dataesr/scientific-paragraphs-categorization huggingface dataset:
These approaches usually are driven by the gradient of some kind of loss (or gain) differentiable function. This circumstance has important consequences for the XAI researcher because the properties and features of the results are radically different. In the declarative realm, equivalence, for example, is a property that holds or does not hold at all. There is not a measure of the degree of equivalence among different objects; hence, it does not make sense to define measures for the degree of equivalence. From the numerical/statistical viewpoint, most of the models learned can be more or less approximated to the original data, so it is absolutely natural and advisable to define accuracy metrics to compare different approaches. Therefore, in general, it seems of low relevance to try to compare, from the accuracy viewpoint, machine learning approaches that guarantee to induce versions equivalent to the observed data (such as ILP) and approaches that learn approximations more or less accurate (such as most of the numerical/statistical models).
• We have checked the expressiveness of our approach (based on LFIT) extending it to a dataset about adult income level from the 1994 US census. In this domain, we have not used any deep learning algorithms to compare, showing that the proposed approach is also applicable under this circumstance. The rest of the paper is structured as follows: Section 2 summarises the related relevant literature. Section 3 describes our methodology including LFIT, GULA, and PRIDE. Section 4 presents the experimental framework, including the datasets and experiments conducted. Section 5 presents our results. Finally Sections 6 and 7 respectively discuss our work and describe our conclusions and further research lines.
General Methodology Figure  2  graphically describes our proposed approach to generate explanations using LFIT of a given black-box classifier. We can see that our purpose is to get declarative explanations in parallel (in a kind of white-blox digital twin) to a given neural network classifier. In the present work, for our first set of experiments, we used the same neural network and datasets described in  [8] , excluding the face images as explained in the following sections. In our second set of experiments (income prediction) we did not consider any machine learning algorithms to compare with. Therefore, the black box of Figure  2  is not considered in that case, although the rest of the figure is still applicable. In that set of experiments, we explore declarative explanations of the input/output relation of the training/testing datasets.
PRIDE Implementation of LFIT GULA  [55, 56]  and PRIDE  [60]  are particular implementations of the LFIT framework  [49]. In the present section we introduce and describe, first informally and then formally, the notation and the fundamentals of both methods. Table  1  summarises the dataset about incomes of adults in USA. It shows the names, meaning, type of data, and codification used in our experiments. In the following points we will explain by means of examples over that table the relevant LFIT concepts. 1  shows multi-valued attributes instead of binary. LFIT translates them into propositional ones (binary) creating as many propositional (binary) variables as possible values for each attribute. Although we keep the typical functional notation var(value), each combination is in fact the propositional variable var value.
The body of rules gives a minimal condition over feature variables to obtain its conclusions over a target variable. Multiple rules can match the same feature state, thus multiple explanations can be possible. Rules can be weighted by the number of observations they match to assert their level of confidence. Output programs of GULA and PRIDE can also be used in order to predict and explain from unseen feature states by learning additional rules that encode when a target variable value is not possible as shown in the experiments of  [56]. The current contribution shows a possible application of a declarative method (such as LFIT) in some scenarios with numerical aspects: in the FairCV db case we are generating white-box explanations to a deep-learner black-box; in the US census case we are explaining a dataset that could be typically tackled by numeric (statistical) approaches.
FairCVdb Dataset FairCVdb comprises 24,000 synthetic resume profiles. Table  2  summarises the structure of these data. Each resume includes 12 features (v i ) related to the candidate merits, 2 demographic attributes (gender and three ethnicity groups), and a face photograph. In our experiments we discarded the face image for simplicity (unstructured image data will be explored in future work). Each of the profiles includes three target scores (T) generated as a linear combination of the 12 features: T = β + 12 ∑ i=1 α i • v i , (3) where α i is a weighting factor for each of the merits (see  [8]  for details): (i) unbiased score (β = 0); (ii) gender-biased scores (β = 0. 2 for male and β = 0 for female candidates); and (iii) ethnicity-biased scores (β = 0. 0, 0. 15 and 0. 3 for candidates from ethnic groups 1, 2, and 3, respectively).
