dataesr/scientific-paragraphs-categorization huggingface dataset:
com/ISA- application, and tools/stato information needed or resulting from statistical methods SWO Software software tools, their Malone Ontology types, tasks, versions, et al. , 2014 provenance and associated data UBERON Uberon multi- An integrated cross- Mungall species species anatomy, et al. , 2012 anatomy covers animals and ontology bridges multiple species- specific ontologies UO Unit Ontology Metrical units for use Gkoutos in conjunction et al. , 2012 with PATO General scientific ontologies -Upper-level ontologies BFO Basic Standardizes upper- Arp et al. , 2015 Formal level structure of Ontology OBO ontologies COB Core Ontology Framework for https:// for Biology building ontologies github. com/ and in the life sciences OBOFoundry/ Biomedicine COB RO Relation Standardizes relations https:// Ontology in OBO oborel.
A score is given for each item, and perdimension scores are calculated by summing the scores for all associated items. Each dimension's score ranges from 0 to 8. The Lequesne index is calculated by summing the scores of the 3 dimensions, ranging from 0 to 24. Based on their Lequesne index, patients were classified into 6 classes: 0, no handicap; 1 to 4, mild handicap; 5 to 7, moderate handicap; 8 to 10, severe handicap; 11 to 13, very severe handicap; and $14, extremely severe handicap. The DN4 questionnaire was designed to screen for neuropathic pain components. Patients are considered likely to have neuropathic pain if their DN4 score is $4. 5  All these data were collected again during an end-of-study visit performed 3 months after its start. Data were then captured in an electronic case report form.
Acknowledgments This study was supported by a grant from  CEDR/Cercle d'Etude et de Traitement de la Douleur , a  French nonprofit  organization. The data analyses were performed by  Karine Andr é ,  Statitec. OASIS9© is protected by international copyright, with all rights reserved to  Dr Serge Perrot. Do not use without permission. For information on, or permission to use the OASIS9©, please contact Mapi Research Trust at https://eprovide. mapi-trust. org.
Working with real data, it is assumed that the measurement for each pixel is degraded by shape noise n s due to the finite average of galaxy intrinsic ellipticities in the bin. This noise is assumed to be white Gaussian, i. e. n s ∼ N(0, Σ n ), where Σ n is the noise covariance matrix of the shear map. Moreover, because of missing data due to survey measurement masks, we need to explicitly consider that there is no measurement in some pixel regions. In practice, we set a very high variance, such as 10 10 , for these pixels in the covariance matrix Σ n. More specific information on the strategy we follow to emulate the COSMOS shape catalog can be found in subsection 6. 3. Thus, the log-likelihood takes the following form: log p(γ|κ) = - 1 2 (γ -F * PFκ) † Σ -1 n (γ -F * PFκ) + constant, (9) where F and F * are respectively direct and inverse Fourier transform.
DeepMass While all the priors described above have closed-form expressions, it is also possible to design a mass-mapping method where the prior is defined implicitly. The first dark matter map reconstruction from weak lensing observational data using deep learning was shown in  Jeffrey et al. (2020b). DeepMass is a Convolutional Neural Network (CNN) trained on pairs of simulated pixelized shear and convergence maps. One can show that under some assumptions, a deep learning model can estimate the mean of the posterior distribution p(κ|γ). In a nutshell, the network needs to be trained to minimize the the mean-squared-error (MSE) of the output convergence κ and the training convergence and shear maps must be drawn respectrively from the prior p(κ) and likelihood distribution p(γ|κ). While the Wiener Filter assumes a Gaussian prior over the convergence, simulated training data for DeepMass are drawn from the "true" prior p(κ) and thus improve the accuracy of the reconstruction.
In order to correct this bias, every sample is considered as a Metropolis-Hastings (MH)  (Metropolis et al. 1953; Hastings 1970)  proposal and is accepted or rejected according to an acceptance probability. This acceptance probability is designed from the Hamiltonian transition and is also only score-dependent as we show in Appendix A. However, in most, if not all but the most trivial, cases sampling in high-dimension by Langevin or Hamiltonian dynamics is made very difficult by the fact that the distribution manifold is never Euclidean, meaning that assuming a diagonal noise covariance for LD, or diagonal momentum matrix for HMC, leads to extremely inefficient sampling. To take a concrete example, let us consider the case of distribution of handwritten digits in the MNIST dataset, and imagine a Langevin Dynamics chain exploring this distribution.
