dataesr/scientific-paragraphs-categorization huggingface dataset:
We then compare this  to the ℎℎ to determine if this  reference is similar to the query. We finally choose the most similar window  with the maximum  of all the similar windows (Step b: in Algorithm 1). The same process is performed to find the most similar window  in  data. In the proposed approach, the dynamics and the shape of data before and after a gap are a key-point of our method. This means we take into account both queries  (after the gap) and  (before the gap). Input:  = { Completing all lines containing missing parameter on ,  by a max trapezoid function  (5)  Construct queries , -temporal windows after and before the gap 𝑄𝑎 = 𝐷𝑎[1 : 𝑇], 𝑄𝑏 = 𝐷𝑏[𝑡 -𝑇 + 1 : 𝑡 -1] (6) for  data do  (7)  Step a: Find the threshold in the  database (8)  ← 1;  ←   (9)  while  ≤ length() do  (10)   ←  +  -1  (11)  Create a reference window: 𝑅(𝑖) = 𝐷𝑏[𝑖 : 𝑘] (12) Calculate a fuzzy-based similarity measure between  and ():   (13)  Save the  to  (14)  ←  +  ℎℎ  (15)  end while  (16)  return ℎℎ = max{}  (17)  Step b: Find similar windows in the  database  (18)   ← 1;  ←   (19)  while  ≤ length() do  (20)   ←  +  -1 Create a reference window: 𝑅(𝑖) = 𝐷𝑏[𝑖 : 𝑘] (22) Calculate a fuzzy-based similarity measure between  and ():   (23)  if  ≥ ℎℎ then  (24)  Save position of () to   (25)  end if  (26)   ←  +     (27)  end while  (28)  return position of  -the most similar window to  having the maximum fuzzy similarity measure in the  list.
Datasets Description. For the assessment of the proposed approach and the comparison of its performance to several published algorithms, we use 3 multivariate time series, one from UCI Machine Learning repository, one simulated dataset (this allows us to handle the correlations between variables and percentage of missing values), and finally a real time series hourly sampled by IFREMER (France) in the eastern English Channel. (i) Synthetic dataset  [54] : The data are synthetic time series, including 10 features, 100,000 sampled points. All data points are in the range -0. 5 to +0. 5. The data appear highly periodic but never exactly repeated. They have structure at different resolutions. Each of the 10 features is generated by independent invocations of the function: 𝑦 = 7 ∑ 𝑖=3 1 2 𝑖 sin (2𝜋 (2 2+𝑖 + rand (2 𝑖 )) 𝑡) ; 0 ≤ 𝑡 ≤ 1 (6) where rand() produces a random integer between 0 and.
We apply the Corgen function of ecodist R-package  [55]  to create the second and the third variables. (iii) MAREL-Carnot dataset  [2] : The third experiment is conducted on MAREL-Carnot dataset. This dataset consists of nineteen series such as phosphate, salinity, turbidity, water temperature, fluorescence, and water level that characterize sea water. These signals were collected from the 1  January 2005 to the 9 ℎ February 2009 at a 20 minute frequency. Here they were hourly sampled, so they have 35,334 time samples. But the data include many missing values, the size of missing data varying on each signal. To assess the performance of the proposed method and compare it with other approaches, we choose a subgroup including fluorescence, water level, and water temperature (the water level and the fluorescence signals are completed data, while water temperature contains isolated missing values and many gaps).
Multivariate Imputation Approaches. In the present study, we perform a comparison of the proposed algorithm with 7 other approaches (comprising Amelia II, FcM, MI, MICE, missForest, na. approx, and DTWUMI) for the imputation of multivariate time series. We use R language to execute all these algorithms. (1) Amelia II (Amelia II R-package)  [57] : The algorithm uses the familiar expectation-maximization algorithm on multiple bootstrapped samples of the original incomplete data to draw values of the complete data parameters. The algorithm then draws imputed values from each set of bootstrapped parameters, replacing the missing values with the drawn values. (2) FcM-Fuzzy -means based imputation: This approach involves 2 steps. The first step is to group the whole data into  clusters using fuzzy- means technique.