Thus, we intentionally introduce bias into the candidate scores. From this point on, we will simplify the name of the attributes considering g for gender, e for ethnic group, and i1 to i12 for the rest of the input attributes. In addition to the bias previously introduced, some other random bias was introduced relating attributes and gender to simulate real social dynamics. The attributes concerned were i3 and i7. Note that merits were generated without bias, assuming an ideal scenario where candidate competencies do not depend on their gender or ethnic group. For the current work we have used only discrete values for each attribute discretising one attribute (experience to take values from 0 to 5, the higher the better) and the scores (from 0 to 3) that were real valued in  [8]. We have experimented with PRIDE on the FairCVdb dataset described in the previous section.
Adult Income Level Dataset In a second set of experiments, we considered a dataset about adult incomes extracted from the 1994 US census  [63]. It contains a total of 48,842 entries with 14 attributes that describe the group of individuals represented by each entry. One of these attributes is the income level discretised to only highlight if it is high (>50k USD) or low (≤50k USD). Table  1  summarises the structure of the dataset. The dataset is usually split into training and testing subsets. Like in the first analysis on the FairCVdb dataset, we fed PRIDE with the complete dataset. Unlike the first set of experiments on FairCVdb, with the adult income dataset there was no guarantee that incomes are biased by attributes like gender or ethnicity. Another difference is that datasets taken from the US census are not synthetic; they collect information about real people.
In addition, an unbiased version of the income level is not available. On the other hand, there is a common belief that the level of income is skewed by gender and ethnicity. The general intuition tells us that males are more likely to have higher incomes than females, and people of white ethnicity are more likely to have higher incomes than other ethnicities. The goal of this second set of experiments over the income dataset was to check PRIDE expressiveness when trying to find a data-driven explanation for this common belief.
Results It is important to pay attention to the properties that the formal model under LFIT guarantees: the learned propositional logic theory is equivalent to the observed data, and the conditions of each clause (rule) are minimal. These properties allow for estimating the complexity of the observed data from the complexity of the learned theory-the simpler the dataset the simpler the theories. In the future, we would like to explore the possibility of defining some kind of complexity measure of the datasets from the complexity of the theories learned by LFIT. It could be something similar to Kolmogorov's compression complexity  [64]. Another important question to take into account when quantitatively analysing these results is the expressiveness of the LFIT models. Propositional logic excludes the use of variables.
Quantitative Summary of the Results In this section, a quantitative summary of the results is discussed. The total number of rules and the frequency of each attribute are shown. In order to compare the influence of each attribute, their normalised frequencies with respect to the total number of rules are also shown. Tables  3  4 show the number of rules and the absolute frequency of each attribute in the rules when comparing ethnicity biased and unbiased datasets. Tables  5  and 6  show the number of rules and the absolute frequency of each attribute in the rules when comparing gender biased and unbiased datasets. In order to compare the effect of each attribute, their normalised frequencies (with respect to the number of rules) are also shown in Figure  4  (when studying ethnicity biases) and in Figure  5  (for gender biases).
In our analysis, the number of examples for compared scenarios are consistent. Depending on PW, we define global weight GW as follows. For any program P and v val j 1 1 , we have: GW v val j 1 1 = ∑ val i 0 ∈val 0 PW v val j 1 1 (v val i 0 0 ) • val i 0. The GW v val j 1 1 is a weighted addition of all the values of the output, and the weight, in our case, is the value of scores. This analysis was performed only on scenario s11, comparing unbiased and genderand ethnicity-biased scores. We have observed a similar behavior of both parameters: partial and global weights. In unbiased scenarios, the distributions of the occurrences of each value could be considered statistically the same (between gender(0) and gender(1) and among ethnicity(0), ethnicity(1) and ethnicity(2)). Nevertheless, in biased datasets the occurrences of gender(0) and ethnic(0) for higher scores are significantly higher.
Attributes Percentage of Absolute Increment (AIP) AIP(ethnicity) is 40% superior than the rest Something similar happens for gender. Figures  8  and 9  show AIP us1-11,gbs1-11 for each attribute when studying gender-biased scores. It is worth mentioning that some differences exist in scenarios s9, s10, and s11, regarding attributes i3 and i7. These apparent anomalies are explained by the random bias introduced in the datasets in order to relate these attributes with gender when the score is biased. Figure  10  shows NP s11 for all attributes. This clearly shows the small relevance of attributes i3 and i7 in the final biased score. As is highlighted elsewhere, this capability of PRIDE to identify random indirect perturbations of other attributes in the bias is a relevant achievement of our proposal.
