dataesr/scientific-paragraphs-categorization huggingface dataset:
Density-Based Clustering BangA performs a density-based clustering on data buckets in a way similar to BANGclustering  [33]. BANG-clustering is a grid clustering approach that relies on a main memory kd-tree accommodated from the BANG file. It is a direct descendant from GRIDCLUS  [34] , itself based on the Grid file. The algorithm computes a density index for each block assigned to a data bucket, and it creates a dendrogram by merging neighbor blocks having the closest density indices. However, BANG-clustering as well as GRIDCLUS compute density indices for each block [X] by means of card([X]), the number of data points it contains, and V(X), the spatial volume of the enclosing region only. This approach does not leverage the non hyper-rectangular blocks built by the BANG file. Thus, we refine the previous proposal and define the spatial volume V([X]) of a BANG directory entry [X] as follows: V([X]) = ∏ 1≤i≤n e i X -∑ Y∈H X ∏ 1≤i≤n e i Y , (6) where X -H X Y is the block where the data points from [X] are located, and X and elements of H X are hyper-rectangular regions.
We purged all records with missing values and were left with a table containing 1 million tuples. We used the attributes Age, Zipcode and Education level as quasi-identifiers. The second data set was "Voter list" taken as is from the experiments conducted by Sweeney  [1]  in her seminal work on k-anonymization. It contains 54,803 records (tuples with missing values are already removed). We used Age, Zipcode and Salary as quasi-identifiers. For stress testing and to study the behavior of both the approaches for high dimensional data, we used a third data set named "Customer" that was synthetically generated using a data generator tool (Datanamic data generator:  [36] ). This data set contains 1 million tuples with 15 attributes and all of them are used as quasi-identifiers. To conduct the experiments in a real database environment, we first populated a PostgreSQL database with all three of the data sets.
For convenience and code efficiency, data has been normalized (see Section 3. 1) on the database level using advanced query facilities provided by PostgreSQL DBMS. We also used database statistics for query optimization. We applied R + -tree and BangA approaches on all the quasi-identifiers of Adults, Voter list and Customer data sets. In the R + -tree approach, the anonymization process is followed as in  [9]. The algorithms are developed in C++ and are tested on a system with 4GB RAM and a Windows 7 operating system (Microsoft Corporation, Redmond, WA, USA).
Performance Execution time of R + -tree and BangA was measured on Voter list, Adults and Customer data sets-thus from 50 K to 1 Million records. Block size and page size was set to five, in order to evaluate the performance of each algorithm under stress of very small bucket and fan-out values. Many runs with different settings have been done and results always confirm those presented here. In this experiment, we evaluated the BangA algorithm with dendrogram construction, against the brute R + -tree construction, i. e. , w/o leaf scan or cut extraction. Results are presented in Table  2. It shows a 50% lower time cost in favor of BangA compared to R + -tree for the Voter list data set, and the difference still increases for large data sets like Adults since it spends up to 36% less execution time for the public release computation.
For high dimensional data in Customer data set with 15 quasi-identifiers, BangA simply outperforms R + -tree based anonymization, as the latter is unable to cope with such high dimensional data. In order to make a verifiable comparison of both approaches, a set of 1 million tuples with seven quasi-identifier attributes was randomly sampled from the Customer data set (having 1 million tuples and 15 quasi-identifier attributes). With a slightly large number of quasi-identifiers, results in Table  2  indicate substantially lower time cost in favor of BangA compared to R + -tree. This shows that whatever the number of dimensions, BangA out performs its counterpart. We did not compare the efficiency of BangA with previous proposal such as Mondrian  [8] , since experiments in  [9]  have shown that R + -tree anonymization outperforms all of the previous algorithms.
