dataesr/scientific-paragraphs-categorization huggingface dataset:
The Jarque-Bera test also indicated that hypothesizing the four data to be normally distributed can be rejected with a very low significance level. Due to these properties, the normal distribution would be an inappropriate model for calculating the daily VaR-as mentioned in the introduction. We thus rather envisage a nonparametric asymmetric approach based on kernel estimation of the CDF. However, as previously mentioned, estimating the VaR using a kernel based approach can be highly biased, since the choice of the kernel has an important impact on assessing the VaR estimate at a given probability level. In this section, we propose to gauge this impact by estimating the VaR at a several probability levels with different types of kernels, whose bandwidths have been adapted to the available datasets.
Nonparametric Estimate of the VaR: Comparing Summative and Maxitive Approaches In this experiment, we have considered estimating the VaR for low probability levels-namely at levels lower than 0. 1-for each of the four datasets. In the first experiment, we have focused on DJI and Nikkei225 indexes. The CDF(s) have been estimated by considering four of the most used summative kernels whose bandwidth have been adapted using the rule of thumb method: Epanechnikov, normal, biweight, and triweight (linear)-see  Silvermann (1986)  for their analytical expressions. Figure  4  illustrates the impact of the kernel choice in the VaR estimation. This impact is more marked with high volatility stocks (Nikkei225). For example, referring to Figure  4a , it can be seen that the VaR estimate based on the Epanechnikov kernel is absolutely greater than the one based on the normal kernel at the probability level of 1% while the opposite situation occurs at the probability level of 2.
025 -0. 027r t-1 + ε t σ 2 t = 0. 03 + 0. 0767ε 2 t-1 + 0. 906σ 2 t-1 -3 -2. 5 -2 -1. 5 -1 0 2 4 6 8 10 ×10 -2 Ω CDF Kernel Estimators 2 -1. 5 -1 (a) DJI (n = 200) -3 -2. 5 -2 -1. 5 -1 0 2 4 6 8 10 ×10 -2 Ω CDF Kernel Estimators 2. 5 -2 -1. 5 Ω (b) DJI (n = 650) -5 -4 -3 0 2 4 6 8 10 ×10 -2 Ω CDF Kernel Estimators -4 -3 Ω (c) Nikkei225 (n = 200) -5 -4 -3 -2 0 2 4 6 8 10 ×10 -2 Ω CDF Kernel Estimators -5 -4 Ω (d) Nikkei225 (n = 650) • Step 2: Generate 1000 simulated samples from each returns data using the coefficients obtained from the above fitted models. The main reason behind proposing GARCH models to simulate our real data is the dependence properties and the volatility phenomena of stock returns; see  Engle (1982). In a first step, we generate an i. i. d series, z t , by the random generator in MATLAB (R2010a) and another series σ t.
LFMM algorithms Consider an n × p response matrix, Y, recording data for n individuals. The individual data can correspond to genotypes, methylation profiles or gene expression levels measured from p genetic markers or probes. In addition, consider an n × d matrix, X, of individual observations, recording variables of primary interest such as phenotypes or exposure levels. Additional covariates including age and gender of individuals as well as observed confounders could be included in the X matrix. Association methods evaluate correlation between the response matrix and the primary variables, and commonly rely on regression models. Latent factor mixed models (LFMMs) are particular regression models defined by a combination of fixed and latent effects  [26, 13, 42]  as follows Y = XB T + W + E, ( 1 ) where W is a n × p latent matrix of rank K.
When X is a phenotypic trait and Y represents a biological measure such as a genotype, direct effect sizes can be estimated by switching the response and explanatory variables in the regression model (X = Y j β j ). In addition, tests based on generalized linear models or mixed linear models could be implemented according to similar principles. In the case of mixed linear models, the covariance matrix for random effects can be computed from the K estimated factors as C = UU T /n. The methods presented in this study and their extensions were implemented in the R package lfmm.