Attributes Percentage of Absolute Increment (AIP) AIP(gender) is between 60% and 270% superior than the rest   Due to the circumstances described in previous sections the goals and analysis on this dataset are simpler than on FairCVdb. In this case, it was enough to study the clauses of the learned program and compute the normalised frequency of the different values of the attributes ethnicity and sex with respect to the total amount of entries and compare the proportion of class(0) and class(1). The results are shown in Figures  12  and 13. In both cases, blue color is used for class(0) and red for class  (1). Their frequency normalised with respect to the total amount of entries are put together to compare them. This simple initial experiment shows that the propositional logic theory learnt by PRIDE supports and explains the common belief about the relationship among sex (idem.
Discussion After running the experiments described in the previous sections we can extract the following conclusions. • PRIDE can explain algorithms learnt by neural networks. The theorems that support the characteristics of PRIDE allow a set of propositional clauses logically equivalent to the systems observed when facing the input data provided. In addition, each proposition has a set of conditions that is minimum. -Insights into the structure of the FairCVd dataset. We have seen (and further confirmed with the authors of the datasets) characteristics of the datasets, e. g. ,  (1)  All attributes are needed for the score. We have learnt the logical version of the system starting from only two input attributes and including one additional attribute at a time and only reached an accuracy of 100% when taking into account all of them.
This is because removing some attributes generates indistinguishable CVs (all the remainder attributes have the same value) with different scores (that correspond to different values in some of the removed attributes). (  2 ) Gender and ethnicity are not the most relevant attributes for scoring: The number of occurrences of these attributes is much smaller than others in the conditions of the clauses of the learnt logical program. (3) While trying to catch the biases we have discovered that some attributes seem to increase their relevance when the score is biased. For example, the competence in some specific languages (attribute i7) seems to be more relevant when the score has gender bias. After discussing with the authors of the datasets, they confirmed a random perturbation of these languages into the biases, that explained our observations.
-Biases in the training FairCVdb datasets were detected. We have analysed the relationship between the scores and the specific values of the attributes used to generate the biased data. We have proposed a simple mathematical model based on the effective weights of the attributes that concludes that higher values of the scores correspond to the same specific values of gender (for gender bias) and ethnic group (for ethnicity bias). On the other hand, we have performed an exhaustive series of experiments to analyse the increase of the presence of the gender and ethnicity in the conditions of the clauses of the learnt logical program (comparing the unbiased and biased versions).
- Insights into the structure of dataset about the adult income from the US census. In this case, there is no unbiased version to compare with, as in the FairCVdb dataset. In addition, we do not have any machine learning approach to be considered for the black-box explanation. Nevertheless, there exists a common belief about the presence of biases (gender and ethnicity) in the income level. PRIDE has been used considering the dataset itself as a black-box, understanding the income level as a function of the other attributes. We have obtained a logic theory that supports this common belief. Our overall conclusion is that in scenarios in which opaque (black-box) machine learning techniques have been used; LFIT, and in particular PRIDE, are able to offer explanations to the algorithm learnt in the domain under consideration.
Acknowledgments: This work was supported by projects:  PRIMA  ( H2020-MSCA-ITN-2019-860315 ), TRESPASS-ETN ( H2020-MSCA-ITN-2019-860813 ),  IDEA-FAST  ( IMI2-2018-15-853981 ),  BIBECA  ( RTI2018-101248-B-I00 MINECO/FEDER ),  RTI2018-095232-B-C22   MINECO ,  PLeNTaS  project  PID2019-111430RB-I00   MINECO ; and also by  Pays de la Loire Region  through  RFI   Atlanstic 2020.
Funding: This research was funded by projects:  PRIMA  ( H2020-MSCA-ITN-2019-860315 ), TRESPASS-ETN ( H2020-MSCA-ITN-2019-860813 ),  IDEA-FAST  ( IMI2-2018-15-853981 ),  BIBECA  ( RTI2018-101248-B-I00 MINECO/FEDER ), and  RTI2018-095232-B-C22 MINECO. Institutional Review  Board Statement: Not applicale. Informed Consent Statement: Not applicable.
