dataesr/scientific-paragraphs-categorization huggingface dataset:
5%. Applying penalized linear regression to 350,000 individuals of the UK Biobank, we predict height with a larger correlation than with the best prediction of C+T ($65% instead of $55%), further demonstrating its scalability and strong predictive power, even for highly polygenic traits. Moreover, using 150,000 individuals of the UK Biobank, we are able to predict breast cancer better than C+T, fitting PLR in a few minutes only. In conclusion, this paper demonstrates the feasibility and relevance of using penalized regression for PRS computation when large individual-level datasets are available, thanks to the efficient implementation available in our R package bigstatsr.
Package bigstatsr now includes an efficient algorithm with a new implementation for computing sparse linear and logistic regressions on huge datasets as large as the UK Biobank  (Bycroft et al. 2018). In this paper, we present a comprehensive comparative study of our implementation of penalized logistic regression (PLR), which we compare to the C+T method and the T-Trees algorithm, a derivation of random forests that has shown high predictive performance  (Botta et al. 2014). In this comparison, we do not include any LMM method, yet, L2-PLR should be very similar to LMM methods. Moreover, we do not include any SVM method because it is expected to give similar results to logistic regression  (Abraham et al. 2012). For C+T, we report results for a large grid of hyper-parameters. For PLR, the choice of hyper-parameters is included in the algorithm so that we report only one model for each simulation.
Genotype data We use real genotypes of European individuals from a casecontrol study for celiac disease  (Dubois et al. 2010). This dataset is presented in Supplemental Material, Table  S1. Details of quality control and imputation for this dataset are available in  Privé et al. (2018). For simulations presented later, we first restrict this dataset to controls from UK in order to remove the genetic structure induced by the celiac disease status and population structure. This filtering process results in a sample of 7100 individuals (see supplemental notebook "preprocessing"). We also use this dataset for real data application, in this case keeping all 15,155 individuals (4496 cases and 10,659 controls). Both datasets contain 281,122 SNPs.
For model "COMP," we simulate liability scores using additive, dominant and interaction-type effects (see Supplemental Materials). We implement three different simulation scenarios, summarized in Table  1. Scenario N°1 uses the whole dataset (all 22 autosomal chromosomes -281,122 SNPs) and a training set of size 6000. For each combination of the remaining parameters, results are based on 100 simulations except when comparing PLR with T-Trees, which relies on five simulations only because of a much higher computational burden of T-Trees as compared to other methods. Scenario N°2 consists of 100 simulations per combination of parameters on a dataset composed of chromosome six only  (18, 941 SNPs). Reducing the number of SNPs increases the polygenicity (the proportion of causal SNPs) of the simulated models.
Reducing the number of SNPs (p) is also equivalent to increasing the sample size (n) as predictive power increases as a function of n=p  (Dudbridge 2013; Vilhjálmsson et al. 2015). For this scenario, we use the additive model only, but continue to vary all other simulation parameters. Finally, scenario N°3 uses the whole dataset as in scenario N°1 while varying the size of the training set in order to assess how the sample size affects predictive performance of methods. A total of 100 simulations per combination of parameters are run using 300 causal SNPs randomly chosen on the genome.
To capture recessive and dominant effects on top of additive effects in PLR, we use simple feature engineering: we construct a separate dataset with three times as many variables as the initial one. For each SNP variable, we add two more variables coding for recessive and dominant effects: one variable is coded 1 if homozygous variant and 0 otherwise, and the other is coded 0 for homozygous referent and 1 otherwise. We then apply our PLR implementation to this dataset with three times as many variables as the initial one; we refer to this method as "PLR3" in the rest of the paper.
Data availability Supplemental Data include a PDF with two sections of methods, two tables and eight figures. Supplemental data also include six HTML R notebooks including all code and results used in this paper, for reproducibility purposes, and available at https://figshare. com/articles/code/7178750. Additional analyses of the UK Biobank are available as three R scripts at https://figshare. com/articles/code_UKB/7531559. Results of simulations are available at https://figshare. com/articles/results_zip/7126964. A tutorial on how to start with R packages bigstatsr and bigsnpr is available at https://privefl. github. io/bigsnpr/articles/demo. html. The two R packages are available on GitHub. Supplemental material available at https://doi. org/10. 25386/genetics. 7851470.
