Benign overfitting in linear regression Bartlett, Peter L.; Long, Philip M.; Lugosi, Gábor ...
Proceedings of the National Academy of Sciences - PNAS,
12/2020, Volume:
117, Issue:
48
Journal Article
Peer reviewed
Open access
The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. ...Motivated by this phenomenon, we consider when a perfect fit to training data in linear regression is compatible with accurate prediction. We give a characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. The characterization is in terms of two notions of the effective rank of the data covariance. It shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size. By studying examples of data covariance properties that this characterization shows are required for benign overfitting, we find an important role for finite-dimensional data: the accuracy of the minimum norm interpolating prediction rule approaches the best possible accuracy for a much narrower range of properties of the data distribution when the data lie in an infinite-dimensional space vs. when the data lie in a finite-dimensional space with dimension that grows faster than the sample size.
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Twitter is a free social networking and micro-blogging service that enables its millions of users to send and read each other's "tweets," or short, 140-character messages. The service has more than ...190 million registered users and processes about 55 million tweets per day. Useful information about news and geopolitical events lies embedded in the Twitter stream, which embodies, in the aggregate, Twitter users' perspectives and reactions to current events. By virtue of sheer volume, content embedded in the Twitter stream may be useful for tracking or even forecasting behavior if it can be extracted in an efficient manner. In this study, we examine the use of information embedded in the Twitter stream to (1) track rapidly-evolving public sentiment with respect to H1N1 or swine flu, and (2) track and measure actual disease activity. We also show that Twitter can be used as a measure of public interest or concern about health-related events. Our results show that estimates of influenza-like illness derived from Twitter chatter accurately track reported disease levels.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
The tumultuous political situation in Brazil carries risks for the environment in the most biologically diverse country in the world, home to the world's largest tropical forests and rivers. Among ...the threats is a proposed one-sentence constitutional amendment (PEC-65) that would revoke 40 years of progress in building a licensing system to evaluate and mitigate environmental impacts of development projects (1). Under PEC-65, the mere submission of an environmental impact assessment (EIA), regardless of its content, would allow any project to go unstoppably forward to completion. The scientific community contributed greatly to Brazil's environmental licensing system and now must redouble its efforts to communicate its importance.
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Jair Bolsonaro (Brazil’s new president) and “ruralists” (large landholders and their representatives) have initiated a series of measures that threaten Amazonia’s environment and traditional peoples, ...as well as global climate. These include weakening the country’s environmental agencies and forest code, granting amnesty to deforestation, approving harmful agrochemicals, reducing protected areas, and denying the existence of anthropogenic climate change. Both the measures themselves and the expectation of impunity they encourage have spurred increased deforestation, which contributes to climate change and to land conflicts with traditional peoples. Countries and companies that import Brazilian beef, soy and minerals are stimulating these impacts.
Host modulation therapy refers to a treatment concept in which drug therapies are used as an adjunct to conventional periodontal treatment to ameliorate destructive aspects of the host inflammatory ...response. This strategy is not new in the treatment of periodontitis. Previously, nonsteroidal anti‐inflammatory drugs have been investigated in this regard, with evidence of reductions in alveolar bone resorption when these drugs are used for prolonged periods of time. However, the risk of significant unwanted effects precludes the use of both nonselective nonsteroidal anti‐inflammatory drugs and the selective cyclooxygenase‐2 inhibitors as adjunctive treatments for periodontitis. Currently, the only available adjunctive host response modulator that is licensed for the treatment of periodontitis is subantimicrobial dose doxycycline, which functions as an inhibitor of matrix metalloproteinases. Although clinical benefits have been shown in carefully conducted randomized controlled trials, the efficacy of subantimicrobial dose doxycycline in routine clinical practice has yet to be determined. Anti‐cytokine therapies have been developed for use in the treatment of rheumatoid arthritis, the pathogenesis of which bears many similarities to that of periodontitis; however, the significant risk of unwanted effects (as well as cost and lack of human trials in the treatment of periodontal diseases) precludes the use of any of the currently available anti‐cytokine therapies in the treatment of periodontitis. The identification of pro‐resolving lipid mediators as well as small molecule biologicals that influence inflammatory responses offers the best potential, at the present time, for the development of novel host response modulators in periodontal therapy, but much research remains to be done to confirm safety and efficacy.
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This paper proposes a distributed estimation and control algorithm that enables a team of mobile robots to search for and track an unknown number of targets. These targets may be stationary or ...moving, and the number of targets may vary over time as targets enter and leave the area of interest. The robots are equipped with sensors that have a finite field of view and may experience false negative and false positive detections. The robots use a novel, distributed formulation of the Probability Hypothesis Density (PHD) filter, which accounts for the limitations of the sensors, to estimate the number of targets and the positions of the targets. The robots then use Lloyd’s algorithm, a distributed control algorithm that has been shown to be effective for coverage and search tasks, to drive their motion within the environment. We utilize the output of the PHD filter as the importance weighting function within Lloyd’s algorithm. This causes the robots to be drawn towards areas that are likely to contain targets. We demonstrate the efficacy of our proposed algorithm, including comparisons to a coverage-based controller with a uniform importance weighting function, through an extensive series of simulated experiments. These experiments show teams of 10–100 robots successfully tracking 10–50 targets in both 2D and 3D environments.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Protect Indigenous peoples from COVID-19 Ferrante, Lucas; Fearnside, Philip M
Science (American Association for the Advancement of Science),
04/2020, Volume:
368, Issue:
6488
Journal Article
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► We identify factors that cause method bias. ► We discuss the psychological mechanisms through which they produce their biasing effects. ► We propose procedural remedies to ...counterbalance or offset these effects.
There is a great deal of evidence that method bias influences item validities, item reliabilities, and the covariation between latent constructs. In this paper, we identify a series of factors that may cause method bias by undermining the capabilities of the respondent, making the task of responding accurately more difficult, decreasing the motivation to respond accurately, and making it easier for respondents to satisfice. In addition, we discuss the psychological mechanisms through which these factors produce their biasing effects and propose several procedural remedies that counterbalance or offset each of these specific effects. We hope that this discussion will help researchers anticipate when method bias is likely to be a problem and provide ideas about how to avoid it through the careful design of a study.
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CEKLJ, GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
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