The Online Submodular Cover Problem

Gupta, Anupam; Levin, Roie

doi:10.1137/1.9781611975994.94

Cited by 19 publications

(24 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Submodularity ensures that a greedy algorithm achieves bounded approximation factor when maximized [20]. Submodular Mutual Information (SMI): Given a set of items S, T ⊆ V, the submodular mutual information (MI) [21,6] is defined as…”

Section: Submodular Mutual Information (Smi) Functionsmentioning

confidence: 99%

Targeted Subset Selection for Limited-data ASR Accent Adaptation

Kothyari¹,

Mekala²,

Iyer³

et al. 2021

Preprint

View full text Add to dashboard Cite

We study the task of personalizing ASR models to a target non-native speaker/accent while being constrained by a transcription budget on the duration of utterances selected from a large unlabelled corpus. We propose a subset selection approach using the recently proposed submodular mutual information functions, in which we identify a diverse set of utterances that match the target speaker/accent. This is specified through a few target utterances and achieved by modelling the relationship between the target subset and the selected subset using submodular mutual information functions. This method is applied at both the speaker and accent levels. We personalize the model by fine tuning it with utterances selected and transcribed from the unlabelled corpus. Our method is able to consistently identify utterances from the target speaker/accent using just speech features. We show that the targeted subset selection approach improves upon random sampling by as much as 2% to 5% (absolute) depending on the speaker and accent and is 2x to 4x more label-efficient compared to random sampling. We also compare with a skyline where we specifically pick from the target and our method generally outperforms the oracle in its selections. 1

show abstract

Section: Submodular Mutual Information (Smi) Functionsmentioning

confidence: 99%

Targeted Subset Selection for Limited-data ASR Accent Adaptation

Kothyari¹,

Mekala²,

Iyer³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Using this lower bound, we derive as a corollary a lower bound for the random order version of SubmodularCover defined in [GL20]. It is tempting to use the method of Theorem 3.1 to improve their competitive ratio of O(log n log(t • f (N )/f min )) in RO (we refer the reader to [GL20] for the definitions of these parameters). We show that removing a log from the bound is not possible in general.…”

Section: Lower Bounds For Extensionsmentioning

confidence: 99%

Random Order Set Cover is as Easy as Offline

Gupta¹,

Kehne²,

Levin³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We give a polynomial-time algorithm for OnlineSetCover with a competitive ratio of O(log mn) when the elements are revealed in random order, essentially matching the best possible offline bound of O(log n) and circumventing the Ω(log m log n) lower bound known in adversarial order. We also extend the result to solving pure covering IPs when constraints arrive in random order.The algorithm is a multiplicative-weights-based round-and-solve approach we call LearnOr-Cover. We maintain a coarse fractional solution that is neither feasible nor monotone increasing, but can nevertheless be rounded online to achieve the claimed guarantee (in the random order model). This gives a new offline algorithm for SetCover that performs a single pass through the elements, which may be of independent interest.

show abstract

“…The submodular mutual information and its conditional variant have been defined in a number of previous works [17,4,9,16].…”

Section: Submodular (Conditional) Mutual Informationmentioning

confidence: 99%

“…Similarly, [4] uses the concept of the multi-set total correlation [53] to study properties of families of deep submodular functions. Finally, [17] also study the submodular mutual information (which they call the Mutual Coverage). They study a few of its properties and use it in characterizing an LP relaxation to the online submodular cover problem.…”

Section: Introductionmentioning

confidence: 99%

Submodular Combinatorial Information Measures with Applications in Machine Learning

Iyer,

Khargonkar,

Bilmes

et al. 2020

Preprint

View full text Add to dashboard Cite

Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a set of random variables is submodular. In this paper, we study combinatorial information measures that generalize independence, (conditional) entropy, (conditional) mutual information, and total correlation defined over sets of (not necessarily random) variables. These measures strictly generalize the corresponding entropic measures since they are all parameterized via submodular functions that themselves strictly generalize entropy. Critically, we show that, unlike entropic mutual information in general, the submodular mutual information is actually submodular in one argument, holding the other fixed, for a large class of submodular functions whose third-order partial derivatives satisfy a non-negativity property. This turns out to include a number of practically useful cases such as the facility location and set-cover functions. We study specific instantiations of the submodular information measures on these, as well as the probabilistic coverage, graph-cut, and saturated coverage functions and see that they all have mathematically intuitive and practically useful expressions. Regarding applications, we connect the maximization of submodular (conditional) mutual information to problems such as mutual-informationbased, query-based, and privacy preserving summarization -and we connect optimizing the multi-set submodular mutual information to clustering and robust partitioning.

show abstract

The Online Submodular Cover Problem

Cited by 19 publications

References 0 publications

Targeted Subset Selection for Limited-data ASR Accent Adaptation

Targeted Subset Selection for Limited-data ASR Accent Adaptation

Random Order Set Cover is as Easy as Offline

Submodular Combinatorial Information Measures with Applications in Machine Learning

Contact Info

Product

Resources

About