𝐹𝐵 (𝑦 When FA2 value is close to 1, a model is considered perfect. 4. 4. Experimental Process. Indeed, evaluating the ability of imputation methods cannot be done because the actual values are lacking. So we must produce artificial missing data on completed time series in order to compare the performance of imputation approaches. We use a technique based on three steps to assess the results detailed in the following: (i) The first step: Generate simulated missing values by removing data values from full time series. (ii) The second step: Apply the imputation methods to fill in missing data. (iii) The third step: Evaluate the ability of proposed approach and compare with state-of-the-art methods using different performance indices abovementioned. In this paper, we perform experiments with seven missing data levels on three large datasets.
On each signal, we create simulated gaps with different rates ranging from 1%, 2%, 3%, 4%, 5%, 7. 5%, to 10% of the data in the complete signal (here the biggest gap of MAREL-Carnot data is 3,533 missing values corresponding to 5 months of hourly sampled). For every missing ratio, the approaches are run 5 times by randomly choosing the positions of missing in the data. We then perform 35 iterations for each dataset.
Quantitative Performance Comparison. Tables Synthetic Dataset. Table  1  presents a comparison of 8 imputation methods on synthetic dataset that contains 7 missing data levels (1-10%). The results clearly show that when a gap size is greater than 2%, the proposed method yields the highest similarity,  2 , FA2, and the lowest RMSE, FB. With this dataset, na. approx gives the best performance at the smallest missing data level for all indices and is ranked second for other ratios of missing values (2-5%) for similarity and FA2, RMSE (2-4%), and  2 (the 1  rank at 2% missing rate, the 2  at 3%, 5%). The results can explain that the synthetic data are generated by a function  (6). na. approx method applies the interpolation function to estimate missing values. So it is easy to find a function to generate values that are approximate real values when missing data rates are small.
But this work is more difficult when the missing sample size rises; that is why the ability of na. approx decreases as  Although this dataset never exactly repeats itself and our approach is proposed under the assumption of recurrent data the FSMUMI approach proves its performance for the imputation task even if the missing size increases. Among the considered methods, the FcM-based approach is less accurate at lower missing rates but it provides better results at larger missing ratios as regards the accuracy indices. Simulated Dataset. Table  2  illustrates the evaluation results of various imputation algorithms on the simulated dataset. The best values for each missing level are highlighted in bold. Our proposed method outperforms other methods for the imputation task on accuracy indices: the highest similarity,  2 , and the lowest RMSE at every missing ratio.
However, when considering other indices such as FA2, FSD, and FB, FSMUMI no longer shows its performance. It gains only at a 4% rate for the FB index and at 10% ratio for FA2. In contrast to FSMUMI, DTWUMI provides the best results for FSD indicator at all missing levels and FA2 at the first 5 missing ratios (from 1% to 5%). Different from the synthetic dataset, on the simulated dataset, the FcM-based method is always ranked the third at all missing rates for similarity and RMSE indicators. Following FcM is missForest algorithm for the both indices. Although, in the second experiment, data are built by various functions but they are quite complex so that na. approx does not provide good results. MAREL-Carnot Dataset. Once again, as reported in Table  3 , our algorithm demonstrates its capability for the imputation task.
FSMUMI method generates the best results as regarding accuracy indices for almost missing ratios (excluding at 2% missing level on all indices, and at 5% missing rate on  2 score). But when considering shape indicators, FSMUMI only provides the highest FA2 values at several missing levels (3%, 5%-10%). In particular, our method illustrates the ability to fill in incomplete data with large missing rates (7. 5% and 10%): the highest similarity,  2 , FA2, and the lowest RMSE, FSD (excluding at 7. 5%), and FB. These gaps correspond to 110. 4 and 147. 2 days sampled at hourly frequency. In contrast to the two datasets above, on the MAREL-Carnot data, na. approx indicates quite good results: the permanent second or third rank for the accuracy indices (the 1  order at 5% missing rate on  2 score), the lowest FSD (from 3% to 5% missing rates), and FB at some other levels of missing data.
