Optimal Semi-supervised Estimation and Inference for High-dimensional Linear Regression Article Swipe
There are many scenarios such as the electronic health records where the outcome is much more difficult to collect than the covariates. In this paper, we consider the linear regression problem with such a data structure under the high dimensionality. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation and inference of the regression parameters in linear models, especially in light of the fact that such linear models may be misspecified in data analysis. In particular, we address the following two important questions. (1) Can we use the labeled data as well as the unlabeled data to construct a semi-supervised estimator such that its convergence rate is faster than the supervised estimators? (2) Can we construct confidence intervals or hypothesis tests that are guaranteed to be more efficient or powerful than the supervised estimators? To address the first question, we establish the minimax lower bound for parameter estimation in the semi-supervised setting. We show that the upper bound from the supervised estimators that only use the labeled data cannot attain this lower bound. We close this gap by proposing a new semi-supervised estimator which attains the lower bound. To address the second question, based on our proposed semi-supervised estimator, we propose two additional estimators for semi-supervised inference, the efficient estimator and the safe estimator. The former is fully efficient if the unknown conditional mean function is estimated consistently, but may not be more efficient than the supervised approach otherwise. The latter usually does not aim to provide fully efficient inference, but is guaranteed to be no worse than the supervised approach, no matter whether the linear model is correctly specified or the conditional mean function is consistently estimated.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://export.arxiv.org/pdf/2011.14185
- OA Status
- green
- Cited By
- 4
- References
- 47
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3109964034
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W3109964034Canonical identifier for this work in OpenAlex
- Title
-
Optimal Semi-supervised Estimation and Inference for High-dimensional Linear RegressionWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2020Year of publication
- Publication date
-
2020-11-28Full publication date if available
- Authors
-
Siyi Deng, Yang Ning, Jiwei Zhao, Heping ZhangList of authors in order
- Landing page
-
https://export.arxiv.org/pdf/2011.14185Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://export.arxiv.org/pdf/2011.14185Direct OA link when available
- Concepts
-
Estimator, Minimax, Inference, Supervised learning, Computer science, Mathematics, Upper and lower bounds, Linear regression, Artificial intelligence, Machine learning, Mathematical optimization, Statistics, Artificial neural network, Mathematical analysisTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
4Total citation count in OpenAlex
- Citations by year (recent)
-
2023: 2, 2022: 1, 2021: 1Per-year citation counts (last 5 years)
- References (count)
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47Number of works referenced by this work
- Related works (count)
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.the | 6, 11, 20, 27, 37, 48, 56, 61, 71, 87, 96, 102, 118, 140, 145, 150, 158, 164, 168, 174, 194, 199, 216, 220, 229, 244, 267, 273, 280 |
| abstract_inverted_index.two | 89, 210 |
| abstract_inverted_index.use | 95, 173 |
| abstract_inverted_index.data | 34, 50, 81, 98, 104, 176 |
| abstract_inverted_index.does | 251 |
| abstract_inverted_index.fact | 72 |
| abstract_inverted_index.from | 167 |
| abstract_inverted_index.goal | 41 |
| abstract_inverted_index.high | 38 |
| abstract_inverted_index.many | 2 |
| abstract_inverted_index.mean | 232, 282 |
| abstract_inverted_index.more | 15, 135, 241 |
| abstract_inverted_index.much | 14 |
| abstract_inverted_index.only | 172 |
| abstract_inverted_index.rate | 114 |
| abstract_inverted_index.safe | 221 |
| abstract_inverted_index.show | 162 |
| abstract_inverted_index.such | 4, 32, 74, 110 |
| abstract_inverted_index.than | 19, 117, 139, 243, 266 |
| abstract_inverted_index.that | 73, 111, 130, 163, 171 |
| abstract_inverted_index.this | 23, 179, 184 |
| abstract_inverted_index.well | 100 |
