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For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended…
Orchestral concert programming is a challenging, yet critical task for expanding audience engagement and is usually driven by qualitative heuristics and common musical practices. Quantitative analysis of orchestral programming has been…
Many people enjoy classical symphonic music. Its diverse instrumentation makes for a rich listening experience. This diversity adds to the conductor's expressive freedom to shape the sound according to their imagination. As a result, the…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…
We present a Bayesian mixture model for estimating the joint distribution of mixed ordinal, nominal, and continuous data conditional on a set of fixed variables. The model uses multivariate normal and categorical mixture kernels for the…
Compositional data analysis is concerned with multivariate data that have a constant sum, usually 1 or 100\%. These are data often found in biochemistry and geochemistry, but also in the social sciences, when relative values are of interest…
In this work we test the most widely used methods for fitting the composition fraction in data, namely maximum likelihood, $\chi^2$, mean value of the distributions and mean value of the posterior probability function. We discuss the…
The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…
Description of system containing classical and quantum subsystems by means of tomographic probability distributions is considered. Evolution equation of the system states is studied.
Charge transfer statistics of quantum particles is obtained by analysing the time evolution of the many-body wave function. Exploiting properly chosen gauge transformations, we construct the probabilities for transfers of a discrete number…
The objective of advanced topic modeling is not only to explore latent topical structures, but also to estimate relationships between the discovered topics and theoretically relevant metadata. Methods used to estimate such relationships…
We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The…
This paper presents a discriminative classifier for compositional data. This classifier is based on the posterior distribution of the Generalized Dirichlet which is the discriminative counterpart of Generalized Dirichlet mixture model.…
This application-oriented study concerns computational musicology, which makes use of grammar systems. We define multi-generative rule-synchronized scattered-context grammar systems (without erasing rules) and demonstrates how to…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…
We develop a likelihood methodology which can be used to search for evidence of burst repetition in the BATSE catalog, and to study the properties of the repetition signal. We use a simplified model of burst repetition in which a number…
Discrete data such as counts of microbiome taxa resulting from next-generation sequencing are routinely encountered in bioinformatics. Taxa count data in microbiome studies are typically high-dimensional, over-dispersed, and can only reveal…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…