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.

Scalable Collaborative Bayesian Preference Learning

Mohammad Emtiyaz Khan, Young Jun Ko, Matthias Seeger

Learning about users’ utilities from preference, discrete choice or implicit feedback data is of integral importance in e-commerce, targeted advertising and web search. Due to the sparsity and diffuse nature of data, Bayesian approaches hold much promise, yet most prior work does not scale up to realistic data sizes. We shed light on why inference for such settings is computationally difficult for standard machine learning methods, most of which focus on predicting explicit ratings only. To simplify the difficulty, we present a novel expectation maximization algorithm, driven by expectation propagation approximate inference, which scales to very large datasets without requiring strong factorization assumptions. Our utility model uses both latent bilinear collaborative filtering and non-parametric Gaussian process (GP) regression. In experiments on large real-world datasets, our method gives substantially better results than either matrix factorization or GPs in isolation, and converges significantly faster.

2014

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

Our brain continuously self-organizes to construct and maintain an internal representation of the world based on the information arriving through sensory stimuli. Remarkably, cortical areas related to different sensory modalities appear to share the same functional unit, the neuron, and develop through the same learning mechanism, synaptic plasticity. It motivates the conjecture of a unifying theory to explain cortical representational learning across sensory modalities. In this thesis we present theories and computational models of learning and optimization in neural networks, postulating functional properties of synaptic plasticity that support the apparent universal learning capacity of cortical networks. In the past decades, a variety of theories and models have been proposed to describe receptive field formation in sensory areas. They include normative models such as sparse coding, and bottom-up models such as spike-timing dependent plasticity. We bring together candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. A surprising result is that our findings are independent of specific details, and allow for robust predictions of the learned receptive fields. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. The Hebbian learning theory substantiates that synaptic plasticity can be interpreted as an optimization procedure, implementing stochastic gradient descent. In stochastic gradient descent inputs arrive sequentially, as in sensory streams. However, individual data samples have very little information about the correct learning signal, and it becomes a fundamental problem to know how many samples are required for reliable synaptic changes. Through estimation theory, we develop a novel adaptive learning rate model, that adapts the magnitude of synaptic changes based on the statistics of the learning signal, enabling an optimal use of data samples. Our model has a simple implementation and demonstrates improved learning speed, making this a promising candidate for large artificial neural network applications. The model also makes predictions on how cortical plasticity may modulate synaptic plasticity for optimal learning. The optimal sampling size for reliable learning allows us to estimate optimal learning times for a given model. We apply this theory to derive analytical bounds on times for the optimization of synaptic connections. First, we show this optimization problem to have exponentially many saddle-nodes, which lead to small gradients and slow learning. Second, we show that the number of input synapses to a neuron modulates the magnitude of the initial gradient, determining the duration of learning. Our final result reveals that the learning duration increases supra-linearly with the number of synapses, suggesting an effective limit on synaptic connections and receptive field sizes in developing neural networks.

EPFL2016

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Emmanouil Angelidis, Alain Destexhe, Egidio Falotico, Emanuele Formento, Marc-Oliver Gewaltig, Auke Ijspeert, Silvestro Micera, Maria Pasquini, Shravan Tata Ramalingasetty, Lorenzo Vannucci, Axel von Arnim

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

FRONTIERS MEDIA SA2020

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

EPFL2016