Simulations and data In this section we describe the simulated data we used to validate our method, designed to emulate the COSMOS field on which we aim to apply our algorithm. 2010 ). The redshifts for bright galaxies (i + < 25) are derived from the COSMOS-30 catalog  (Ilbert et al. 2009) , while the n(z) distribution for faint galaxies (i + > 25) is based on an extrapolation to fainter magnitudes as described in  Schrabback et al. (2010). ƭ.
Mock COSMOS data To act as our prior for the reconstruction of the COSMOS field, and for validation tests, we emulate from κTNG simulations mock COSMOS lensing catalogs. Using the binned galaxy distribution from the S10 catalog at the same 0. 29 arcmin resolution, we define a binary mask that captures the limits of the survey as well as missing data within the survey area due to bright stars or image artifacts that prevent the reliable measurement of galaxy shapes in some regions of the survey. This binning also yields noise variance maps, defined by the standard deviation of intrinsic galaxy ellipticities, rescaled by the number of galaxies per pixels N i : Σ (i,i) =      σ 2 e N i if N i > 0 10 10 otherwise ( 26 ) for each pixel i. Note that in empty pixels, we assume a large variance instead of infinity.
Posterior mean As for the Wiener filter, a way to validate the posterior distribution is to look at the posterior mean solution. In this section, we compare to the state of the art method to date, DeepMass, which is an other deep-learning based method. We trained DeepMass on examples drawn from our prior and likelihood model with the exact same U-net architecture as our denoiser. Using the convergence maps from our simulated dataset, we mocked noisy shear maps according to the likelihood in Equation  25. DeepMass   1  shows a quantitative comparison of the Kaiser-Squires, the Wiener Filter, MCALens, GLIMPSE, DeepMass and our mass-mapping method, based on two metrics: -The root mean square error (RMSE) defined as: RMSE κ, κ gt = 1 n n i=1 κi -κ gt i 2 , ( 27 ) where i is the pixel index, κ the mean-subtracted estimated convergence map, κ gt the mean-subtracted ground truth convergence map we aim to recover.
We used the code from the lenspack 2  repository to 6 × 10 14 9 × 10 14 Cluster Mass [M ] Fig. 9. Comparison of the probability of cluster detection given the input data and the detection method with respect to the SNR. The ratio of detection corresponds the the number of samples above 5σ over the total number of samples. The SNR was computed by dividing the maximum κ value of the NFW profile by the noise in the κ field. We considered clusters at redshift z h = 0. 5 and concentration c = 1 varying the halo mass. ƭ build the NFW shear map, that is summed to the mocked shear field from our test dataset. In this section, all the maps are filtered with an aperture mass filter with starlets functions  (Leonard et al. 2012). Starlets are well localized in real space, hence it is well very adapted to cluster detection  (Starck et al.
On large scales, the prior is mostly driven by the analytic power spectrum and thus easy on condition on cosmology, while on small scales, only the non-Gaussian residuals are captured by the neural network. This implies that the cosmology-dependent part of the model that needs to be learned on simulations is mostly on small scales. This makes it very likely that in the close future one could develop such a cosmology-dependent residual prior from suites of numerical simulations of smaller cosmological volume, would be an ideal dataset for this purpose. Another avenue for future work would be extending the method to the sphere, which is simply a matter of defining a U-net for instance using a Deep-Sphere  (Perraudin et al. 2019 ) approach for convolutions on a spherical domain.
Conclusion In this paper, we have presented a unified view of the massmapping problem as a Bayesian posterior estimation problem. Most existing methods either rely on simple priors (i. e. Gaussian prior for the Wiener filter) and/or only return a point estimate of the mass-mapping posterior. Instead, we have proposed a framework which allows us to 1) use numerical simulations to provide a full non-Gaussian prior on the convergence field; 2) sample from the full Bayesian posterior of the mass-mapping problem under this simulation-driven prior and a physical likelihood. The proposed approach, dubbed DLPosterior, relies first on using a Denoising Score Matching technique to learn a prior from high resolution hydrodynamical simulations (the κTNG dataset  (Osato et al. 2021 )), an approach that has proven to be extremely scalable and easy to implement.