Simulations varying number of SNPs and sample size First, when reproducing simulations of scenario N°1 using chromosome six only (scenario N°2), the predictive performance of PLR always increase (Figure  2 ). There is a particularly large increase when simulating 3000 causal SNPs: AUC from PLR increases from 60% to nearly 80% for Gaussian effects and a disease heritability of 80%. On the contrary, when simulating only 30 or 300 causal SNPs with the corresponding dataset, AUC of "C+T-max" does not increase, and even decreases for a heritability of 80% (Figure  2 ). Second, when varying the training size (scenario N°3), we report an increase of AUC with a larger training size, with a faster increase of AUC for PLR as compared to "C+T-max" (Figure  3 ).
Joint estimation improves predictive performance In this comparative study, we present a computationally efficient implementation of PLR. This model can be used to build PRS based on very large individual-level SNP datasets such as the UK biobank  (Bycroft et al. 2018). In agreement with previous work  (Abraham et al. 2013) , we show that jointly estimating SNP effects has the potential to substantially improve predictive performance as compared to the standard C+T approach in which SNP effects are learned independently. PLR always outperforms the C+T method, except in some highly underpowered cases (AUC values always ,0. 6), and the benefits of using PLR are more pronounced with an increasing sample size or when causal SNPs are correlated with one another. When there are many small effects and a small sample size, PLR performs worse than (the best result for) C+T.
Efficient Penalized Regression for PRS For highly polygenic traits such as height and when using huge datasets such as the UK Biobank, the algorithm might iterate over. 100,000 variables, which is computationally demanding. On the contrary, for traits like celiac disease or breast cancer that are less polygenic, the number of variables included in the model is much smaller so that fitting is very fast (only 13 min for 150K women of the UK Biobank for breast cancer). Memory requirements are tightly linked to computation time. Indeed, variables are accessed in memory thanks to memory-mapping when they are used  (Privé et al. 2018 ). When there is not enough memory left, the operating system (OS) frees some memory for new incoming variables. Yet, if too many variables are used in the gradient descent, the OS would regularly swap memory between disk and RAM, severely slowing down computations.
A possible approach to reduce computational burden is to apply penalized regression on a subset of SNPs by prioritizing SNPs using univariate tests (GWAS computed from the same dataset). Yet, this strategy was shown to reduce predictive power  (Abraham et al. 2013; Lello et al. 2018 ), which we also confirm in this paper. Indeed, when using only the 100K most significantly associated SNPs, correlation between predicted and true heights is reduced from 0. 656/ 0. 657 to 0. 634/0. 643 within women/men. A key advantage of our implementation of PLR is that prior filtering of variables is no more required for computational feasibility, thanks to the use of sequential strong rules and early stopping criteria. Limitations Our approach has one major limitation: the main advantage of the C+T method is its direct applicability to summary statistics, allowing to leverage the largest GWAS results to date, even when individual cohort data cannot be merged because of practical or legal reasons.
Our implementation of PLR does not allow yet for the analysis of summary data, but this represents an important future direction. The current version is of particular interest for the analysis of modern individual-level datasets including hundreds of thousands of individuals. Finally, in this comparative study, we did not consider the problem of population structure  (Vilhjálmsson et al. 2015; Márquez-Luna et al. 2017; Martin et al. 2017) , and also did not consider nongenetic data such as environmental and clinical data  (Van Vliet et al. 2012; Dey et al. 2013).
Conclusions In this comparative study, we have presented a computationally efficient implementation of PLR that can be used to predict disease status based on genotypes. A similar penalized linear regression for quantitative traits is also available in R package bigstatsr. Our approach solves the dramatic memory and computational burdens faced by standard implementations, thus allowing for the analysis of large-scale datasets such as the UK biobank  (Bycroft et al. 2018). We also demonstrated in simulations and real datasets that our implementation of penalized regressions is highly effective over a broad range of disease architectures. It can be appropriate for predicting autoimmune diseases with a few strong effects (e. g. , celiac disease), as well as highly polygenic traits (e. g. , standing height) provided that sample size is not too small.
