Stochastic Greedy Algorithm Is Still Good: Maximizing Submodular + Supermodular Functions

Ji, Sai; Xu, Dianguo; Li, Min; Wang, Yishui; Zhang, Dongmei

doi:10.1007/978-3-030-21803-4_49

Cited by 7 publications

(8 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We remark that our work is different from (Qian et al, 2018;Ji et al, 2020), which are seemingly similar to ours. Their algorithms for non-monotone objectives are not SG-style ones but variants of the aforementioned random greedy algorithm.…”

Section: Related Worksupporting

confidence: 67%

Guarantees of Stochastic Greedy Algorithms for Non-monotone Submodular Maximization with Cardinality Constraint

Sakaue

2019

Preprint

View full text Add to dashboard Cite

Submodular maximization with a cardinality constraint can model various problems, and those problems are often very large in practice. For the case where objective functions are monotone, many fast approximation algorithms have been developed. The stochastic greedy algorithm (SG) is one such algorithm, which is widely used thanks to its simplicity, efficiency, and high empirical performance. However, its approximation guarantee has been proved only for monotone objective functions. When it comes to non-monotone objective functions, existing approximation algorithms are inefficient relative to the fast algorithms developed for the case of monotone objectives. In this paper, we prove that SG (with slight modification) can achieve almost 1/4-approximation guarantees in expectation in linear time even for non-monotone objective functions. Our result provides a constantfactor approximation algorithm with the fewest oracle queries for non-monotone submodular maximization with a cardinality constraint. Experiments confirm that (modified) SG can run far faster than and achieve as good objective values as existing algorithms.

show abstract

Section: Related Worksupporting

confidence: 67%

Guarantees of Stochastic Greedy Algorithms for Non-monotone Submodular Maximization with Cardinality Constraint

Sakaue

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In this section, we do some numerical experiments to compare the effectiveness of the two algorithms for Problem 1. In this article, we use the same instance in Bai and Bilmes, 22 whose ground set

𝒳

is partitioned into

𝒳_{1} = {x_{1}, \dots, x_{k}}

and

𝒳_{2} = 𝒳 ∖ 𝒳_{1}

. Function

f_{s u b}

and

g_{s u p}

are defined as follows.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…(ii) Function

g_{s u p}

is supermodular and non‐modular. When function Q is monotone, Bai and Bilmes 22 provide an approximation algorithm with ratio

false[1 - e^{- (1 - 𝒦^{g_{s u p}}) 𝒦_{f_{s u b}}} false] / 𝒦_{f_{s u b}}

, where

𝒦^{g_{s u p}}

is the supermodular curvature of the supermodular function.…”

Section: Introductionmentioning

confidence: 99%

“…Qian et al 12 provide a

α^{2} μ / (p + α^{2} μ)

‐approximation stochastic general greedy (SGG) algorithm, where

μ

is the expectation of random parameter generated in their algorithm and

α

is the submodularity ratio of the non‐submodular function. In the conference version of this article, Ji et al 23 provide that the SGG algorithm can achieve an approximation guarantee of

{(1 - 𝒦^{g_{s u p}})}^{2} μ / false(p + {(1 - 𝒦^{g_{s u p}})}^{2} μ false)

.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic greedy algorithms for maximizing constrained submodular + supermodular functions

et al. 2021

Concurrency and Computation

View full text Add to dashboard Cite

Summary The problem of maximizing the sum of a constrained submodular and a supermodular function has many applications such as social networks, machine learning, and artificial intelligence. In this article, we study the monotone submodular + supermodular maximization problem under a cardinality constraint and a p‐system constraint, respectively. For each problem, we provide a stochastic algorithm and prove the approximation ratio of each algorithm theoretically. Since the algorithm of the latter problem can also solve the former problem, we do some numerical experiments of the two algorithms to compare the time as well as the quality of the two algorithms in solving the former problem.

show abstract

“…In this case f (X) + f (Y ) ≤ f (X ∪ Y ). While there exists a robust set of literature dedicated to the theory of supermodular maximization, [11][12][13][14] these functions have rarely been applied to the analysis of biological data. The one example we are aware of uses a surrogate function to estimate the supermodular relationship between fragment ions in database searching.…”

Section: Introductionmentioning

confidence: 99%

MS1Connect: a mass spectrometry run similarity measure

Lin

Kaiser

Hutchison

et al. 2022

Preprint

View full text Add to dashboard Cite

Interpretation of newly acquired mass spectrometry data can be improved by identifying, from an online repos- itory, previous mass spectrometry runs that resemble the new data. However, this retrieval task requires comput- ing the similarity between an arbitrary pair of mass spectrometry runs. This is particularly challenging for runs acquired using different experimental protocols. We propose a method, MS1Connect, that calculates the simi- larity between a pair of runs by examining only the intact peptide (MS1) scans, and we show evidence that the MS1Connect score is accurate. Specifically, we show that MS1Connect outperforms several baseline methods on the task of predicting the species from which a given proteomics sample originated. In addition, we show that MS1Connect scores are highly correlated with similarities computed from fragment (MS2) scans, even though this data is not used by MS1Connect.

show abstract

Stochastic Greedy Algorithm Is Still Good: Maximizing Submodular + Supermodular Functions

Cited by 7 publications

References 14 publications

Guarantees of Stochastic Greedy Algorithms for Non-monotone Submodular Maximization with Cardinality Constraint

Guarantees of Stochastic Greedy Algorithms for Non-monotone Submodular Maximization with Cardinality Constraint

Stochastic greedy algorithms for maximizing constrained submodular + supermodular functions

MS1Connect: a mass spectrometry run similarity measure

Contact Info

Product

Resources

About