Thus, these experiments validate the very good behavior of BangA regarding performance and scalability. Moreover, the second storage structure of the BANG file guarantee that it could handle very large data sets without any drop in the performance. The second result is as follows: we could argue that bottom-up spatial indexing is not systematically more efficient than top-down approach as conjectured in  [9]. This result is given by our own experiments comparing in the same running environment R + -tree approach (bottom-up) with BangA (top-down). Following the usual analysis on spatial access methods, we claim that the performance is mainly dependent from the splitting strategy. In BangA, we use regular decomposition following the grid, whereas the original R + -tree grows by means of a quadratic procedure comparing pairwise distances of elements in an overflowed bucket.
Quality of the Public Release Since the k-anonymity problem relies on the trade-off between privacy of individuals and utility of the public release, we computed and compared quality of the public releases built, respectively, with BangA and with the R + -tree, by means of several measures of information loss. The main idea is to evaluate the extent to which the data set has been distorted when generalizing records. We adopted generic quality measures, i. e. , measures that do depend on the application domain or on a specific usage of the public release. Then, we first followed the experimental protocol described by Iwuchukwu et al. [9] , with three different measures: discernibility penalty [3], KL-divergence  [4]  and the certainty metric proposed in  [5]. We conducted experiments on the Adults and Customer data sets.
Results for Adults data set are presented on Figures 9-11 for certainty metric, discernibility penalty and KL-divergence, respectively. Roughly speaking, all of the experiments show that BangA provides higher quality public releases than the R + -tree since BangA curves systematically remain lower than those from the R + -tree and quality measures are actually "penalty" measures. Next, curves are all increasing since the higher the k parameter, the lower the overall quality. We could notice that the gap between the R + -tree and BangA increases with k in the discernibility penalty. Here, we face the usefulness of the density-based clustering of BangA since merging elementary blocks give birth to very accurate equivalence classes even for higher k values, compared to the R + -tree. To focus on specific values rather than analysis trends in large scale curves, we consider numbers for k = 100 since it represents a descent rate of 0.
We used the randomly sampled Customer data set containing 1 million tuples and seven quasi-identifier attributes for these experiments. The point queries are relatively easier to handle. The above mentioned seven-dimensional query is dynamically created by using the upper and lower bounds on the range of each participating attribute. These bounds are defined as follows: A COUNT query Q on the anonymized data set R * fetches the count of tuples matching the query Q. For point query, the result set contains those tuples with the lowest value on the region level. A window query Q returns a count of the records in R * that matches Q. A tuple t ∈ R * is said to be a matching tuple for Q if the region spanned by t and the query Q have a non-null intersection i. e. , t must intersect Q on all quasi-identifier attributes.
We conducted the experiments using query dimensionality parameter. The query error rate is calculated using Equation  (9). We considered 300 randomly generated queries for conducting these experiments and calculated the average relative error. For these experiments, we anonymized the Customer data set on all seven quasi-identifiers and varied the query dimensionality parameter i. e. , the number of QI attributes in query predicate. The results for point and window queries with varying query dimensionality are shown in Figures  12  and 13. As the query dimension increases, average relative error rate decreases. Thus, the anonymized data performs better for queries with a larger query dimensions. BangA tends to be more stable than an R + based approach showing less relative error rate for any query dimension.
This is often necessary for stability if the physical timescale of, e. g. , vegetation, soil, snow, or ice surface is short compared to the model time step. The ideal solution for stability is to combine the boundary layer heat diffusion and, e. g. , the snow or ice layer diffusion in a single implicit solver. This has been demonstrated in a series of papers describing developments in the ORCHIDEE model  (Polcher et al. , 1998; Ryder et al. , 2016; Wang et al. , 2013). The same method was used by  Schulz et al. (2001)  in the Hamburg model. However, not all models do have sufficient modularity of the code to make it practical. The complication of processes like phase changes and water percolation also require implementation of conserved variables to support full implicitness  (Wang et al. , 2013).
Acknowledgements. The authors would like to thank  Alex West  and  Jan Polcher  for their comprehensive reviews and for suggesting numerous improvements to the manuscript. F. Lemarié  acknowledges the support of the  French National Research Agency (ANR)  through contract  ANR-16-CE01-0007. We also thank  Erland Källén  and  Nils Wedi  for careful reading of an early version of the manuscript. Edited by: S. Valcke Reviewed by:  A. E. West ,  F. Lemarié 4  , and  J. Polcher.
