You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
This paper describes a computational model of loudness variations in expressive ensemble performance. The model predicts and explains the continuous variation of loudness as a function of information extracted automatically from the written score. Although such models have been proposed for expressive performance in solo instruments, this is (to the best of our knowledge) the first attempt to define a model for expressive performance in ensembles. To that end, we extend an existing model that was designed to model expressive piano performances, and describe the additional steps necessary for the model to deal with scores of arbitrary instrumentation, including orchestral scores. We test both linear and non-linear variants of the extended model n a data set of audio recordings of symphonic music, in a leave-one-out setting. The experiments reveal that the most successful model variant is a recurrent, non-linear model. Even if the accuracy of the predicted loudness varies from one recording to another, in several cases the model explains well over 50 of the variance in loudness.

Cited Abstract(s):
[1]: 

[2]: Abstract The quest for understanding how pianists interpret notated music to turn it into a lively musical experience, has led to numerous models of musical expression. Several models exist that explain expressive variations over the course of a performance, for example in terms of phrase structure, or musical accent. Often however expressive markings are written explicitly in the score to guide performers. We present a modelling framework for musical expression that is especially suited to model the influence of such markings, along with any other information from the musical score. In two separate experiments, we demonstrate the modelling framework for both predictive and explanatory modelling. Together with the results of these experiments, we discuss our perspective on computational modelling of musical expression in relation to musical creativity.

[3]: Expressive interpretation forms an important but complex aspect of music, in particular in certain forms of classical music. Modeling the relation between musical expression and structural aspects of the score being performed, is an ongoing line of research. Prior work has shown that some simple numerical descriptors of the score (capturing dynamics annotations and pitch) are effective for predicting expressive dynamics in classical piano performances. Nevertheless, the features have only been tested in a very simple linear regression model. In this work, we explore the potential of a non-linear model for predicting expressive dynamics. Using a set of descriptors that capture different types of structure in the musical score, we compare the predictive accuracies of linear and non-linear models. We show that, in addition to being (slightly) more accurate, non-linear models can better describe certain interactions between numerical descriptors than linear models.
Among the machine learning methods for musical expression is the model proposed by [1] . This model uses artificial neural networks (NNs) in a supervised fashion in two different contexts: 1) to learn and predict the rules proposed by the KTH model and 2) to learn the performing style of a professional pianist using an encoding of the KTH rules as inputs. Similarly, the (see Section ) used by [2] and [3] represents a bottom-up approach that uses a lower level encoding of a musical score in order to learn how different aspects of the score contribute to generate an expressive performance of a musical piece.