Acknowledgments We are grateful to  Félix Balazard  for useful discussions about  T-Trees , and to  Yaohui Zeng  for useful discussions about R package biglasso. We are grateful to the two anonymous reviewers who contributed to improving this paper. The authors acknowledge  LabEx Pervasive Systems and Algorithms (PERSYVAL)-Lab [Agence Nationale de Recherche (ANR) -11-LABX-0025-01 ] and  ANR  project  French Regional Origins in Genetics for Health (FROGH)  ( ANR-16-CE12-0033 ). The authors also acknowledge the  Grenoble Alpes Data Institute , which is supported by the  French National Research Agency  under the " Investissements d'avenir" program  ( ANR-15-IDEX-02 ). This research was conducted using the UK Biobank Resource under Application Number  25589.
In order to obtain good quality radar terrain images using an aerial-based synthetic aperture radar, a motion compensation procedure must be applied. This procedure can use a precise navigation system in order to determine the aircraft's position and velocity. A major challenge is to design a motion compensation procedure that can operate in real time, which is crucial to ensure convenient data for a human analyst. The article discusses a possibility of Inertial Measurement System (INS)/Global Positioning System (GPS) navigation system usage in such a radar imaging system. A Kalman filter algorithm designed for this system is described herein, and its modifications introduced by the authors allow the use of navigational data not aligned in time and captured with different frequencies. The presented navigation system was tested using measured data.
Echo signals corrections determined using INS allow one to reduce Sensors 2019,  19 , 3895 2 of 20 geometric distortions of images; however, they can be used only for short measuring sessions  [10] , which is not convenient in real-world applications, where it is important to have smooth and undistorted images during long-term observation missions. The allowed duration of a session varies from dozen to several tens of seconds depending on the class of the inertial unit used, and it is related to the process of INS error accumulation. The mentioned property of the INS prompted the authors to study and develop an integrated navigation system combining INS and Global Positioning System (GPS) to estimate the UAV position and velocity deviations. In the proposed system, the INS and the GPS data integration was implemented using a Kalman filter  [13] [14] [15] [16].
Initially, it was assumed that the power spectral densities of noises of the accelerometers and the gyroscopes were equal for all INS axes, and respective values were derived from the sensor manual [18]: S vN = S vE = S vD ≈ 1. 218•10 -11 rad 2 s S φN = S φE = S φD ≈ 1. 365•10 -6 m 2 s 3 (43) In the integrated navigation system, the estimation of the reference system errors (INS) is possible due to the GPS receiver, which provides a redundancy of the measurement data. The process of integration, however, requires bringing INS and GPS measurements to a common moment of time and a point in space, which is neglected in solutions presented in the MOCO literature  [1] [2] [3]  but is considered in the method presented in this paper. The data synchronization was achieved by interpolating results obtained at a higher frequency [from the inertial measurement unit (IMU)] to the time of data obtained at a lower frequency (GPS data).
In the MOCO using an integrated INS/GPS system, there is a common assumption that INS and GPS produce data at the same frequency, which simplifies the construction of the measurement vector ()  [1] [2] [3]. In our system, the GPS position was determined at 5 Hz, while GPS velocity was at 20 Hz. To use these measurements with their maximal frequencies, the measurement vector was divided into two vectors, a vector of position difference z  () and a vector of velocity difference   (): In the next step, the INS result at t k,GPS time was calculated using the interpolated IMU data, i. e. , f s1 is1 t k,GPS and ∆Θ 1. At the moment of GPS data time, the Kalman filter procedure presented in the following section was also executed. The INS solutions at the time t k,IMU were calculated using INS results from the artificial time t k,GPS , the measured specific force vector f s1 is1 t k,IMU from the time t k,IMU , and the remaining delta angle vector ∆Θ 2.