But when looking at the shape of imputation values generated from this method, it absolutely gives the worst results (Figure  6 ). Other approaches (including FcM-based imputation, MI, MICE, Amelia, and missForest) exploit the relations between attributes to estimate missing values. However, three considered datasets have low correlations between variables (roundly 0. 2 for MAREL-Carnot data, ≤ 0. 1 for simulated and synthetic datasets). So these methods do not demonstrate their performance for completing missing values in low/uncorrelated multivariate time series. Otherwise, our algorithm shows its ability and stability when applying to the imputation task for this kind of data. DTWUMI approach was proposed to fill large missing values in low/uncorrelated multivariate time series. However, this method is not as powerful as the FSMUMI method.
DTWUMI only produces the best results at 2% missing level on the MAREL-Carnot dataset and is always at the second or the third rank at all the remaining missing rates on the MAREL-Carnot and the simulated datasets. That is because the DTWUMI method only finds the most similar window to a query either before a gap or after this gap, and it uses only one similarity measure, the DTW cost, to retrieve the most similar window. In addition, another reason may be that DTWUMI has directly used data from the window following or preceding the most similar window to completing the gap.
Visual Performance Comparison. In this paper, we also compare the visualization performance of completion values yielded by various algorithms. Figures  4  and 5  illustrate the form of imputed values generated from different approaches on the synthetic series at two missing ratios 1% and 5%. At a 1% missing rate, the shape of imputation values produced by na. approx method is closer to the one of true values than the form of completion values given by our approach. However, at a 5% level of missing data, this method no longer shows the performance (Figure  5 ). In this case, the proposed method proves its relevance for the imputation task. The shape of FSMUMI's imputation data is almost similar to the form of true values (Figure  5 ). Looking at Figure  6 , FSMUMI one more time proves its capability for uncorrelated multivariate time series imputation: completion values yielded by FSMUMI are virtually identical to the real data on the MAREL-Carnot dataset.
Conclusion This paper proposes a novel approach for uncorrelated multivariate time series imputation using a fuzzy logic-based similarity measure, namely FSMUMI. This method makes it possible to manage uncertainty with the comprehensibility of linguistic variables. FSMUMI has been tested on different datasets and compared with published algorithms (Amelia II, FcM, MI, MICE, missForest, na. approx, and DTWUMI) on accuracy and shape criteria. The visual ability of these approaches is also investigated. The experimental results definitely highlight that the proposed approach yielded improved performance in accuracy over previous methods in the case of multivariate time series having large gaps and low or noncorrelation between variables. However, it is necessary to make an assumption of recurrent data and sufficiently large dataset to apply the algorithm.
This means that our approach needs patterns (in our case the two queries (before and after the considered gap)) existing somewhere in the database. This enables us to predict missing values if the patterns occur in the past or in the following data from the considered position. Thus a satisfactory and sufficient dataset (large dataset) is required. In future work, we plan to (i) combine FSMUMI method with other algorithms such as Random Forest or Deep learning in order to efficiently fill incomplete values in any type of multivariate time series; (ii) investigate this approach applied to short-term/long-term forecasts in multivariate time series. We could also investigate complex fuzzy sets (  [63] ) instead of ordinary fuzzy sets that have given good results using an adaptive scheme in the case of the bivariate time series with small dataset.
These data are very large so we choose only a subset of 3 signals for performing experiments. In the second experiment, a simulated dataset including 3 signals is produced as follows: for the first variable, we use 5 sine functions that have different frequencies and amplitudes  = { 1 ,  2 ,  3 ,  4 ,  (ii) Simulated dataset: 5 }. Next, 3 various noise levels are added to data ,  = {,  + 1,  + 2,  + 3}. We then repeat  4 times (this dataset has 32,000 sampled points). In this study, we treat with missing data in low/uncorrelated multivariate time series. So to satisfy this condition, the two remaining signals are generated based on the first signal with the correlations between these signals are low (≤ 0. 1%).
