# Multivariate Relationship in Big Data Collection of Ocean Observing System
## 1 Introduction
In the aforementioned model, a Bayesian approach was introduced, and experimental results confirmed that this method resulted in a better generalization of the output results. Finally, this methodology is circumscribed to the Mediterranean Sea (with the _canyon-med_[15]), which is currently the state of the art in this area as it leads to a lower error in the predictions. Previous results confirmed that restricting the geographical area of application leads to an improvement in predictive performance. In fact, even if the amount of data for the training decreases, it allows for a better representation of variable relationships that characterize the peculiar biogeochemical and physical features of confined areas, such as the Mediterranean Sea. The Mediterranean is characterized by high salinity, oligotrophy, and relevant spatial gradients [16]. Indeed, the Mediterranean Sea is considered an ocean in miniature, as it is distinguished by peculiar biogeochemical characteristics, especially in the eastern basin, caused by the difference in nutrient sources in terms of quantity and quality [17]. The technique proposed in this paper has significant differences to the previous studies cited. First of all, our approach is based on a regional dataset, as with [15] and unlike [10; 14]. In addition, it should be noted that our network does not follow a Bayesian approach, in contrast to the works by [10; 15]. The decision to adopt a deterministic architecture was made following a preliminary investigation, which revealed that employing a Bayesian approach did not result in performance gains, but rather increased the computational demands for training. Leveraging from the previous deep learning applications, we aim to introduce and test novel elements such as the use of a larger in situ dataset (_EMODnet_) for training and validation [18], which is richer with respect to the datasets exploited in previous applications both in terms of the quantity of samples and contained variable. Another contribution that we wish to provide with our paper is the definition and application of a novel two-step training procedure used for the quality check of the data. We propose this routine for the removal of the incorrect data by relying again on a deep learning framework to perform such tasks. This technique represents the first approach to semi-automatize the quality of a dataset, as these operations are usually performed by hand by experts in the oceanographic field. We consider as necessary the introduction of a quality check procedure since _EMODnet_ consists of an ensembling of multiple datasets created by different providers. Even if quality check procedures for data collection exist [18], the process of merging multiple sources is not free from generating inconsistencies among data due to different measurement techniques and standards, transcriptions, and communication. The deep learning model used together with the two-step quality check routine introduced lead to a wide reduction of both fitness measures used to test the validity of the model. Finally, a confidence interval for the predictions is introduced, exploiting the concept of deep ensembles of neural networks [19], and its validity is checked through practical results. Quantifying the uncertainty related to a prediction becomes essential when dealing with values collected over large and not-homogeneous areas. The goal of this paper, in fact, is not only to provide a more accurate tool for the prediction of low-sampled variables, but also a comprehensive study of the performances of the proposed model, providing information such as the confidence interval, the quality of the prediction at different geolocations, at different depths and so on. The paper is organized as follows: Section 2 introduces and describes in detail the characteristics of the model and the relative experimental settings. The experimental results are then presented and discussed in Section 3. Finally, Section 4 provides the conclusions and proposes some directions for future works.