Learning causal networks from large-scale genomic data remains challenging in absence of time series or controlled perturbation experiments. We report an information-theoretic method which learns a large class of causal or non-causal graphical models from purely observational data, while including the effects of unobserved latent variables, commonly found in many genomic datasets. Starting from a complete graph, the method iteratively removes dispensable edges, by uncovering significant information contributions from indirect paths, and assesses edge-specific confidences from randomization of available data. The remaining edges are then oriented based on the signature of causality in observational data. The approach and associated algorithm, miic, outperform earlier methods on a broad range of benchmark networks.
Thus, they cannot uncover nor rule out causality in observational data. By contrast, constraint-based methods  [7] [8] [9] [10] , which identify structural constraints corresponding to all dispensable edges in a graph, can in principle uncover causality from purely observational data. Advanced constraint-based methods  [9, 10]  reconstruct Markov equivalent models of a broad class of "ancestral graphs"  [11] , that include undirected (-), directed (!) and possibly bidirected ($) edges originating from latent common causes, L, unobserved in the available data (i. e. ⇠ L ⇢). However, constraint-based methods are often not robust on small datasets and have algorithmic complexity issues when including unobserved latent variables  [9] [10] [11] [12]. Yet, latent variables are commonly found in many real applications, as in the case of an unobserved transcription factor TF co-regulating two co-expressed genes, i.
The method builds on an earlier information-theoretic approach  [14] , in order to i) include latent variables, a notorious conceptual and algorithmic difficulty in causal network reconstruction  [9] [10] [11] [12] [13] , and ii) provide an edge specific confidence assessment of retained edges, which lacks in traditional constraint-based methods. Both aspects are important in practice to reconstruct robust networks from actual biological data. The approach is applied to reconstruct causal networks from a variety of genomic datasets at different biological size and time scales, from single cells to organisms and entire phyla.
Beyond v-structures, colliders may also be found in series along a collider path, as in X ! Z $ Y W, Fig 1B & 1C , where the bidirected edge, Z $ Y, indicates that Z is not a cause of Y nor Y a cause of Z. It implies that the correlation between Z and Y is due to at least one latent common cause, L, unobserved in the available dataset, Z ⇠ L ⇢ Y, as outlined above. Hence, statistical dependencies and independencies in purely observational data can, in principle, provide structural constraints for network reconstruction as well as information on causal relationships across observed and possibly unobserved latent variables. These results underline the wealth of information which cannot be captured from two-point correlations only.
Conditional independence, I(X; Y|{A i }) = 0, then implies that {A i } is a 'separation set' which intercepts all indirect paths contributing to the total mutual information, i. e. I(X; Y) = I(X; Y; {A i }). In practice, however, conditional mutual information cannot be exactly zero for finite datasets but the probability that the XY edge should be removed can be estimated from the available data as, P XY * exp(-NI(X; Y|{A i })), up to some normalization constant, where N is the number of independent samples (S1 File). The undirected network 'skeleton', resulting from the removal of all dispensable edges, is then partially directed by orienting all v-structures (Fig 1D  , step 2 ), based on the signature of causality, outlined above, and propagating these orientations on The main computational complexity of constraint-based methods is to uncover a valid combination of contributing nodes {A i } for each dispensable edge XY.
In absence of latent variables, the combinatorial search can be restricted to the sole neighbors of X or Y, which are sufficient to intercept all information contributions from indirect paths  [7, 8]. However, this efficient algorithm cannot be used in the presence of latent variables, as collider paths may require to extend the combinatorial search for conditioning set {A i } to non-adjacent variables of X and Y  [9] , as illustrated in Fig 1C. In practice, this intrinsic difficulty stemming from latent variables has been addressed through more complex algorithmic approaches, such as the FCI algorithm  [9]  and its more recent approximate variant, RFCI  [10]. Beyond algorithmic complexity issues, traditional constraint-based methods are also known to be highly sensitive to sampling noise inherent to finite datasets and are not robust on typical datasets of interest (e.