Sequencing and processing Whole genome sequencing (WGS) of the tumor-normal pairs from patients included in the Institut Curie cohort (MuM10, MuM12, MuM15-18) was performed in the New York Genome Center (NYGC). DNA libraries were prepared using TruSeq PCR-free approach following the protocols implemented in the NYGC. WGS of the tumornormal pairs of the Rigshospitalet cohort (MuM1, MuM11, MuM13, MuM14) was performed by Edinburgh Genomics (The Roslin Institute, University of Edinburgh) using TruSeq Nano library preparation method. Sequencing was performed on Illumina HiSeqX machine for both the cohorts with aimed coverage of 30X and 60X for normal (blood) and tumor samples respectively. Whole genome sequencing BAM files of other primary mucosal melanomas (MuM2-MuM9) and primary cutaneous melanomas 6 (Cut1-Cut54) were downloaded from EGA using accession ID EGAS00001001552 using ASPERA(v3.
13 Structural variants were determined using DELLY  35  (v0. 8. 1) with default parameters. Mutational signatures were determined by fitting somatic single nucleotide variants with tri-nucleotide context to the 30 COSMIC mutational signatures using deconstructSigs(v1. 8. 0) 36 package using default parameters. Signatures with contribution weights less than 6% were excluded. Copy number alterations were determined using Sequenza 37 (v2. 1. 9999b0) package with parameters (mufreq. treshold = 0. 05, min. reads = 10, min. fw. freq = -0. 1). One cutaneous sample with missing gender information in clinical data was excluded from the analysis. Fraction of genomic alteration for each sample was calculated using an in-house script. FIGURE LEGENDS.
ACKNOWLEDGEMENTS R. M. is supported by  Wellcome Trust  ( 100282/Z/12/Z ),  European Research Council  ( ERC-ADG-2014 671262 ),  Cancer Research UK  ( A27412  and  A22902 ). M. R. and M-H. S. are funded by  Institut Curie , the  Ligue Nationale Contre le Cancer (Labellisation) , and  Site de Recherche Intégrée sur le Cancer (SiRIC) de l'Institut Curie. M-H. S. is also funded by  Institut National de la Santé et de la Recherche Médicale. L. H. M. was funded by a non-restricted  Candys Foundation  grant. J. S. R. -F. is funded in part the  Breast Cancer Research Foundation. S. V. is supported by a  Harry J Lloyd Charitable Trust. WGS costs were partly supported by the  Manchester NIHR Biomedical Research Centre.
DATA AVAILABILITY The whole-genome sequencing data generated in this study from conjunctival melanoma samples have been deposited in the EGA database under accession code EGAS00001004697 [https://www. ebi. ac. uk/ega/studies/EGAS00001004697]. The data is available under restricted access, which can be obtained by contacting Prof Richard Marais. The whole-genome sequencing data corresponding to cutaneous melanoma and other mucosal melanoma samples is available from the EGA database under accession code EGAS00001001552 [https://www. ebi. ac. uk/ega/studies/EGAS00001001552].
Sequencing Data Analysis The data generated by the sequencing platform were demultiplexed and the datasets consisted of two separate fastq files (forward and reversed). The sequences were subsequently analyzed through the OCToPUS pipeline as described in  Mysara et al. (2017) : In short, reads went successively through preassembly denoising  (Bankevich et al. , 2012) , contig assembly, quality filtering using mothur  (Schloss et al. , 2009) , denoising using IPED  (Mysara et al. , 2016) , chimera removal using CATCh  (Mysara et al. , 2015)  and finally Operational Taxonomic Unit (OTU) clustering with 97% cut-off using UPARSE  (Edgar, 2013). All resulting OTUs were taken into account for further analyses without applying a minimum abundance threshold. The OTUs were then taxonomically assigned using the mothur classify.
seqs command with the RDP dataset (version 16) as reference. In order to properly compare the samples from both campaigns combined, they were rarefied to the same read count as the smallest sample (11,683 reads), using the mothur sub. sample command. Although a large number of reads is typically removed during this process, this does not significantly affect the subsequent alpha and beta diversity analyses. Rarefaction curves were obtained by using the mothur rarefaction. single command and subsequently plotting the data in the R software. Sample metadata are included in Supplementary Table  1. Alpha (Inversed Simpson index) and beta [Theta-YC distance calculation followed by non-metric multi-dimensional scaling (NMDS)] diversity analyses were also performed in mothur using the summary. single, dist.