In this respect, we also showed that the recovered posterior can be interpreted to quantify uncertainties, by establishing a close correlation between posterior convergence values and the SNR for clusters artificially introduced into a field. Finally, we have applied the validated method to the reconstruction of the HST/ACS COSMOS field based on the shape catalog from  Schrabback et al. (2010) , and produced the highest quality convergence map of this field to date. In the spirit of reproducible and reusable research, all software, scripts, and analysis notebooks are publicly available at: https://github. com/CosmoStat/jax-lensing Software: Astropy  (Robitaille et al. 2013; Price-Whelan et al. 2018) , IPython  (Perez & Granger 2007) , Jupyter  (Kluyver et al. 2016) , Matplotlib  (Hunter 2007) , Numpy  (Harris et al.
Acknowledgements. The authors are grateful  Zaccharie Ramzi  for fruitful discussions on inverse problems and very helpful discussions on neural network architecture. Benjamin Remy acknowledges support by the  Centre National d'Etudes Spatiales  and the  Université Paris-Saclay Doctoral Program in Artificial Intelligence (UDOPIA). KO is supported by  JSPS Research Fellowships for Young Scientists. This work was supported by  Grant-in-Aid for JSPS Fellows Grant Number   JP21J00011. This work used the  Extreme Science and Engineering Discovery Environment (XSEDE) , which is supported by  NSF  Grant No. ACI-1053575. This work was granted access to the  HPC resources of IDRIS  under the allocation 2021-AD011011554R1 made by  GENCI  ( Grand Equipement National de Calcul Intensif ). We thank  New Mexico State University (USA)  and  Instituto de Astrofisica de Andalucia CSIC (Spain)  for hosting the Skies & Universes site for cosmological simulation products.
Recent advances in high-throughput sequencing technologies have enabled the extraction of multiple features that depict patient samples at diverse and complementary molecular levels. The generation of such data has led to new challenges in computational biology regarding the integration of highdimensional and heterogeneous datasets that capture the interrelationships between multiple genes and their functions. Thanks to their versatility and ability to learn synthetic latent representations of complex data, deep learning methods offer promising perspectives for integrating multi-omics data. These methods have led to the conception of many original architectures that are primarily based on autoencoder models. However, due to the difficulty of the task, the integration strategy is fundamental to take full advantage of the sources' particularities without losing the global trends.
This paper presents a novel strategy to build a customizable autoencoder model that adapts to the dataset used in the case of high-dimensional multi-source integration. We will assess the impact of integration strategies on the latent representation and combine the best strategies to propose a new method, CustOmics (https://github. com/HakimBenkirane/CustOmics). We focus here on the integration of data from multiple omics sources and demonstrate the performance of the proposed method on test cases for several tasks such as classification and survival analysis.
This high diversity of data comes with two significant challenges. The first one is linked to the high-dimensionality of the data. Due to the genetic complexity of the human molecular profile, omics data generally suffers from the 'curse of dimensionality' resulting from the high number of features compared to the smaller number of samples  Misra et al. [2018]. This high-dimensional space often contains correlated features that result in high redundancy, reducing the prediction performance of algorithms  James et al. [2013]. The second issue lies in data heterogeneity: having its origins from different sources and expressing different phenomena in humans' biological system, omics data is very diverse  Bersanelli et al. [2016]. For example, transcriptomics and proteomics are normalized differently from other omics data and use different scaling before their analysis, leading to different ranges and data distributions.
Finally, omics data like metabolomics can also generate sparsity, as some variables can be below the detection limit and hence be assigned null values. To overcome those challenges and alleviate overfitting in prediction tasks, standard methods either manually select a small subset of molecular features based on domain knowledge  Bush et al. [2009]  or use dimensionality reduction techniques before downstream analysis. However, due to the high heterogeneity of the sources, those methods can overlook some genome-wide hidden patterns that justify the need for more flexible methods. In the past few years, multi-omics integration has been a very active research subject in health science and precision medicine  [Zitnik et al. , 2019]. Multiple statistical learning methods have been proposed from the desire to investigate various complex molecular systems behind cancer.
