Hierarchical representations provide powerful and principled approaches for analyzing many musical genres. Such representations have been broadly studied in music theory, for instance via Schenkerian analysis (SchA). Hierarchical music analyses, however, are highly cost-intensive; the analysis of a single piece of music requires a great deal of time and effort from trained experts. The representation of hierarchical analyses in a computer-readable format is also a further challenge. Given recent developments in hierarchical deep learning and increasing quantities of computer-readable data, there is great promise in extending such work for an automatic hierarchical representation framework. This paper thus introduces a novel approach, AutoSchA, which extends recent developments in graph neural networks (GNNs) for hierarchical music analysis. AutoSchA features three key contributions: 1) a new graph learning framework for hierarchical music representation, 2) a new graph pooling mechanism based on node isolation that directly optimizes learned pooling assignments, and 3) a state-of-the-art architecture that integrates such developments for automatic hierarchical music analysis. We show, in a suite of experiments, that AutoSchA performs comparably to human experts when analyzing Baroque fugue subjects.

Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in recent years due to their improved approximation accuracy and better calibrated uncertainty estimates compared to Random Fourier Feature (RFF) methods. However, a key limitation of QFF is that its performance can suffer from well-known pathologies related to highly oscillatory quadrature, resulting in mediocre approximation with limited features. We address this critical issue via a new Trigonometric Quadrature Fourier Feature (TQFF) method, which uses a novel non-Gaussian quadrature rule specifically tailored for the desired Fourier transform. We derive an exact quadrature rule for TQFF, along with kernel approximation error bounds for the resulting feature map. We then demonstrate the improved performance of our method over RFF and Gaussian QFF in a suite of numerical experiments and applications, and show the TQFF enjoys accurate GP approximations over a broad range of length-scales using fewer features.

Music composition and analysis is an inherently creative task, involving a combination of heart and mind. However, the vast majority of algorithmic music models completely ignore the "heart" component of music, resulting in output that often lacks the rich emotional direction found in human-composed music. Models that try to incorporate musical sentiment rely on a "valence-arousal" model, which insufficiently characterizes emotion in two dimensions. Furthermore, existing methods typically adopt a black-box, music agnostic approach, treating music-theoretical and sentimental understanding as a by-product that can be inferred given sufficient data. In this study, we introduce two major novel elements: a nuanced mixture-based representation for musical sentiment, including a web tool to gather data, as well as a sentiment- and theory-driven harmonization model, SentHYMNent. SentHYMNent employs a novel Hidden Markov Model based on both key and chord transitions, as well as sentiment mixtures, to provide a probabilistic framework for learning key modulations and chordal progressions from a given melodic line and sentiment. Furthermore, our approach leverages compositional principles, resulting in a simpler model that significantly reduces computational burden and enhances interpretability compared to current state-of-the-art algorithmic harmonization methods. Importantly, as shown in our experiments, these improvements do not come at the expense of harmonization quality. We also provide a web app where users can upload their own melodies for SentHYMNent to harmonize.

Software testing is essential for the reliable and robust development of complex software systems. This is particularly critical for cyber-physical systems (CPS), which require rigorous testing prior to deployment. The complexity of these systems limits the use of formal verification methods. Furthermore, testing and fault localization can be very costly. To mitigate this cost, we outline in this work a holistic machine-learning-guided test case design and fault localization (MaLT) framework, which leverages recent probabilistic machine learning methods to accelerate the testing of complex software systems. MaLT consists of three steps: (i) the construction of a suite of test cases using a covering array for initial testing, (ii) the investigation of posterior root cause probabilities via a Bayesian fault localization procedure, then (iii) the use of such Bayesian analysis to guide selection of subsequent test cases via active learning. The proposed MaLT framework can thus facilitate efficient identification and subsequent diagnosis of software faults with limited test runs. This framework has potential for integration with an assertion-based test oracle approach, which may prove to be an efficient and cost-effective way of integrating light-weight formal methods with testing.

The fast-growing demand for algorithmic music generation is found throughout entertainment, art, education, etc. Unfortunately, most recent models are practically impossible to interpret or musically fine-tune, as they use deep neural networks with thousands of parameters. We introduce an interpretable, flexible, and interactive model, SchenkComposer, for melody generation that empowers users to be creative in all aspects of the music generation pipeline and allows them to learn from the process. We divide the task of melody generation into steps based on the process that a human composer using music-theoretical domain knowledge might use. First, the model determines phrase structure based on form analysis and identifies an appropriate number of measures. Using concepts from Schenkerian analysis, the model then finds a fitting harmonic rhythm, middleground harmonic progression, foreground rhythm, and melody in a hierarchical, scaffolded approach using a probabilistic context-free grammar based on musical contours. By incorporating theories of musical form and harmonic structure, our model produces music with long-term structural coherence. In extensive human experiments, we find that music generated with our approach successfully passes a Turing test in human experiments while current state-of-the-art approaches fail, and we further demonstrate superior performance and preference for our melodies compared to existing melody generation methods. Additionally, we developed and deployed a public website for SchenkComposer, and conducted preliminary user surveys. Through analysis, we show the strong viability and enjoyability of SchenkComposer.

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The main technique is based on the concentration inequalities of continuous-time martingales. We compare our method to the previously-derived asymptotic Hawkes process confidence interval, and demonstrate the strengths of our method in an application to neuronal connectivity reconstruction.

We propose a novel, information-theoretic mask construction method, called MaxEnt, for efficient data acquisition for low-rank matrix recovery. Fundamental to this design approach is the maximum entropy principle, which states that the measurement masks which maximize the entropy of observations also maximize the information gain on the unknown matrix X. Coupled with a low-rank stochastic model for X, such a principle (i) reveals novel connections between information-theoretic sampling, compressive sensing and coding theory, and (ii) yields efficient mask construction algorithms for recovering X, which significantly outperform random measurements. We demonstrate the usefulness of MaxEnt in two real-world applications on image recovery and text document indexing1.