Results and Discussion Simulation study. In a series computer experiments, we simulated quantitative trait variables for a worldwide sample of 1,758 human individuals from the 1000 Genomes Project database  [1]. Our simulations considered various levels of confounding and numbers of causal variables in the data. For each simulation setting, five data sets were created, representing a total number of 125 data sets. As a baseline, we fitted simple linear regression models (LRM) without adjusting the data for potential confounding effects. This procedure was expected to result in a severe inflation of the test statistic. Six additional association methods were applied to the simulated data: PCA, two variants of SVA, CATE  [42]  and two variants of LFMM. Additionnally, we implemented an oracle method that performed association tests aware of the generating mechanism and confounders.
Rheumatoid arthritis Simulations Human GEAS. To detect genomic signatures of adaptation to climate in humans, we performed a GEAS using 5,397,214 SNPs for 1,409 individus from the 1,000 Genomes Project  [1] , and bioclimatic data from the WorldClim database  [12]  (Fig. S6 ). Nine confounders were estimated by LFMM2, mainly describing correlation between population structure and climate in the sample (Fig. 2A , Fig. S7 , Fig. S8 ). Four methods for confounder adjustement led to a list of 836 (1335) SNPs after pooling the list of candidates from the four methods (expected FDR = 1%-5%). A variant prediction analysis reported a large number of SNPs in intergenic and intronic regions, with an over-representation of genic regions (Fig. 2B ). Top hits represented genomic regions important for adaptation of humans to environmental conditions.
Compared to PCA approaches, LFMMs gained power by removing the part of genetic variation that could not be explained by the primary variables  [13]. In GWAS, LFMM extends tests performed by the EIGENSTRAT program by improving estimates of principal components  [32]. For EWAS, LFMMs extended surrogate variable analysis (SVA)  [26]  also achieving an increased power. In comparison with other algorithms, LFMM1 and LFMM2 have mathematical guarantees to provide globally optimal solutions of leastsquares estimation problems, and the proposed estimates could be shown to reach oracle asymptotical efficiency for large sample sizes  [42]. Like several factor methods, the computational speed of LFMM methods is mainly influenced by the algorithmic complexity of low rank approximation of large matrices.
The coefficient of proportionality was chosen so that the percentage of variance of X explained by the latent factors ranged between (0. 1, 1). The effect size matrix, B, was generated by setting a proportion of effect sizes to zero. Non-zero effect sizes were sampled according to a standard Gaussian distribution N (0, 1). The proportion of null effect sizes ranged between 80% and 99%. We eventually created a response matrix, Y, by simulating from the generative model of the latent factor model as follows Y = XB T + UV T + E. (11) In those simulations, K latent variables had the same variance as original PCs from the 1,000 Genomes Project data set, and we controlled the correlation between simulated phenotypes (primary variables) and confounders. To evaluate the capabilities of methods to identify true positives, we used the area under the precision-power curve (AUC) as a global estimate of power.
Precision is the proportion of true positives in a candidate list of positive tests. Power is the number of true positives divided by the number of true associations. To evaluate whether the methods have inflated number of false positives, we computed a genomic inflation factor using the median of squared z-scores divided by the median of the chi-squared distribution with one degree of freedom  [5]. Rheumatoid arthritis (RA) data set. We performed an EWAS using whole blood methylation data from a study of patients with rheumatoid arthritis  [28, 34, 45]. The RA data are publicly available and were downloaded from the GEO database (accession number GSE42861). For this study, beta-normalized methylation levels at 485,577 probed CpG sites were measured for 354 cases and 335 controls  [28]. Following [45], probed CpG sites having a methylation level lower than 0.
2 or greater than 0. 8 were filtered out. Then, the data were centered and scaled for a standard deviation of one. Since the cell composition of blood in RA patients typically differs from that in the general population, there is a risk for false discoveries that stem from unaccounted-for cell type heterogeneity  [34]. Age, gender and covariates such as tobacco consumption may also have significant effects on DNA methylation. To evaluate whether the methods presented here can correct confounding due to those factors, we did not include them as covariates in regression analyses. Seven EWAS methods were applied to the RA data set, including LRM, PCA, two variants of SVA, CATE and two variants of LFMM. Candidate lists of CpG sites were controlled for a false discovey rate of 1% after recalibration of the test significance values, and compared to the candidates obtained with a reference-based method and controlling for age, gender and smocking status.
