Grammar induction for mildly context sensitive languages using variational Bayesian inference

The following technical report presents a formal approach to probabilistic minimalist grammar induction. We describe a formalization of a minimalist grammar. Based on this grammar, we define a generative model for minimalist derivations. We then present a generalized algorithm for the application of variational Bayesian inference to lexicalized mildly context sensitive language grammars which in this paper is applied to the previously defined minimalist grammar

Predicting Music Hierarchies with a Graph-Based Neural Decoder

This paper describes a data-driven framework to parse musical sequences into dependency trees, which are hierarchical structures used in music cognition research and music analysis. The parsing involves two steps. First, the input sequence is passed through a transformer encoder to enrich it with contextual information. Then, a classifier filters the graph of all possible dependency arcs to produce the dependency tree. One major benefit of this system is that it can be easily integrated into modern deep-learning pipelines. Moreover, since it does not rely on any particular symbolic grammar, it can consider multiple musical features simultaneously, make use of sequential context information, and produce partial results for noisy inputs. We test our approach on two datasets of musical trees -- time-span trees of monophonic note sequences and harmonic trees of jazz chord sequences -- and show that our approach outperforms previous methods.Comment: To be published in the Proceedings of the International Society for Music Information Retrieval Conference (ISMIR

TELMA: Technology enhanced learning environment for minimally invasive surgery

Background: Cognitive skills training for minimally invasive surgery has traditionally relied upon diverse tools, such as seminars or lectures. Web technologies for e-learning have been adopted to provide ubiquitous training and serve as structured repositories for the vast amount of laparoscopic video sources available. However, these technologies fail to offer such features as formative and summative evaluation, guided learning, or collaborative interaction between users. Methodology: The "TELMA" environment is presented as a new technology-enhanced learning platform that increases the user's experience using a four-pillared architecture: (1) an authoring tool for the creation of didactic contents; (2) a learning content and knowledge management system that incorporates a modular and scalable system to capture, catalogue, search, and retrieve multimedia content; (3) an evaluation module that provides learning feedback to users; and (4) a professional network for collaborative learning between users. Face validation of the environment and the authoring tool are presented. Results: Face validation of TELMA reveals the positive perception of surgeons regarding the implementation of TELMA and their willingness to use it as a cognitive skills training tool. Preliminary validation data also reflect the importance of providing an easy-to-use, functional authoring tool to create didactic content. Conclusion: The TELMA environment is currently installed and used at the Jesús Usón Minimally Invasive Surgery Centre and several other Spanish hospitals. Face validation results ascertain the acceptance and usefulness of this new minimally invasive surgery training environment

The Learnability of the Grammar of Jazz: Bayesian Inference of Hierarchical Structures in Harmony

Musical grammar describes a set of principles that are used to understand and interpret the structure of a piece according to a musical style. The main topic of this study is grammar induction for harmony --- the process of learning structural principles from the observation of chord sequences. The question how grammars are learnable by induction from sequential data is an instance of the more general question how abstract knowledge is inducible from the observation of data --- a central question of cognitive science. Under the assumption that human learning approximately follows the principles of rational reasoning, Bayesian models of cognition can be used to simulate learning processes. This study investigates what prior knowledge makes it possible to learn musical grammar inductively from Jazz chord sequences using Bayesian models and computational simulations. The theoretical part of the thesis presents how questions about learnability can be studied in a unified framework involving music analysis, cognitive modeling, Bayesian statistics, and computational simulations. A new grammar formalism, called Probabilistic Abstract Context-Free Grammar (PACFG), is proposed that allows for flexible probability models which facilitate the grammar-induction experiments of this study. PACFG can jointly model multiple musical dimensions such as harmony and rhythm, and can use coordinate ascent variational inference for grammar learning. The empirical part of the thesis reports supervised and unsupervised grammar-learning experiments. To train and evaluate grammar models, a ground-truth dataset of hierarchical analyses of complete Jazz standards, called the Jazz Harmony Treebank (JHT), was created. The supervised grammar-learning experiments, in which grammars for Jazz harmony are learned from the JHT analyses, show that jointly modeling harmony and rhythm significantly improves the grammar models' prediction of the ground truth. The performance and robustness of the grammars are further improved by a transpositionally invariant parameterization of rule probabilities. Following the supervised grammar learning, unsupervised grammar learning was performed by inducing harmony grammars merely from Jazz chord sequences, without the observation of the JHT trees. The results show that the best induced grammar performs similarly well as the best supervised grammar. In particular, the goal-directedness of functional harmony does not need to be assumed a priori, but can be learned without usage of music-specific prior knowledge. The findings of this thesis show that general prior knowledge enables an ideal learner to acquire abstract musical principles by statistical learning. In conclusion, it is plausible that much aspects of musical grammar have been learned by Jazz musicians and listeners, instead of being innate predispositions or explicitly taught concepts. This thesis is moreover embedded into the context of empirical music research and digital humanities. Current studies either describe complex musical structures qualitatively or investigate simpler aspects quantitatively. The computational models developed in this thesis demonstrate that deep insights into music and statistical analyses are not mutually exclusive. They enable a new kind of data-driven music theory and musicology, for instance through comparative analyses of musical grammar for different styles such as Jazz, Rock, and Western classical music

Axiomatic scale theory

Scales are a fundamental concept of musical practice around the world. They commonly exhibit symmetry properties that are formally studied using cyclic groups in the field of mathematical scale theory. This paper proposes an axiomatic framework for mathematical scale theory, embeds previous research, and presents the theory of maximally even scales and well-formed scales in a uniform and compact manner. All theorems and lemmata are completely proven in a modern and consistent notation. In particular, new simplified proofs of existing theorems such as the equivalence of non-degenerate well-formedness and Myhill's property are presented. This model of musical scales explicitly formalizes and utilizes the cyclic order relation of pitch classes

The Learnability of Goal-directedness in Jazz Music

Musicians and listeners perceive dependency structures between musical events such as chords and keys. Music theory postulates the goal-directedness of such dependencies, which manifests in formal grammar models as right-headed (head-final, left-branching) phrase structure. Goal-directedness has a direct cognitive interpretation; dependencies that point forward in time can be understood as creating expectation, and the empirical correlates of this relationship are a topic of current psychological research. This study presents a computational grammar model that represents the abstract concept of headedness but does not encode properties specific to music. Bayesian grammar learning is applied to infer a grammar for Jazz and its headedness proportions from a corpus of Jazz-chord sequences. The results show that the inferred grammar is right-headed. A second simulation using artificial data was conducted to verify the correct functionality of the headedness induction. The goal-directedness of Jazz harmony is thus demonstrated to be learnable without music-specific prior knowledge