Algorithmic performance on causal and non-causal benchmark datasets We have assessed the performance of miic on a broad range of causal and non-causal benchmark networks from real-life as well as simulated datasets from P ' 30 up to 500 variables and N = 10 up to 50,000 independent samples (Materials and methods). The causal benchmark networks, which include an increasing fraction (0% to 20%) of hidden latent variables, are derived using partially observed Bayesian networks, that is, considering some variables as hidden. These unobserved variables are usually present in many real applications and cannot be ignored in practice, as they actually impact the causal relationships between observed variables, as illustrated in Fig 1B  -1D. The non-causal benchmark datasets have been obtained from Monte Carlo sampling of Ising-like interacting networks sharing approximately the same twopoint direct correlations with real-life benchmark causal networks but lacking causality.
Monte Carlo sampling leads, however, to significant correlations between successive samples, which needs to be taken into account through an effective number of independent samples (Materials and methods). Reconstructed causal networks have been compared to partial ancestral graphs (PAGs)  [23] , which are the representatives of the Markov equivalent class of all ancestral graphs consistent with the conditional independences in the available data. In practice, benchmark PAGs have been derived by hiding some variables in benchmark directed acyclic graphs (DAG) using the dag2pag function of the pcalg package with slight modifications  [25, 26]. The alternative inference methods used for comparison with miic are the FCI algorithm  [9]  and its recent approximate variant RFCI  [10]  implemented in the pcalg package  [25, 26].
The results obtained with FCI and RFCI are in fact very similar and we only present here comparisons with the more recent RFCI algorithm  [10]. RFCI's results are shown for an adjustable significance level α = 0. 01 and using the stable implementation of the skeleton learning algorithm, as well as the majority rule for the orientation and propagation steps  [27] , which give overall the best results. The results have been evaluated in terms of running time, as well as, Precision (or positive predictive value), Recall or Sensitivity (true positive rate), and F-score, which is the harmonic mean of Precision and Recall (Materials and methods). Precision, Recall and Fscore have been derived for the undirected skeleton of the networks (dashed lines in   [12]. Furthermore, no causality is predicted by miic for non causal datasets, even from small effective numbers of independent samples (Materials and methods and S6 and S7 Figs).
Edge confidence assessments This information-theoretic method and its algorithmic implementation (S1 Software) are very general and can be applied to a wide range of datasets, provided a sufficient number of independent samples is available. We report here the results obtained with genomic datasets spanning a broad range of biological size and time scales from single cells and tissues to organisms and entire phyla. In addition to including latent causal variables, we have also assessed the confidence of predicted edges with an edge specific confidence ratio C XY ¼ P XY =hP rand XY i, where P XY is the probability to remove the XY edge, introduced above, and hP rand XY i the average of the same probability after randomizing the datasets for each variable (see Materials and methods, and S1 File section 2.
All network reconstructions presented in Figs 2, 3 & 4 have been obtained with an edge specific confidence C XY < 10 -3 , while network skeletons obtained before edge filtering are displayed in S11, S14 and S15 Figs. The general three-step reconstruction scheme of miic (i. e. Step 1-graph skeleton, Step 2edge filtering, Step 3-edge orientation) is also sensitive to the fine tuning of other algorithmic parameters such as the complexity criterion introduced to estimate finite size effects. All results presented in this paper have been obtained with the decomposable Normalized Maximum Likelihood (NML) criterion introduced in  [28, 29] , which was shown to yield significantly better results than more traditional BIC/MDL criterion on benchmark networks, especially on small datasets, leading to simultaneous improvements in both recall and precision  [19].