FDR control was implemented through the qvalue function of the R program  [38]. Celiac disease (CD) data set. We performed a GWAS using SNPs from a study of patients with celiac disease  [8]. The CD data were downloaded from the Wellcome Trust Case Control Consortium https:// www. wtccc. org. uk/. For this study, SNP genotypes were recorded at 485,577 loci for 4,496 cases and 10,659 controls. The genotype matrix was preprocessed so that SNPs with minor allele frequency lower than 5% and individuals with relatedness greater than 8% were removed from the matrix. We used the program BEAGLE to impute missing data in the genotype matrix  [4]. We performed LD pruning to retain SNPs with the highest frequency in windows of one hundred SNPs. The filtering steps were implemented in the PLINK software  [33] , and resulted in a subset of 80,275 SNPs.
Five GWAS methods were applied to the CD data set: LRM, PCA (EIGENSTRAT), CATE, and two LFMM estimation algorithms. For the last four methods, the confounders were identified based on the 80,275 pruned genotypes. The tests were performed on the full set of imputed genotypes, and the SNP positions were grouped into clumps of correlated SNPs, using the clumping algorithm implemented in PLINK. The significance value for a clump of SNPs was considered to be the lowest value among all positions. FDR control was applied on the clumped significance values using qvalue. Candidates resulting from the five analyses were compared to the GWAS catalog for known association with CD  [29]. Chromosome 6, which contained the strongest association signals with CD, was treated separately. For this chromosome, all methods performed equally well at detecting six SNPs from the HLA locus referenced in the GWAS catalog.
Gene-environment association study. We performed a GEAS using whole genome sequencing data and bioclimatic variables to detect genomic signatures of adaptation to climate in humans. The data are publicly available, and they were downloaded from the 1,000 Genomes Project phase 3  [1]  and from the WorldClim database  [12]. The genomic data included 84. 4 millions of genetic variants genotyped for 2,506 individuals from 26 world-wide human populations. Nineteen bioclimatic data were downloaded for each individual geographic location, considering capital cities of their country of origin. The bioclimatic data were summarized by projection on their first principal component axis. The genotype matrix was preprocessed so that SNPs with minor allele frequency lower than 5% and individuals with relatedness greater than 8% were removed from the matrix.
Admixed individuals from Afro-american and Afro-Caribbean populations were also removed from the data set. After those filtering steps, the response matrix contained 1,409 individus and 5,397,214 SNPs. We performed LD pruning to retain SNPs with the highest frequency in windows of one hundred SNPs, and identified a subset of 296,948 informative SNPs. Four GEAS methods were applied to the 1,000 Genomes Project data set: PCA (EIGENSTRAT), CATE, and two LFMM estimation algorithms. For all methods the latent factors were estimated from the pruned genotypes, and association tests were performed for all 5,397,214 loci. Candidates obtained from clumps with an expected FDR level of 1% were analyzed using the Variant Effect Predictor (VEP) program  [30]. Cross-validation and model choice. Choosing regularization parameters and the number of latent factors can be achieved by using cross-validation methods.
( 12 ) In this notation, the brackets indicate which subsets of rows and columns of a matrix were selected. A prediction error was computed as follows Error = 1 #I#J Y[I, J] -Û-J V-I [J, ] T -X[I, ] B-I [J, ] T F. (13) Parameters leading to the lowest prediction errors were retained for data analysis. Additional heuristics were used to determine the number of latent factors and the nuclear norm parameter for LFMM1 latent matrix estimates. For choosing the number of latent factors, K, we considered the matrix D λ defined in the statement of Theorem 1, and the Q unitary matrix obtained from the SVD of X. The number of latent factors, K, was estimated after a spectral analysis of the matrix D 0 Q T Y. We determined it by estimating the number of components in a PCA of the matrix D 0 Q T Y. In our experiments, we used the "elbow" method based on the scree-plot of PC eigenvalues.