⎢ ⎡ φ -φ 0 ⎥ ⎤ ⎢ ⎢ ⎡ 0 𝑣 , , -𝑣 , , 0 ⎥ ⎥ ⎤ Due to different mounting points of the GPS antennas and the IMU onboard the UAV, the measured data initially referred to different points in space. where C n b converts a vector from the b-frame to the n-frame, and C e n converts a vector from the n-frame to the e-frame. In the MOCO using an integrated INS/GPS system, there is a common assumption that INS and GPS produce data at the same frequency, which simplifies the construction of the measurement vector z(k)  [1] [2] [3]. In our system, the GPS position was determined at 5 Hz, while GPS velocity was at 20 Hz. To use these measurements with their maximal frequencies, the measurement vector was divided into two vectors, a vector of position difference z r (k) and a vector of velocity difference z v (k): z(k) = z r (k) + z v (k) =                         ϕ INS b -ϕ GPS b 0 λ INS b -λ GPS b 0 h INS b -h GPS b 0                         +                           0 v n,INS is1,N -v n,GPS A1,N 0 v n,INS is1,E -v n,GPS A1,E 0 v n,INS is1,D -v n,GPS A1,D                           (49) where ϕ b is the latitude of the b-frame origin, λ b is its longitude, and h b is its altitude above the reference ellipsoid (the upper index describes the system used to determine the respective coordinate, INS or GPS), v n,INS is1,N v n,INS is1,E v n,INS is1,D is the velocity vector of the s-frame with reference to the i-frame expressed in the n-frame and measured by the INS, whereas v n,GPS A1,N v n,GPS A1,E v n,GPS A1,D is an analogous velocity vector measured by the GPS receiver.
This solution allowed us to use maximal sensor output update rates because-due to the independent treatment of velocity and position measurements-there was no need to limit the rate of velocity data to the rate of position data. The proposed approach, however, makes it impossible to use a classical Kalman filter algorithm, and therefore a sequential Kalman filter was used. In the considered INS/GPS system, the observation matrix H(k) is given as follows: H(k) =                             1 R+h INS b 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 (R+h INS b ) cos(ϕ INS b ) 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0                             (50) and the measurement errors covariance matrix R can be described using the formula: R = diag σ 2 ϕ σ 2 vN σ 2 λ σ 2 vE σ 2 h σ 2 vD ( 51 ) where σ 2 ϕ , σ 2 λ , σ 2 h are the variances of latitude, longitude, and altitude errors, and σ 2 vN , σ 2 vE , σ 2 vD are the variances of north, east, and down velocity errors of the GPS data.
Kalman Filter An algorithm of sequential Kalman filter used in the proposed system consisted of four stages: initialization, state prediction, measurement update, and reference system (INS) correction (Figure  2 ). In the initialization phase, the initial values of the system state vector elements were assumed to be zeroes, since the INS was initialized using the GPS data with zero-mean errors. Moreover, the initial value of the covariance matrix P( 0|0) was determined using the formula  [12, 13] : P( 0|0) = P(0) = diag σ 2 ϕ R + h INS b 2 σ 2 vN σ 2 φE σ 2 λ R + h INS b cos ϕ INS b 2 σ 2 vE σ 2 φN σ 2 h σ 2 vD σ 2 φD ( 52 ) where the elements P 11 , P 44 , P 77 are the GPS position errors variances expressed in m 2 units converted from rad 2 , P 22 , P 55 , P 88 are the GPS velocity errors variances, and P 33 , P 66 , P 99 represent the initial variances of INS orientation errors, which could be determined using the IMU documentation or a dedicated experiment.
