Dataset Information

Inferring Mathematical Equations Using Crowdsourcing.

ABSTRACT: Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.

SUBMITTER: Wasik S

PROVIDER: S-EPMC4701001 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Publications

Inferring Mathematical Equations Using Crowdsourcing.

Wasik Szymon S Fratczak Filip F Krzyskow Jakub J Wulnikowski Jaroslaw J

PloS one 20151229 12

Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain ex ...[more]

PMID: 26713846

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Project description:BACKGROUND: The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging. RESULTS: To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions. CONCLUSIONS: The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Project description:Systematically evaluating scientific literature is a time consuming endeavor that requires hours of coding and rating. Here, we describe a method to distribute these tasks across a large group through online crowdsourcing. Using Amazon's Mechanical Turk, crowdsourced workers (microworkers) completed four groups of tasks to evaluate the question, "Do nutrition-obesity studies with conclusions concordant with popular opinion receive more attention in the scientific community than do those that are discordant?" 1) Microworkers who passed a qualification test (19% passed) evaluated abstracts to determine if they were about human studies investigating nutrition and obesity. Agreement between the first two raters' conclusions was moderate (??=?0.586), with consensus being reached in 96% of abstracts. 2) Microworkers iteratively synthesized free-text answers describing the studied foods into one coherent term. Approximately 84% of foods were agreed upon, with only 4 and 8% of ratings failing manual review in different steps. 3) Microworkers were asked to rate the perceived obesogenicity of the synthesized food terms. Over 99% of responses were complete and usable, and opinions of the microworkers qualitatively matched the authors' expert expectations (e.g., sugar-sweetened beverages were thought to cause obesity and fruits and vegetables were thought to prevent obesity). 4) Microworkers extracted citation counts for each paper through Google Scholar. Microworkers reached consensus or unanimous agreement for all successful searches. To answer the example question, data were aggregated and analyzed, and showed no significant association between popular opinion and attention the paper received as measured by Scimago Journal Rank and citation counts. Direct microworker costs totaled $221.75, (estimated cost at minimum wage: $312.61). We discuss important points to consider to ensure good quality control and appropriate pay for microworkers. With good reliability and low cost, crowdsourcing has potential to evaluate published literature in a cost-effective, quick, and reliable manner using existing, easily accessible resources.

Dataset Information

Inferring Mathematical Equations Using Crowdsourcing.

Publications

Inferring Mathematical Equations Using Crowdsourcing.

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