Let (x t+1 ) be the sequence of values defined by the block-coordinate descent algorithm x t+1 i ∈ arg min χ∈Ai f (x t 1 ,. , x t i-1 , χ, x t i+1 ,. , x t m ) , i = 1,. , m. Then a limit point of (x t ) defines a global minimum of f. Accession codes. SNP genotypes used in our simulation analysis are publicly available and were downloaded from the 1000 Genome Project database. The RA data are publicly available and were downloaded from the GEO database (accession number GSE42861). The CD data are publicly available and were downloaded from the Welcome Trust Case Control Consortium database (agreement number 1248).
Material and Methods Sources of data. Laboratory-confirmed cases of influenza A(H7N9) virus infection in China were reported to the Chinese Centres for Disease Control and Prevention, and information on these cases was recorded in a comprehensive database including case demographics, medical history, history of potential exposures, and clinical outcomes. The case definitions and laboratory test assays have been described previously  10, 11. In this study, we focused on cities with larger numbers of laboratory-confirmed cases (≥5 urban cases), and distinct dates of live poultry market closures, that would permit joint analysis of human infection dynamics and the impact of live poultry market closures. We therefore selected three cities during the first epidemic wave in spring 2013, namely Shanghai, Nanjing and Hangzhou  3  , five cities during the second epidemic wave in winter and spring of 2013-14, namely Shenzhen, Guangzhou, Hangzhou, Foshan and Ningbo 2 , and four cities during the third waves in winter and spring 2014-15, namely Shenzhen, Suzhou, Xiamen and Shanghai.
Acknowledgements We thank staff members of the  Bureau of Disease Control and Prevention  and  Health Emergency Response Office of the National Health and Family Planning Commission  and provincial and local departments of health for providing assistance with administration and data collection; staff members at county-, prefecture-, and provincial-level Centers for Disease Control and Prevention in the provinces where human A(H7N9) cases occurred for providing assistance with field investigation, administration and data collection. The views expressed are those of the authors and do not necessarily represent the policy of the  Chinese Center for Disease Control and Prevention. This study was funded by grants from the  National Science Fund for Distinguished Young Scholars  ( 81525023 ), the  US National Institutes of Health (Comprehensive International Program for Research on AIDS  grant  U19 AI51915 ),  China CDC's Key Laboratory of Surveillance and Early-warning on Infectious Disease , the  Harvard Center for Communicable Disease Dynamics  from the  National Institute of General Medical Sciences  (grant no.
Joint Estimation Seasonality and trend estimation can be performed using, e. g. , general linear abstraction of seasonality (GLAS), widely used in econometrics  [4]. Existing software, e. g. , X-12-ARIMA, TRAMO-SEATS, and STAMP, is available for general purpose time series decomposition, but such programs do not provide the same kind of analysis as the decomposition we provide in the present paper. For instance, it is well known that ARMA estimation is based on a non-convex likelihood optimisation step for which no current method can be proved to provide a global optimiser. Singular spectrum analysis (SSA) is also widely used, and the steps of this algorithm are similar to those of PCA, but especially tailored for time series  [14]. Neither a parametric model nor stationarity are postulated for the method to work.
Specific heat Specific heat C of BP was measured between 2 K and 100 K using a relaxation method of the heat capacity option in a Quantum Design, PPMS instrument. A single-crystalline BP was used for the measurement. Our specific heat data agree well with the previous report  (12)  as shown in Fig. S3A. Below 5 K, the specific heat follows a T 3 behavior and is fitted to an expression C = βT 3 with β = 6. 7 × 10 -5 J/molK 4 , as expected from the Debye model (Fig. S3B ). The Debye temperature Θ D estimated from β is Θ D = 306 K, which is consistent with those obtained from the theoretical calculation  (13). The calculated specific heat based on the phonon dispersions from the first principles (Fig. 6A ) reasonably reproduces not only the T 3 dependence but also matches the magnitude of the measured specific heat within a margin of 25 percent as shown in the inset of Fig.