[2021]. Such methods can be divided into several categories including Bayesian methods  [Lock and Dunson, 2013 ] that use assumptions on data distribution and dependencies to build a statistical model, as well as network-based methods that rely on a network representation and can identify modules of the disease-associated mechanisms. The genes are represented by nodes, and edges represent the association between those genes  [Vaske et al. , 2010 , Bonnet et al. , 2014]. Other more specific methods have been explored, mainly for clustering. For example  Newman and Cooper [2010]  that presented AutoSOME which is a framework using the Self-organizing Map approach and couples it with a density equalizer; this equalizer reduces dimension and preserves the local topology of the gene expressions.
Another well-known multi-omics clustering method is iCluster  [Shen et al. , 2012] , which uses the same idea as NMF but without the non-negative constraint and allows more diversity in data distributions. With the rise of deep learning as the new state-of-the-art approach in many medical applications, several studies have explored the interest of these methods for multi-omics data integration. The primary use of these methods has been with autoencoders  Rumelhart et al. [1986] , notably by  Chaudhary et al. Chaudhary et al. [2017]  in the context of survival prediction. The framework OmiVAE  [Zhang et al. , 2019]  introduced new improvements for standard representation learning and OmiEmbed  [Zhang et al. , 2021]  for multitask learning. [Simidjievski et al. , 2019 ] also proposed multiple deep learning architectures based on variational frameworks for multiple tasks.
Huang et al. [Huang et al. , 2019]  developed a neural network architecture to integrate multi-omics data for survival by feeding the eigengene matrix instead of the raw data. Based on these methods, several application studies on specific cancer cases were presented, like  Hira et al. [2021]  that used the OmiVAE framework to conduct an in-depth study of the Ovarian Cancer's mechanisms. Tong et al. [2020]  also used standard autoencoders to explore multi-view learning in survival analysis for Breast Cancer. To our knowledge, no benchmarking study has explored and compared the different deep learning approaches and strategies for multi-omics data integration in the context of multitask learning. In this work, we discuss different strategies for the integration of high-dimensional multi-source data to learn lowdimensional latent representation from multi-omics datasets.
Moreover, we introduce a new architecture called CustOmics that combines the advantages of the different strategies and alleviates some of their limitations. We evaluate the impact of this new method on different test cases: we first apply it to a pan-cancer dataset and then study how it handles smaller datasets by evaluating it on specific cohorts. We also provide a new package to help bioinormaticians and computational biologists build deep learning architectures that allow an easy switch between the multiple strategies to adapt to specific use cases.
Representation Learning for Multi-Omics Integration Representation Learning is a field of statistical learning that aims to automatically discover relevant representations of the input data  [Bengio et al. , 2013]. In the field of multiple omics data integration, it can help synthesize the heterogeneous distributions into a common space, revealing the interaction between the different sources. From a biological point of view, each omics source represents a specific view of the processes involved. Therefore, the main goal behind integration is to uncover a broader view of the phenomenon of interest and to better understand the underlying processes. Each patient is characterized by K omics vectors (x k ) 1≤kK ∈ R M k with M k the number of features of the k-th source. The models presented in this paper aim at mapping the set of omics vectors to a vector z ∈ R m with m K k=1 M k , the latent representation.
Early Integration An early integration autoencoder is an autoencoder applied to the concatenated data from various sources. This type of architecture was reported in  Viaud et al. [2021]  as the SDAE (Standard Deep Autoencoder). The drawback of such an integration is that the resulting concatenation of every dataset results in a noisier and more complex high-dimensional matrix that makes the training more difficult. Moreover, this type of integration does not consider the specific data distribution of each source separately and thus leads the model to learn irrelevant patterns that can, in the worst case, mask the essential signals. For those reasons, even though this strategy has been introduced in the benchmark, it is not recommended in a real setting for complex multi-source datasets such as omics data.
