# Towards a Vectorial Approach to Predict Beef Farm Performance
Among the possible causes of a herd's fertility reduction, those intrinsic to feeding system, infectious, hygienic-sanitary, or endocrine-gynecological ones and those of environmental nature are of major importance. Not to forget that all stressful conditions, such as uncomfortable housing, insufficient lighting, and crumbling shelters, can negatively affect fertility and, therefore, the calving. Indeed, the free housing allows a greater mobility and a greater exposure to light, with a positive influence on biological activity and, consequently, recovery after birth. In order to investigate the production of Piemontese calves and to understand the mechanisms of breeding performance, we analyzed the corresponding data and model in two pilot studies [15; 16]. A Genetic Programming (GP) approach, whose results were compared with other common ML methods, was adopted, as generated models are resumed in accessible and interpretable expressions, and they extract critical information, i.e., informative attributes. In both studies [15; 16], it was possible to simplify the candidate models, to obtain clear and intelligible expressions, and to analyze the features extracted by the algorithm [17]. These interesting aspects of GP, in particular the intrinsic feature selection ability, encouraged a deeper investigation into the scenario offered by this family of algorithms to search for possible ways to improve the predictive capacity of the generated models. Moreover, it would reasonably be more beneficial to exhaust the available information left previously unexploited. Indeed, data recorded in the years prior to the target year were not involved in the prediction itself, as the previously considered methods can only handle a point variables, and they were only used to determine the pool of representative farms. In fact, due to their structures, they could only exploit punctual data extracted from one year, targeting the following year. To clarify, it is not impossible to deal with past data. The sequences can be split into different observations in order to maintain the structure of a panel dataset, but the algorithms cannot detect the temporal patterns, as in this case, the observations would be treated as distinct instances [18; 19]. Of necessity, the strategy entails the loss of valuable information useful to predict the corresponding target. So far, data from 2017 were used exclusively with targets on 2018. In order to properly tackle the prediction, instead of incorporating the data into a standard panel (see Table 1), in this study, we encapsulate all the values recorded over the years, for each variable, into vectors. Stated otherwise, we introduced the vectorial variables containing data from 2014 to 2017 as input, while targeting the same values in 2018. We opted for this approach since GP was recently developed as Vectorial-Genetic Programming (VE-GP), offering indeed the possibility to exploit vectors as well as scalars and looking promising as its flexibility allows for tackling many different tasks [18; 19]. Consequently, we decided to investigate the usefulness of VE-GP among the breeding farms used in [16]. More specifically, we compared the VE-GP approach with Standard-Genetic Programming (ST-GP) and other state-of-the-art ML techniques, including Long Short-Term Memory (LSTM) recurrent neural networks. This study is presented here for the first time. The article is organized as follows: In Section 2, the application background is discussed, also highlighting the main limits of the prediction methods that have been used so far. The dataset is analyzed, and the basic steps to prepare the benchmark are also described. Afterwards, the ST- and VE-GP approaches, as well as the other studied ML methods, are presented. The obtained results, achieved by all applied ML methods, are provided in Section 3, with particular emphasis on the features selected by the two GP-based methods. The experimental comparisons are discussed in Section 4. Finally, Section 5 concludes the work, also proposing ideas for further developments.