Analysis of expression data in single cells At cellular level, we reconstructed regulatory networks from single cell expression data at the time of endothelial and hematopoietic differentiations from the primitive streak cells of the mouse early embryo, Fig 2A. This concerns the formation of primitive erythroid cells, a distinct and transient red blood cell lineage arising directly from mesodermal progenitors with restricted hematopoietic potential  [32] , by contrast to the highly studied definitive erythroid cells which arise from multipotent hematopoietic stem cells. The dataset for this application is from Moignard et al  [24]  and includes the expression of 33 transcription factors (TFs) along with 13 non-TF genes (markers) in 3,934 single cells extracted at 4 different times of the mouse embryo development (days E7.
Analysis of genomic and ploidy alterations in breast tumors At tissue and organismal levels, we analyzed genomic alterations on breast tumors from the online Catalog of Somatic Mutations in Cancer (COSMIC) datase  [34] , Fig 3A  -3C. The dataset, which contains 807 samples without predisposing BRCA1/2 germline mutations, includes somatic mutations (from whole exome sequencing) and expression level information for 91 genes. These 91 genes have been selected based on earlier studies on mutation and/or expression alterations in breast cancer, Materials and Methods. Gene non-synonymous mutation status is binarized (yes / no) and gene expression status is categorized as under-, normal-or over-expressed by the COSMIC database. S12  predicted to be largely indirect and mediated by TP53 mutations which lead to dysregulation of mitosis controling genes, such as the under-expression of PPP2R2A  [35]  and over-expression of AURKA and CENPA genes.
5,504 ohnolog genes retained from the two rounds of whole genome duplications (WGDs) in the common vertebrate ancestor were obtained from the 'Ohnologs' server based on multi-species comparison of synteny  [45]. All the small scale duplicates (SSDs) in the human genome were obtained from Ensembl Compara using BioMart  [46] , and were restricted to the 4,506 genes duplicated after the WGDs. Genes with copy number variants (CNVs) were obtained from the Database of Genomic Variants  [47]. A total of 5,185 genes were identified to be CNV genes as their entire coding sequence fell within one of the CNV regions in this database. We then collected information on the genomic properties of these 20,415 human genes, including their sequence conservation ('Ka/Ks ratio'), protein autoinhibitory folds and participation to protein complexes, their expression levels across tissues, association with dominant or recessive diseases and susceptibility to cancer mutations as well as their essentiality for development and reproduction, see Materials and methods.
More specifically, miic relies on the analysis of multivariate information  [14] [15] [16] [17] [18] [19] , which extends the concept of mutual information to more than two variables. In practice, miic integration of constraint-based methods within an information-theoretic framework leads to greatly improved performances in both prediction accuracy (Fig  1E  The likelihood ratio formalism also enables to derive an edge specific confidence index, C XY , which allows to filter predicted edges to obtain an enhanced and tunable precision of the reconstructed networks. This might be desirable in many applications for which the correctness of predicted edges is more important than the occasional dismissal of less certain edges. We have used miic to reconstruct causal networks from a variety of genomic datasets at different biological size and time scales, from gene regulation in single cells (.
Beyond the three genomic network reconstructions presented in this paper (Figs 2, 3 and 4), we anticipate that this information-theoretic approach may help uncover cause-effect relationships in other information-rich datasets from different fields of biological interest, such as developmental biology, neuroscience, clinical data analysis and epidemiology. The causal network learning tool, miic, is implemented in an R-package software with open source code and freely available under a General Public License (S1 Software).
Materials and methods Application Gene functional classification in hematopoiesis/epithelial differentiation. The early hematopoiesis single cell transcription data come from  Moignard et al. , 2015 [24]. The expression of 33 TFs and 13 non-TF genes (markers) have been obtained by single cell qRT-PCR and binarized (on/off) by the authors. The 33 TFs can be classified into 3 categories related to their function, using the Mouse Genome Database  [34]  as well as the TF expressions at the different time points in the original experiment  [24] : • "Hematopoietic": This group gathers the TFs for which we found a function in hematopoietic differentiation, without finding any evidence of a role in endothelium formation in the litterature. The corresponding genes linked to hematopoietic function are: Eto2, Sfpi1/PU.