Moreover, and importantly, this conditional version is free of the curse of dimensionality, as it only involves lagged values of the returns for financial institution A. Empirical applications are conducted using daily market returns for a sample of 90 large banks from around the world. The data run from 12 September 2003 to 19 February 2018, and include the global financial crisis of 2007-2008. The dataset includes almost every global systemically important bank (G-SIBs) identified by the Financial Stability Board (FSB). The results show that our measure gives a meaningful ranking of the systemic importance of financial institutions that is found to be consistent with the ranking of G-SIBs provided by the FSB. Moreover, the new measure of systemic importance from the viewpoint of interconnectedness is shown to be a robust and significant early-warning indicator of large losses from a systemic event.
The remainder of the article is structured as follows. Section 2 is devoted to a review of the literature on network measures of systemic risk, covering both theoretical and empirical issues. Second 3 provides, in the line of  Basu et al. (2017) , a critical assessment of measures of systemic risk contributions based on pair-wise Grangercausality tests. In Section 4, we present the new measure based on the LOO approach, and we assess its reliability using real datasets in Section 5. Section 6 searches for the micro-economic determinants of the LOO measure using balance-sheet data, and the last section concludes the article.
Comparative Assessment As underlined in the previous sections, spurious causalities arising from indirect contagion can severely impair the results of Granger-causality tests, and can lead the Granger-causality network to produce inconsistent rankings of the systemic importance of financial institutions. This is particularly the case for the measure InOut k of BGLP. We thus introduced a new measure we denoted ∆LGC k that is based on the LOO concept. The goal of this section is to highlight the differences between our measure and that of BGLP, and to this end, we compute these two measures for our three sub-periods. 4 ote that both the BGLP measure InOut k and our LOO measure ∆LGC k are summaries of outcomes from multiple pair-wise Granger-causality tests and hence are subject to data snooping  (White, 2000) , a phenomenon that occurs when the same dataset is used more than once for inference.
We exploit a new dataset of consolidated balance sheets for some 1,850, mostly nonlisted, French corporate groups, in order to investigate the relationship between corporate investment and the cost of capital. Our empirical model is motivated by a standard Qtheory of investment and relates the rate of investment to a proxy for profits, the cost of capital and firm-and sector-level controls. We notably construct firm-level measures of the weighted average cost of capital (WACC) that account for industry-specific values of the cost of equity and reflect the actual capital structure of firms. We find a confirmation that a high WACC drags down investment: a one SD increase in the real WACC (+2 pp) is associated on average with a reduction by 0. 65 pp in the investment rate. The effect is somewhat larger for manufacturing firms and when firms are highly leveraged or more dependent on external finance.
Recently, some observers have indeed blamed "excessive" levels of corporates' COE for the persistent sluggishness of productive investment in developed economies after the 2008 crisis in spite of central banks' success in driving down nominal interest rates to very low levels. In this paper, we assess the impact of the WACC on corporate investment using new firmlevel data for some 1,850 French, mostly non-listed, non-financial corporate groups from 2005 to 2015. We motivate our empirical model by referring to a standard Q-model of investment, where Tobin's Q appears to be negatively correlated to the firm's WACC. We construct firm-level measures of the WACC that incorporate estimates of the COE based on industry-specific stock market information and a standard dividend-discount model. Controlling for all potentially relevant firm-and sector-level factors, we find new evidence that fluctuations in a firm's WACC matters for investment, notably in the manufacturing sector and for larger firms.
Recently, some observers have indeed blamed "excessive" levels of corporates' COE for the persistent sluggishness of productive investment in developed economies after the 2008 crisis in spite of central banks' success in driving down nominal interest rates to very low levels. 1 In this paper, we assess the impact of the WACC on corporate investment using new firm-level data for some 1,850 French, mostly non-listed, non-financial corporate groups from 2005 to 2015. We motivate our empirical model by referring to a standard Q-model of investment, where Tobin's Q appears to be negatively correlated to the firm's WACC. We construct firmlevel measures of the WACC that incorporate estimates of the COE based on industry-specific stock market information and a standard dividend-discount model. Controlling for all potentially relevant firm-and sector-level factors, we find confirmation of a significant impact of the WACC on investment: on average, an increase in the WACC by one standard deviation (+2pp) is associated in our baseline with a decrease in the investment rate by 0.