Alpha and Beta Diversity Analyses The alpha diversity showed a peak in diversity at the start of each cycle, followed by a subsequent downward trend (Supplementary Figure  4 ). This was true for both sampling campaigns, which further confirmed the robustness of the system under study. For the beta diversity analysis, an NMDS was performed on all the samples using the mothur program  (Schloss et al. , 2009). As can be observed in Figure  5 , all shutdown samples from the first campaign clustered together, indicating that the community returns to an equilibrium after each cycle. Cycles 1 and 2 also clustered together in the top right quadrant, whereas cycle 3 was clustered separately in the bottom right quadrant, indicating a shift in the community at this point in time. This was also confirmed in Figure  3.
ACKNOWLEDGMENTS We thank  Hans Ooms ,  Dirk Meynen ,  Emre Sikik ,  Bart Thijs , and  Steven Van Dyck  for providing valuable information about the BR2 reactor and the radiation control department for verifying sample activity. We also thank  Robby Nijs ,  Patrick Claes ,  Job Cools ,  Eddy Kox , and  May Van Hees  for ensuring all lab work involving radioactivity was performed according to ALARA regulations,  Hugo Moors  for providing advice on filtration methodologies, and  Rob Van Houdt  for providing advice on the manuscript structure.
, 2019) ; and (iii) the Global Southern Ocean Array and the Global Argentine Basin Array, which are networks of fixed and moored platforms and mobile profilers (gliders) deployed south-west of Chile and in the Argentinian basin, respectively, to monitor waves, air-sea fluxes of heat, moisture and momentum, and physical, biological, and chemical properties throughout the water column  (Trowbridge et al. , 2019). Buoys have also been deployed in the Antarctic marginal ice zone to monitor waves in ice and sea ice drift (e. g. Meiners et al. , 2016; Ackley et al. , 2020; Meylan et al. , 2014; Vichi et al. , 2019; Alberello et al. , 2020a). A database covering the Southern Ocean more uniformly is provided by polar-orbiting microwave radar satellites such as altimeters, scatterometers, and synthetic aperture radar (SAR).
, 2020; Schmale et al. , 2019; Smart et al. , 2020; Thurnherr et al. , 2020). Here we present a database of underway sea state observations, comprising of concurrent records of winds, surface currents, and waves. In Sects. 2 and 3, details of the expedition, the instrumentation, and its calibration are presented. An overview of the database is presented in Sect. 4. A comparison against available satellite data and an assessment of uncertainties is given in Sect. 5. Concluding remarks are made in the last section. The voyage was divided into three legs. Leg 1 was along the Indian Ocean from Cape Town, South Africa, to Hobart, Australia, with stops at Marion Island, Iles de Crozet et Kerguelen, and Heard Island. Leg 2 went across the Pacific Ocean to Punta Arenas, Chile, with stations at Mertz Glacier, Balleny Islands, Scott Island, Mount Siple (the southernmost station), Peter I Island, and Diego Ramírez.
Sea state climate during ACE Excluding the regions south of the 60th parallel, which undergo a strong seasonal sea ice cycle  (Eayrs et al. , 2019) , the Southern Ocean is normally characterised by weak seasonal variability  (Young et al. , 2020). Therefore, extreme sea states remain likely even during summer. As a reference, wind, current, and wave climate statistics in the form of the 50th and 90th percentiles (hereafter P50 and P90, respectively) aggregated in 2 • × 2 • regions for the summer months (December, January, February) are reported in Fig. 5. Data of wind speed and wave height are from all satellite missions mounting altimeter sensors that are available from 1985 to 2019  (Ribal and Young, 2019). Data of current speed are from the Copernicus GlobCurrent database -https://marine.