Exemplar areas of application include bioinformatics  (Olshen et al. , 2004; Futschik et al. , 2014) , ion channels  (Hotz et al. , 2013) , climate records  (Reeves et al. , 2007) , oceonagraphic data  (Killick et al. , 2010 (Killick et al. , , 2012) )  and finance  (Kim et al. , 2005). What has received less attention is the problem of distinguishing between changepoints and outliers. To give an example of the issue outliers can cause when attempting to detect changepoint, consider the problem of detecting changes in well-log data. An example of such data, taken originally from Ó  Ruanaidh and Fitzgerald (1996) , is shown in Figure  1. This data was collected from a probe being lowered into a bore-hole. As it is lowered the probe takes measurements of the rock that it is passing through. As the probe moves from one type of rock strata to another, there is an abrupt change in the measurements.
These are examples of what we are calling outliers. The real challenge with detecting the changes is to distinguish between actual changes and these outliers. Most existing methods for changepoint detection are unable to do so; hence the reason that most analysis of this data has used the "cleaned" data set in the top-left plot. For example in the bottom row of Figure  1  we show the results of estimating the changepoints based on minimising a square-error-loss criteria with a penalty for each detected changepoint. Whilst this method performs well when analysing the cleaned dataset, it is unable to distinguish between changes and outliers when analysing the real data. This lack of robustness for detecting a change in mean in the presence of outliers for many changepoint methods stems from explicit or implicit modelling assumptions of Gaussian noise.
This includes performing better than methods that pre-process the data in an attempt to remove outliers. By comparison our approach is easier to implement as it does not require any pre-processing steps. Finally we consider the problem of detecting tampering of wireless security devices. Results here show our method can reliably distinguish between actual tampering events and changes in the data caused by short-term environmental factors. Proofs of results are given in the Appendices in the supplementary material. Code implementing the new methods in this paper is available from https://github. com/guillemr/robust-fpop.
, 2015)  which enables simulation of realistic CN profiles by resampling real datasets for which the truth is known. A standard way to analyse such data is to use the smooth. CNA function of the well known DNAcopy package  (Bengtsson et al. , 2016). This function shrinks outliers towards the value of its neighbors. Once this is done one can run a preferred segmentation approach. As we will see below, this heuristic preprocessing procedure greatly improves changepoint detection. We want to compare such a two-stage approach to a simpler analysis where we analyse data using our penalised cost approach with the biweight loss. To assess the performance of our approach on DNA copy number data we used the jointseg package. We simulated profiles of length n = 4000 with 10 change-points with segments of at least 40 datapoints.
The package propose two real datasets, GSE11976 and GSE29172, to resample from. For both we considered four levels of difficulty corresponding to different tumor fractions: 0. 34, 0. 50, 0. 79 and 1 for GSE11976; and 0. 3, 0. 5, 0. 7 and 1 for GSE29172. We consider four approaches: FPOP (L2), FPOP after using smooth. CNA to remove outliers (Rout L2), robust binary segmentation (Cusum) and our biweight loss with a threshold value of 3. All approaches are implemented for a range of penalty values. For every simulated profile and each run of a method we computed the number of true positive (TP) and false positive (FP) change-points. For all true change-point we counted one TP if there is at least one change-point identified within a window of 15 data-points. We then computed the number of FPs as the number of predicted changes minus the number of TPs.
We then average, over 200 simulated profiles, the number of TPs and FPs per approach, penalty value and difficulty to recover ROC curves. Overall our robust biweight loss outperforms the L2 loss following outlier removal and the Cusum approach. For low tumor fractions (0. 3 and 0. 5 GSE29172 and 0. 34 GSE11976) the biweight loss is possibly slightly better than the Cusum approach. For a tumor fraction of 1 the biweight loss is slightly better than the L2 following outlier removal. In other cases it is clearly better. Results are shown for the two datasets and a tumor fraction of 0. 7 and 0. 79 in Figure  10. Results for other tumor fractions are provided in figures in Appendix E.
acknowledgements We thank the co-Editor in Chief,  Professor Franco Giannessi , for clarifications on the conceptual differences between Minty and Stampacchia Variational inequality problems, and some pointers to the relevant literature. P. Mertikopoulos was partially supported by the  French National Research Agency (ANR)  grant  ORACLESS  ( ANR-16-CE33-0004-01 ) and the  COST Action CA16228 "European Network for Game Theory " (GAMENET). The research of M. Staudigl is partially supported by the  COST Action CA16228 "European Network for Game Theory " (GAMENET).