Second, a key contribution of our study is that we construct a new database of industrylevel, time-varying measures of the COE for some 30 industries, that we then merge with a rich dataset of firm balance sheet with an annual cross-section of some 5,000 listed and nonlisted corporate groups headquartered in France, which is maintained by the Banque de France (FIBEN groupes). 2 The WACC is by definition an average of the (tax-adjusted) costs of debt and equity funding, weighted by leverage. While the cost of debt is commonly measured by the apparent interest rate paid on existing long-term debt, estimating a firm's COE requires information about its stock price and expected return. As a consequence, researchers tend to either focus on large, listed corporations, or ignore the COE altogether and proxy the cost of capital using a firm-specific or even a macroeconomic measure of the interest rate.
We circumvent this problem by mimicking a common practice among financial analysts, who try and guess the cost of capital of a non-listed firm by estimating the COE of similar listed firms in the same industry. We collect stock market information on the almost entire population of French listed non-financial companies (some 600 corporations) and merge it with industry-level profit forecasts from I/B/E/S. For the average listed firm in each industry, we compute a time-varying measure of the COE using a standard dividend-discount model. We then derive a firm-specific WACC for each of the some 1,850 firms in our cleaned dataset of corporate groups by combining our sector-specific estimate of the COE and firm-specific measures of the tax-adjusted cost of debt and leverage. Although the raw balance sheet data starts in the late 1980s, the scope of the database increased only gradually and we therefore focus our analysis on the period from 2004 to 2015 when data coverage is deemed stable enough.
III. Data. A. Data sources and construction of the main variables. To construct our dataset, we use three different sources of information: consolidated accounting information for a large sample of French corporate groups from the Banque de France's FIBENgroupes database, stock market information for listed French corporations from Datastream, non-consolidated income statements for French enterprises from Banque de France's FIBEN database. Consolidated balance sheet data. We draw consolidated balance sheet and income statement data for non-financial French groups from the annual consolidated FIBEN-groupes database. The raw database covers the period between 1988 and 2017. Consolidation is an accounting method used by corporate groups composed of several legal entities in order to publish a combined statement that shows the financial position of the holding company and its subsidiaries.
This is a compact and accurate picture of the financial position of the whole group. Using consolidated data is a clear advantage for anyone who aims to relate corporate investment to the cost of capital. Indeed, when several legal entities are part of a same group, investment and financing decisions may be undertaken globally at the top by the parent company. In this case, intra-group lending and partition of investment may lead to noisy measures of investment and biases at the subsidiary-level. The consolidated FIBEN database is strongly unbalanced over this period in part because consolidation is only mandatory for listed groups and groups with characteristics (size, turnover, number of employees) above a legal threshold. 7 In some cases, consolidation is not mandatory but is done on a voluntary basis, for transparency reasons, essentially in order to get a Banque de France investment grade.
Our raw consolidated database gathers 98, 204 group-year observations and 13, 387 distinct groups. There are only 14 and 31 observations in 1988 and 2017 respectively and more than 5000 observations per year from 2009 to 2013. We define net fixed assets as the sum of net tangible assets (which include leasing) and net intangibles. The gross investment rate is defined as net capital expenditure in fixed assets (acquisition minus sales) divided by the stock of lagged net fixed assets. The net investment rate is equal to the gross investment rate minus the depreciation of fixed assets over lagged net fixed assets. Depreciation is defined as net depreciation and provisions. We define profitability as the ratio of EBITDA to lagged net fixed assets. Firm size is the log of total assets. We use firm book financial leverage defined as financial debt over financial debt plus book equity as the main measure of leverage for non-listed firms.