Dynamic Bayesian networks for symbolic polyphonic pitch modeling

National audienceThe performance of many MIR analysis algorithms, most importantly polyphonic pitch transcription, can be improved by introducing musicological knowledge to the estimation process. We have developed a probabilistically rigorous musicological model that takes into account dependencies between consequent musical notes and consequent chords, as well as the dependencies between chords, notes and the observed note saliences. We investigate its modeling potential by measuring and comparing the cross-entropy with symbolic (MIDI) data

Melody harmonisation with interpolated probabilistic models

Automatic melody harmonisation aims to create a matching chordal accompaniment to a given monophonic melody. Several methods have been proposed to this aim, which are generally based on musicological expertise or on unsupervised probabilistic modelling. Among the latter category of methods, most systems use the generative hidden Markov model (HMM), in which the chords are the hidden states and the melody is the observed output. Relations to other variables, such as the tonality and scale or the metric structure, are handled by training multiple HMMs or are often simply ignored. In this paper, we propose a means of combining multiple probabilistic models of various musical variables into a versatile harmonisation system by means of model interpolation. The result is a joint model belonging to the class of discriminative models, which in recent years have proven to be capable of outperforming generative models in many tasks. We first evaluate our models in terms of their normalized negative log-likelihood, or cross-entropy. We observe that log-linear interpolation offers lower cross-entropy than linear interpolation and that combining several models by means of log-linear interpolation lowers the cross-entropy compared to the best of the component models. We then perform a series of harmonisation experiments and show that the proposed log-linearly interpolated model offers higher chord root accuracy than a reference musicological rule-based harmoniser by up to 5% absolute.L'harmonisation automatique de mélodies vise à créer une suite d'accords accompagnant une mélodie donnée. Plusieurs méthodes ont été proposées dans ce but, généralement basées sur des règles musicologiques expertes ou sur une modélisation probabiliste non supervisée. Parmi cette dernière catégorie de méthodes, la plupart utilisent un modèle de Markov caché (MMC) génératif, dont les états cachés sont les accords et l'observation la mélodie. Les dépendances aux autres variables telles que la tonalité ou la structure métrique sont modélisées par des MMCs multiples ou simplement ignorées. Dans ce papier, nous proposons un moyen de combiner plusieurs modèles probabilistes de différentes variables musicales par le biais d'une interpolation de modèles. Cela aboutit à un modèle combiné appartenant à la catégorie des modèles discriminants, dont il a été démontré ces dernières années qu'ils dépassent la performance des modèles génératifs pour de nombreuses tâches. Nous évaluons d'abord nos modèles en terme de l'opposé de leur log-vraisemblance normalisée, ou entropie croisée. Nous observons que l'interpolation log-linéaire diminue l'entropie croisée par rapport à l'interpolation linéaire et que la combinaison de plusieurs modèles par interpolation log-linéaire diminue l'entropie croisée par rapport au meilleur modèle individuel. Nous effectuons ensuite un ensemble d'expériences d'harmonisation et montrons que le modèle par interpolation log-linéaire proposé améliore la précision d'estimation de la fondamentale des accords de 5% dans l'absolu par rapport un algorithme d'harmonisation de référence basé sur des règles musicologiques expertes

A music structure inference algorithm based on symbolic data analysis

International audienceThe present document describes a music structure inference algorithm submitted to the MIREX 2011 evaluation campaign (structural segmentation task). It consists of 3 stages : symbolic feature extraction, structural segment boundary estimation, and structural segment clustering. We consider as inputs chord estimations from the system of Ueda et al., expressed at the 2-beat scale. Beats and downbeats are estimated by the system of Davies et al. The structural segmentation step uses a regularity-constrained Viterbi approach. It assumes that the structure of pop songs is generally based on a few typical segments, whose sizes are called structural pulsation periods. The segments are then clustered according to their similarity, through the minimization of an adaptive model selection criterion

Continuous Simulation, Differential Inclusions, Uncertainty, and Traveling in Time

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A market model: uncertainty and reachable sets

Uncertain parameters are always present in models that include human factor. In marketing the uncertain consumer behavior makes it difficult to predict the future events and elaborate good marketing strategies. Sometimes uncertainty is being modeled using stochastic variables. Our approach is quite different. The dynamic market with uncertain parameters is treated using differential inclusions, which permits to determine the corresponding reachable sets. This is not a statistical analysis. We are looking for solutions to the differential inclusions. The purpose of the research is to find the way to obtain and visualise the reachable sets, in order to know the limits for the important marketing variables. The modeling method consists in defining the differential inclusion and find its solution, using the differential inclusion solver developed by the author. As the result we obtain images of the reachable sets where the main control parameter is the share of investment, being a part of the revenue. As an additional result we also can define the optimal investment strategy. The conclusion is that the differential inclusion solver can be a useful tool in market model analysis

Simulation of The Dynamic Interactions Between Terror and Anti-Terror Organizational Structures

A discrete-event model of the dynamics of certain social structures is presented. The structures include terrorist organizations, anti-terrorism and terrorism-supporting structures. The simulation shows the process of creating the structures and their interactions. As a result, we can see how the structure size changes and how the interactions work, and the process of destroying terrorist organization links by the anti-terrorist agents. The simulation is agent-oriented and uses the PASION simulation system.Simulation, Modeling, Terrorism, Discrete Event, Agent-Oriented, Social Simulation, Soft Systems