Then, elements of the residual vector e, diagonal elements of the innovation covariance matrix R e , and columns of Kalman gains matrix K were determined in a loop  [11]. Based on them, the estimate of the state vector xi ( k|k) and the covariance matrix P i ( k|k) were calculated after each i-th inner loop iteration  [9]. After processing all the non-zero elements of the measurement vector, the correction phase ended, and the results obtained in the inner loop were assigned to the final measurement update results: x(k|k ) = x 6 (k|k ) and P(k|k ) = P 6 (k|k ). The last phase of the navigation data processing was the INS errors correction using a feedback loop. The vector of corrections c(k) was calculated using the following equation: c(k) = M(k) x( k|k) (53) where M is a matrix, which ensures appropriate translation from the n-frame to the e-frame: M(k) = diag 1 R+h INS b 1 1 1 (R+h INS b ) cos(ϕ INS b ) 1 1 -1 1 1 (54) The vector of corrections c(k) was subtracted from the current values of the navigation elements determined by the INS, and therefore the system errors were bounded, and the Kalman filter estimated only the residual errors (i.
The obtained results indicate that the integration of INS and GPS data allowed us to eliminate the effect of the INS system error growth, making the integrated system a potentially good source of navigational corrections for the MOCO procedure. In addition, the INS/GPS system update rate was greater than the rate obtained using the GPS alone. The output from the integrated navigation system was then loaded into the navigation correction algorithm, as presented in  [21]. Choosing appropriate values of the scaling coefficients is an experimental process, and sometimes achieving the target of 95. 5% samples within the ± 2 standard deviations range for each component of the e vector is impossible due to the limited number of scaling coefficients. However, the proposed set of coefficients was enough to ensure that all the residual vector values approximately had the desired statistical parameters, which is visible in Table  1.
In Figure  9  (with INS corrections), the north edge of the taxiway is indicated by a yellow dotted line. This edge deviates in the southern direction in relation to the analogous edge determined in the INS/GPS image (Figure  10 ), which is marked as a red line. For comparison purposes, the yellow line from Figure  9  was translated the Figure  10. In the INS corrected image, the erroneous deviation of the taxiway is visible in the final The obtained results indicate that the integration of INS and GPS data allowed us to eliminate the effect of the INS system error growth, making the integrated system a potentially good source of navigational corrections for the MOCO procedure. In addition, the INS/GPS system update rate was greater than the rate obtained using the GPS alone. The output from the integrated navigation system was then loaded into the navigation correction algorithm, as presented in  [21].
In the case of the INSbased image, this angle equaled 157°, whereas in the image obtained using INS/GPS system, the angle matched the true one and was 159°. This leads to the conclusion that the INS-based MOCO can be used only for time-limited measurement sessions. On the contrary, the INS/GPS MOCO procedure provides a better reduction of geometric distortions and can be used without these time limitations, thus it could be an attractive solution for SAR imaging MOCO. the taxiway was compared to the true one, which equals 159°. The reference angle was measured using an aerial image and image processing software, where three points located on the north edge of the taxiway were determined in order to produce two intersected lines. In the case of the INSbased image, this angle equaled 157°, whereas in the image obtained using INS/GPS system, the angle matched the true one and was 159°.
This leads to the conclusion that the INS-based MOCO can be used only for time-limited measurement sessions. On the contrary, the INS/GPS MOCO procedure provides a better reduction of geometric distortions and can be used without these time limitations, thus it could be an attractive solution for SAR imaging MOCO. the taxiway was compared to the true one, which equals 159°. The reference angle was measured using an aerial image and image processing software, where three points located on the north edge of the taxiway were determined in order to produce two intersected lines. In the case of the INSbased image, this angle equaled 157°, whereas in the image obtained using INS/GPS system, the angle matched the true one and was 159°. This leads to the conclusion that the INS-based MOCO can be used only for time-limited measurement sessions.
This language is indeed managed and understood by all the research community. Yet, works on data from other languages can also be found. Among the pre-selected publications, we can for instance mention: Chinese, addressed through the manually annotated dataset containing 540 breast radiology reports  [5] ; Italian, addressed through 5,432 non-annotated medical reports belonging to patients with rare arrhythmias and the manually curated hospital database  [6] ; French, addressed for detecting medical events as an epidemiological purpose  [7] , or through the clinical data warehouse for thousands of patients  [8] ; Japanese, addressed through the data set of 5,000 patient pharmacovigilance complaints  [9] ; and Korean, addressed through 30 rheumatic patients discharge summaries annotated with temporal information  [10].