Test Cases and Datasets In this study, we use datasets extracted from the Genomic Data Commons (GDC) pan-cancer multi-omics study  Grossman et al. [2016]. It is one of the most comprehensive datasets for multi-omics analysis, with high-dimensional omics data and corresponding phenotype data from The Cancer Genome Atlas (TCGA). In our experiments, we use three types of omics data, Copy Number Variations (CNV), RNA-Seq gene expressions, and DNA methylation. The CNV dataset comprises Gistic2 measurements on a total of 19,729 genes. The RNA-Seq expression dataset profile comprises around 60,484 identifiers referring to corresponding exons and measuring log2 transformed Fragments Per Kilobase of transcript per Million mapped reads (FPKM). Finally, the DNA methylation dataset was produced using the Infinium HumanMethylation450 BeadChip (450K) arrays with 485,578 probes in which beta values of probes indicate the methylation ratio of corresponding CpG sites.
Moreover, we also evaluate our method on six smaller cohorts from TCGA: Bladder Urothelial Carcinoma (BLCA, n=437), Breast Invasive Carcinoma (BRCA, n=1022), Lung Adenocarcinoma (LUAD, n=498), Glioblastoma & Lower Grade Glioma (GBMLGG, n=515) and Uterine Corpus Endometrial Carcinoma (UCEC, n=538). We will perform in this study 4 different evaluations on 4 test cases for clasification and survival. The first task in our set of experiments is classifying the different tumor types in the pan-cancer study. The classification performance was measured using five metrics: Accuracy, Macro-averaged F1 score, precision, recall, and ROC-AUC  Yang et al. [2021]. We also perform a second classification task to validate our findings on a smaller dataset and test the robustness of our method. This task aims at performing a tumor subtype classification based on the PAM50 classification (IlluminlA, ILluminalB, Basal, and HER2), we use the same setup as the pan-cancer case.
The third test case will be a survival study of the Pancancer dataset. Finally, the fourth test case will be about evaluating the survival performances on the 5 datasets presented earlier. For all those test cases, We compare the CustOmics model to several reference methods for multi-omics integration: first with a combination of dimensionality reduction methods, Multiple Factor Analysis (MFA), Uniform Manifold Approximation and Projection (UMAP) and non-negative matrix factorization (NMF), and also with different deep learning methods corresponding to the various strategies described in the Methods section.
Data Preprocessing The data required some preprocessing before analysis. • For RNA gene expression profiles, 594 exons located on the Y chromosome were removed, along with 1,904 ones with zero expression and 248 with missing values. • For DNA methylation data, the same strategy as with gene expression profiles was used, in addition to removing probes that cannot be mapped to the human reference genome. It leaves us with 438,831 CpG sites. Afterward, we intersected each combination of omics data in order to retrieve the maximum number of samples for each test case. We then identified and removed features with missing/consistently zero/NA values for other omic files. Finally, for non-normalized datasets such as CNVs and RNA-Seq data, we applied a min-max normalization to ensure that each omic source was scaled identically and thus would have the same importance during integration.
Implementation Details The CustOmics framework is based on the Pytorch deep-learning library. It can be applied to any combination of high-dimensional datasets and incorporates different integration strategies depending on the type of data and task to perform. As done in Zhang et al. Zhang et al. [2021] , DNA methylation data can be divided into 23 separate blocks, each feeding a hidden layer corresponding to a chromosome to avoid overfitting and save GPU memory. The whole architecture is built using fully-connected blocks. We use a batch normalization technique in each layer composing the neural network to address the internal covariate shift problemIoffe and Szegedy  [2015]. Also, to avoid overfitting problems, we use dropout  Srivastava et al. [2014] ; its rate is considered a hyperparameter.
The input dataset was randomly split into training, validation, and testing set (60-20-20%) by using a stratified 5-fold cross-validation so that the proportion of samples in each tumor type between the different sets is preserved in all the folds. We perform Bayesian optimization  Snoek et al. [2012]  using the validation set to find our model's best possible combination of hyperparameters. All models were trained using an Nvidia Tesla V100S with 32 GB memory.