera

Key challenge: 
 
 Extract small, representative subset 


  • ut of a massive stream of data
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SLIDE 7

5

Constrained Non-Monotone Submodular Maximization

constraints

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[Chekuri et al., 2015]

Set system: a pair (𝓞,𝓙), where 𝓞 is the ground set and 𝓙 ⊆ 2𝓞 is the set of independent sets p-matchoid: a set system (𝓞,𝓙) where there exist m matroids (𝓞i,𝓙i) such that every element of 𝓞 appears in the ground set of at most p matroids and

I = {S ⊆ 2N | ∀1≤i≤m S ∩ Ni ∈ Ii}

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SLIDE 8

6

Keep with probability q =

1 p+√ p(p+1)+1

Data Stream

Ui ← Exchange-Candidate(Si−1, ui)

Si−1

ui

ui+1 ui+2 ui+3 ui+5

The Sample-Streaming Algorithm

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SLIDE 9

7

Constrained Submodular Maximization

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SLIDE 10

7

Constrained Submodular Maximization

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SLIDE 11

7

Constrained Submodular Maximization

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SLIDE 12

Conclusion

8

  • Our algorithm provides the best of three worlds:
  • the tightest approximation guarantees in various settings
  • minimum memory requirement
  • fewest queries per element

Poster: Today (Thu Dec 6th) 10:45 AM-12:45 PM @ Room 210 & 230 AB #75