| abstract_inverted_index.when | 45 |
| abstract_inverted_index.with | 31 |
| abstract_inverted_index.There | 0 |
| abstract_inverted_index.based | 202 |
| abstract_inverted_index.bound | 153, 166 |
| abstract_inverted_index.close | 183 |
| abstract_inverted_index.first | 146 |
| abstract_inverted_index.fully | 226, 256 |
| abstract_inverted_index.light | 69 |
| abstract_inverted_index.lower | 152, 180, 195 |
| abstract_inverted_index.model | 275 |
| abstract_inverted_index.tests | 129 |
| abstract_inverted_index.under | 36 |
| abstract_inverted_index.upper | 165 |
| abstract_inverted_index.where | 10 |
| abstract_inverted_index.which | 192 |
| abstract_inverted_index.worse | 265 |
| abstract_inverted_index.attain | 178 |
| abstract_inverted_index.bound. | 181, 196 |
| abstract_inverted_index.cannot | 177 |
| abstract_inverted_index.faster | 116 |
| abstract_inverted_index.former | 224 |
| abstract_inverted_index.health | 8 |
| abstract_inverted_index.latter | 249 |
| abstract_inverted_index.linear | 28, 65, 75, 274 |
| abstract_inverted_index.matter | 271 |
| abstract_inverted_index.models | 76 |
| abstract_inverted_index.paper, | 24 |
| abstract_inverted_index.second | 200 |
| abstract_inverted_index.address | 86, 144, 198 |
| abstract_inverted_index.attains | 193 |
| abstract_inverted_index.collect | 18 |
| abstract_inverted_index.improve | 55 |
| abstract_inverted_index.labeled | 97, 175 |
| abstract_inverted_index.minimax | 151 |
| abstract_inverted_index.models, | 66 |
| abstract_inverted_index.outcome | 12 |
| abstract_inverted_index.problem | 30 |
| abstract_inverted_index.propose | 209 |
| abstract_inverted_index.provide | 255 |
| abstract_inverted_index.records | 9 |
| abstract_inverted_index.unknown | 230 |
| abstract_inverted_index.usually | 250 |
| abstract_inverted_index.whether | 272 |
| abstract_inverted_index.approach | 246 |
| abstract_inverted_index.consider | 26 |
| abstract_inverted_index.function | 233, 283 |
| abstract_inverted_index.powerful | 138 |
| abstract_inverted_index.proposed | 205 |
| abstract_inverted_index.setting. | 160 |
| abstract_inverted_index.analysis. | 82 |
| abstract_inverted_index.approach, | 269 |
| abstract_inverted_index.construct | 106, 124 |
| abstract_inverted_index.correctly | 277 |
| abstract_inverted_index.difficult | 16 |
| abstract_inverted_index.efficient | 136, 217, 227, 242, 257 |
| abstract_inverted_index.establish | 149 |
| abstract_inverted_index.estimated | 235 |
| abstract_inverted_index.estimator | 109, 191, 218 |
| abstract_inverted_index.exploited | 53 |
| abstract_inverted_index.following | 88 |
| abstract_inverted_index.important | 90 |
| abstract_inverted_index.inference | 59 |
| abstract_inverted_index.intervals | 126 |
| abstract_inverted_index.parameter | 155 |
| abstract_inverted_index.proposing | 187 |
| abstract_inverted_index.question, | 147, 201 |
| abstract_inverted_index.scenarios | 3 |
| abstract_inverted_index.specified | 278 |
| abstract_inverted_index.structure | 35 |
| abstract_inverted_index.unlabeled | 49, 103 |
| abstract_inverted_index.additional | 211 |
| abstract_inverted_index.confidence | 125 |
| abstract_inverted_index.electronic | 7 |
| abstract_inverted_index.especially | 67 |
| abstract_inverted_index.estimated. | 286 |
| abstract_inverted_index.estimation | 57, 156 |
| abstract_inverted_index.estimator, | 207 |
| abstract_inverted_index.estimator. | 222 |
| abstract_inverted_index.estimators | 170, 212 |
| abstract_inverted_index.guaranteed | 132, 261 |
| abstract_inverted_index.hypothesis | 128 |
| abstract_inverted_index.inference, | 215, 258 |
| abstract_inverted_index.otherwise. | 247 |
| abstract_inverted_index.parameters | 63 |
| abstract_inverted_index.questions. | 91 |
| abstract_inverted_index.regression | 29, 62 |
| abstract_inverted_index.supervised | 119, 141, 169, 245, 268 |
| abstract_inverted_index.conditional | 231, 281 |
| abstract_inverted_index.convergence | 113 |
| abstract_inverted_index.covariates. | 21 |
| abstract_inverted_index.estimators? | 120, 142 |
| abstract_inverted_index.investigate | 44 |
| abstract_inverted_index.particular, | 84 |
| abstract_inverted_index.consistently | 285 |
| abstract_inverted_index.misspecified | 79 |
| abstract_inverted_index.consistently, | 236 |
| abstract_inverted_index.dimensionality. | 39 |
| abstract_inverted_index.semi-supervised | 108, 159, 190, 206, 214 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |