Extending and Improving Learned CountSketch Article Swipe
Simin Liu
,
Tianrui Liu
,
Ali Vakilian
,
Yulin Wan
,
David P. Woodruff
·
YOU?
·
· 2020
· Open Access
·
YOU?
·
· 2020
· Open Access
·
A sketching algorithm is a way to solve an optimization problem approximately and in a fraction of the usual time. We consider classical sketching algorithms which first compress data by multiplication with a random matrix. Our work improves and extends the paradigm, in which sketch matrices are optimized to yield better expected performance. This technique has only been used for a suboptimal variant of sketched low-rank decomposition (LRD). Our work extends the problem coverage to optimal sketched LRD, least-squares regression (LS), and $k$-means clustering. We improve sketch learning for all three problems and very significantly for LS and LRD: experimental performance increases by $12\%$ and $20\%$, respectively. (Interestingly, we can also prove that we get a strict improvement for LRD under certain conditions.) Finally, we design two sketching algorithm modifications that leverage the strong expected performance of learned sketches, provide worst-case performance guarantees, and have the same time complexity as classical sketching. We prove the worst-case property for each of the problems and their modified algorithms.
Related Topics
Concepts
Sketch
Leverage (statistics)
Computer science
Fraction (chemistry)
Cluster analysis
Matrix multiplication
Property (philosophy)
Algorithm
Mathematical optimization
Matrix (chemical analysis)
Theoretical computer science
Mathematics
Artificial intelligence
Materials science
Quantum mechanics
Philosophy
Composite material
Quantum
Epistemology
Organic chemistry
Physics
Chemistry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/abs/2007.09890v2
- OA Status
- green
- Cited By
- 2
- References
- 41
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3132394523
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W3132394523Canonical identifier for this work in OpenAlex
- Title
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Extending and Improving Learned CountSketchWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2020Year of publication
- Publication date
-
2020-07-20Full publication date if available
- Authors
-
Simin Liu, Tianrui Liu, Ali Vakilian, Yulin Wan, David P. WoodruffList of authors in order
- Landing page
-
https://arxiv.org/abs/2007.09890v2Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/abs/2007.09890v2Direct OA link when available
- Concepts
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Sketch, Leverage (statistics), Computer science, Fraction (chemistry), Cluster analysis, Matrix multiplication, Property (philosophy), Algorithm, Mathematical optimization, Matrix (chemical analysis), Theoretical computer science, Mathematics, Artificial intelligence, Materials science, Quantum mechanics, Philosophy, Composite material, Quantum, Epistemology, Organic chemistry, Physics, ChemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
-
2021: 2Per-year citation counts (last 5 years)
- References (count)
-
41Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.which | 25, 46 |
| abstract_inverted_index.yield | 52 |
| abstract_inverted_index. This | 56 |
| abstract_inverted_index.$12\%$ | 106 |
| abstract_inverted_index.(LRD). | 70 |
| abstract_inverted_index.better | 53 |
| abstract_inverted_index.design | 128 |
| abstract_inverted_index.random | 33 |
| abstract_inverted_index.sketch | 47, 89 |
| abstract_inverted_index.strict | 119 |
| abstract_inverted_index.strong | 136 |
| abstract_inverted_index.$20\%$, | 108 |
| abstract_inverted_index.certain | 124 |
| abstract_inverted_index.extends | 40, 73 |
| abstract_inverted_index.improve | 88 |
| abstract_inverted_index.learned | 140 |
| abstract_inverted_index.matrix. | 35 |
| abstract_inverted_index.optimal | 78 |
| abstract_inverted_index.problem | 10, 75 |
| abstract_inverted_index.provide | 142 |
| abstract_inverted_index.variant | 65 |
| abstract_inverted_index.Finally, | 126 |
| abstract_inverted_index.compress | 27 |
| abstract_inverted_index.consider | 21 |
| abstract_inverted_index.coverage | 76 |
| abstract_inverted_index.expected | 54, 137 |
| abstract_inverted_index.fraction | 15 |
| abstract_inverted_index.improves | 38 |
| abstract_inverted_index.learning | 90 |
| abstract_inverted_index.leverage | 134 |
| abstract_inverted_index.low-rank | 68 |
| abstract_inverted_index.matrices | 48 |
| abstract_inverted_index.modified | 167 |
| abstract_inverted_index.problems | 94, 164 |
| abstract_inverted_index.property | 159 |
| abstract_inverted_index.sketched | 67, 79 |
| abstract_inverted_index.$k$-means | 85 |
| abstract_inverted_index.algorithm | 2, 131 |
| abstract_inverted_index.classical | 22, 153 |
| abstract_inverted_index.increases | 104 |
| abstract_inverted_index.optimized | 50 |
| abstract_inverted_index.paradigm, | 44 |
| abstract_inverted_index.sketches, | 141 |
| abstract_inverted_index.sketching | 1, 23, 130 |
| abstract_inverted_index.technique | 57 |
| abstract_inverted_index.algorithms | 24 |
| abstract_inverted_index.complexity | 151 |
| abstract_inverted_index.regression | 82 |
| abstract_inverted_index.sketching. | 154 |
| abstract_inverted_index.suboptimal | 64 |
| abstract_inverted_index.worst-case | 143, 158 |
| abstract_inverted_index.algorithms. | 168 |
| abstract_inverted_index.clustering. | 86 |
| abstract_inverted_index.guarantees, | 145 |
| abstract_inverted_index.improvement | 120 |
| abstract_inverted_index.performance | 103, 138, 144 |
| abstract_inverted_index.conditions.) | 125 |
| abstract_inverted_index.experimental | 102 |
| abstract_inverted_index.optimization | 9 |
| abstract_inverted_index.performance. | 55 |
| abstract_inverted_index.approximately | 11 |
| abstract_inverted_index.decomposition | 69 |
| abstract_inverted_index.least-squares | 81 |
| abstract_inverted_index.modifications | 132 |
| abstract_inverted_index.respectively. | 109 |
| abstract_inverted_index.significantly | 97 |
| abstract_inverted_index.multiplication | 30 |
| abstract_inverted_index.(Interestingly, | 110 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |