The Empirical Variance of a Set of Fuzzy Intervals

To improve the generalization ability of neural networks, we propose a novel regularization method that regularizes the empirical risk using a penalty on the empirical variance of the features. Intuitively, our approach introduces confusion into feature extraction and prevents the models from learning features that may relate to specific training samples. According to our theoretical analysis, our method encourages models to generate closer feature distributions for the training set and unobservable true data and minimize the expected risk as well, which allows the model to adapt to new samples better. We provide a thorough empirical justification of our approach, and achieves a greater improvement than other regularization methods. The experimental results show the effectiveness of our method on multiple visual tasks, including classification (CIFAR100, ImageNet, fine-grained datasets) and semantic segmentation (Cityscapes).

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The Empirical Variance Estimator for Computer Aided Diagnosis: Lessons for Algorithm Validation

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2014 - Lecture Notes in Computer Science ◽

10.1007/978-3-319-10470-6_30 ◽

2014 ◽

pp. 236-243 ◽

Cited By ~ 1

Author(s):

Alex F. Mendelson ◽

Maria A. Zuluaga ◽

Lennart Thurfjell ◽

Brian F. Hutton ◽

Sébastien Ourselin

Keyword(s):

Computer Aided Diagnosis ◽

Variance Estimator ◽

Algorithm Validation ◽

Computer Aided ◽

Empirical Variance ◽

Aided Diagnosis

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Comparison of the local pivotal method and systematic sampling for national forest inventories

Forest Ecosystems ◽

10.1186/s40663-020-00266-9 ◽

2020 ◽

Vol 7 (1) ◽

Author(s):

Minna Räty ◽

Mikko Kuronen ◽

Mari Myllymäki ◽

Annika Kangas ◽

Kai Mäkisara ◽

...

Keyword(s):

Sampling Design ◽

Measurement Data ◽

Systematic Sampling ◽

National Forest ◽

Systematic Design ◽

Auxiliary Data ◽

Variance Estimators ◽

Forest Inventories ◽

National Forest Inventories ◽

Empirical Variance

Abstract Background The local pivotal method (LPM) utilizing auxiliary data in sample selection has recently been proposed as a sampling method for national forest inventories (NFIs). Its performance compared to simple random sampling (SRS) and LPM with geographical coordinates has produced promising results in simulation studies. In this simulation study we compared all these sampling methods to systematic sampling. The LPM samples were selected solely using the coordinates (LPMxy) or, in addition to that, auxiliary remote sensing-based forest variables (RS variables). We utilized field measurement data (NFI-field) and Multi-Source NFI (MS-NFI) maps as target data, and independent MS-NFI maps as auxiliary data. The designs were compared using relative efficiency (RE); a ratio of mean squared errors of the reference sampling design against the studied design. Applying a method in NFI also requires a proven estimator for the variance. Therefore, three different variance estimators were evaluated against the empirical variance of replications: 1) an estimator corresponding to SRS; 2) a Grafström-Schelin estimator repurposed for LPM; and 3) a Matérn estimator applied in the Finnish NFI for systematic sampling design. Results The LPMxy was nearly comparable with the systematic design for the most target variables. The REs of the LPM designs utilizing auxiliary data compared to the systematic design varied between 0.74–1.18, according to the studied target variable. The SRS estimator for variance was expectedly the most biased and conservative estimator. Similarly, the Grafström-Schelin estimator gave overestimates in the case of LPMxy. When the RS variables were utilized as auxiliary data, the Grafström-Schelin estimates tended to underestimate the empirical variance. In systematic sampling the Matérn and Grafström-Schelin estimators performed for practical purposes equally. Conclusions LPM optimized for a specific variable tended to be more efficient than systematic sampling, but all of the considered LPM designs were less efficient than the systematic sampling design for some target variables. The Grafström-Schelin estimator could be used as such with LPMxy or instead of the Matérn estimator in systematic sampling. Further studies of the variance estimators are needed if other auxiliary variables are to be used in LPM.

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Windows of Opportunity: Window Subseries Empirical Variance Estimators in International Relations

Political Analysis ◽

10.1093/pan/10.3.304 ◽

2002 ◽

Vol 10 (3) ◽

pp. 304-317 ◽

Cited By ~ 12

Author(s):

Patrick Heagerty ◽

Michael D. Ward ◽

Kristian Skrede Gleditsch

Keyword(s):

International Relations ◽

Statistical Model ◽

International Conflict ◽

Covariance Structure ◽

Covariance Structures ◽

Nonparametric Approach ◽

Variance Estimators ◽

Windows Of Opportunity ◽

Empirical Variance ◽

The Impact

We show that temporal, spatial, and dyadic dependencies among observations complicate the estimation of covariance structures in panel databases. Ignoring these dependencies results in covariance estimates that are often too small and inferences that may be more confident about empirical patterns than is justified by the data. In this article, we detail the development of a nonparametric approach, window subseries empirical variance estimators (WSEV), that can more fully capture the impact of these dependencies on the covariance structure. We illustrate this approach in a simulation as well as with a statistical model of international conflict similar to many applications in the international relations literature.

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Contractual Mix in Southern Agriculture since the Civil War: Facts, Hypotheses, and Tests

The Journal of Economic History ◽

10.1017/s0022050700027467 ◽

1982 ◽

Vol 42 (2) ◽

pp. 327-353 ◽

Cited By ~ 66

Author(s):

Lee J. Alston ◽

Robert Higgs

Keyword(s):

Civil War ◽

Agricultural Production ◽

Transactions Costs ◽

Contractual Arrangements ◽

Land Rental ◽

Wage Payment ◽

Property Owners ◽

Empirical Variance ◽

Tests Of Hypotheses ◽

Over Time

In the South after 1865, workers and property owners employed a variety of contracts—wage payment, crop sharing, and land rental—to bring together cooperating resources in agricultural production. The contractual mix varied over time and space, depending on the relative resource endowments of the contracting parties, the prevailing risk conditions, and the transactions costs of alternative contractual arrangements. To understand the contractual mix, certain empirical distinctions must be made, and the major hypotheses advanced to explain the mix must be seen as complementary rather than mutually exclusive. These hypotheses, however, differ in their demonstrated ability to account for the empirical variance. In addition to factual clarification and theoretical explication, the paper presents a new sample of plantation data and a new econometric procedure for performing more detailed and better controlled tests of hypotheses.

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