In jazz, a contrafact is a new melody composed over an existing, but often reharmonized chord progression. Because reharmonization can introduce a wide range of variations, detecting contrafacts is a challenging task. This paper develops a novel vector-space model to represent chord progressions, and uses it for contrafact detection. The process applies principles from music theory to reduce the dimensionality of chord space, determine a common key signature representation, and compute a chordal co-occurrence matrix. The rows of the matrix form a basis for the vector space in which chord progressions are represented as piecewise linear functions, and harmonic similarity is evaluated by computing the membrane area, a novel distance metric. To illustrate our method's effectiveness, we apply it to the Impro-Visor corpus of 2,612 chord progressions, and present examples demonstrating its ability to account for reharmonizations and find contrafacts.

Inspired by the success of control barrier functions (CBFs) in addressing safety, and the rise of data-driven techniques for modeling functions, we propose a non-parametric approach for online synthesis of CBFs using Gaussian Processes (GPs). Mathematical constructs such as CBFs have achieved safety by designing a candidate function a priori. However, designing such a candidate function can be challenging. A practical example of such a setting would be to design a CBF in a disaster recovery scenario where safe and navigable regions need to be determined. The decision boundary for safety in such an example is unknown and cannot be designed a priori. In our approach, we work with safety samples or observations to construct the CBF online by assuming a flexible GP prior on these samples, and term our formulation as a Gaussian CBF. GPs have favorable properties, in addition to being non-parametric, such as analytical tractability and robust uncertainty estimation. This allows realizing the posterior components with high safety guarantees by incorporating variance estimation, while also computing associated partial derivatives in closed-form to achieve safe control. Moreover, the synthesized safety function from our approach allows changing the corresponding safe set arbitrarily based on the data, thus allowing non-convex safe sets. We validate our approach experimentally on a quadrotor by demonstrating safe control for fixed but arbitrary safe sets and collision avoidance where the safe set is constructed online. Finally, we juxtapose Gaussian CBFs with regular CBFs in the presence of noisy states to highlight its flexibility and robustness to noise. The experiment video can be seen at: https://youtu.be/HX6uokvCiGk.

Political science research often requires constructing a race/ethnicity proxy variable for datasets that do not contain it, like voter registration files, lists of electoral candidates, or political donation records. Constructing such a proxy is an important step for conducting ecological inference in voting rights litigation (Barreto et al. [2019], Imai and Khanna [2016]), redistricting (DeLuca and Curiel [2022], Kenny et al. [2021]), and substantive research on the role of race/ethnicity in politics (Enos [2016], Enos et al. [2019], Grumbach and Sahn [2020]). The most common method for proxying race/ethnicity is Bayesian Improved Surname Geocoding (BISG), which uses Bayes' rule to compute a probability distribution over race/ethnicity categories conditional on a voter's surname and where they live (Elliott et al. [2008, 2009]). BISG has attained widespread popularity due to its parsimony, computational efficiency, and superior performance when compared to existing alternatives, namely spatial interpolation of Census racial-ethnic composition from Census geographies (Imai and Khanna [2016], Clark et al. [2021], Shah and Davis [2017]). While BISG performs well compared to the small suite of existing alternatives, it has not yet been benchmarked against machine learning (ML) models, which can produce race/ethnicity predictions from more flexible and potentially more accurate models. In this paper I present the results of such a benchmark. I train a range of machine learning models using voter registration data from Florida, Georgia, North Carolina, and a portion of California where voters self-report their race/ethnicity upon registration. The registries in these states contain over 26 million labelled observations, which equates to greater than a five percent non-representative sample of the United States electorate. I then compare BISG against predictions from these models made out-of-state.

--States of quantum many-body systems are defined in a high-dimensional Hilbert space, where rich and complex interactions among subsystems can be modelled. In machine learning, complex multiple multilinear correlations may also exist within input features. In this paper, we present a quantum-inspired multilinear model, named Residual T ensor Train (ResTT), to capture the multiple multilinear correlations of features, from low to high orders, within a single model. ResTT is able to build a robust decision boundary in a high-dimensional space for solving fitting and classification tasks. In particular, we prove that the fully-connected layer and the V olterra series can be taken as special cases of ResTT . Furthermore, we derive the rule for weight initialization that stabilizes the training of ResTT based on a mean-field analysis. We prove that such a rule is much more relaxed than that of TT, which means ResTT can easily address the vanishing and exploding gradient problem that exists in the existing TT models. Numerical experiments demonstrate that ResTT outperforms the state-of-the-art tensor network and benchmark deep learning models on MNIST and Fashion-MNIST datasets. Moreover, ResTT achieves better performance than other statistical methods on two practical examples with limited data which are known to have complex feature interactions. Impact Statement --Optimal learning may require considering high-order multilinear feature interactions. Recently, quantum-inspired tensor networks have been proposed to exploit high-order correlations. However, the vanilla tensor networks are specialized in capturing only one type of multilinear feature interaction.

Existing studies on data imbalance focus on single-domain settings, i.e., samples are from the same data distribution. However, natural data can originate from distinct domains, where a minority class in one domain could have abundant instances from other domains. We formalize the task of Multi-Domain Long-Tailed Recognition (MDLT), which learns from multi-domain imbalanced data, addresses label imbalance, domain shift, and divergent label distributions across domains, and generalizes to all domain-class pairs. We first develop the domain-class transferability graph, and show that such transferability governs the success of learning in MDLT. We then propose BoDA, a theoretically grounded learning strategy that tracks the upper bound of transferability statistics, and ensures balanced alignment and calibration across imbalanced domain-class distributions. We curate five MDLT benchmarks based on widely-used multi-domain datasets, and compare BoDA to twenty algorithms that span different learning strategies. Extensive and rigorous experiments verify the superior performance of BoDA. Further, as a byproduct, BoDA establishes new state-of-the-art on Domain Generalization benchmarks, highlighting the importance of addressing data imbalance across domains, which can be crucial for improving generalization to unseen domains. Code and data are available at: https://github.com/YyzHarry/multi-domain-imbalance.

Information on cyber-related crimes, incidents, and conflicts is abundantly available in numerous open online sources. However, processing the large volumes and streams of data is a challenging task for the analysts and experts, and entails the need for newer methods and techniques. In this article we present and implement a novel knowledge graph and knowledge mining framework for extracting the relevant information from free-form text about incidents in the cyberdomain. The framework includes a machine learning based pipeline for generating graphs of organizations, countries, industries, products and attackers with a non-technical cyber-ontology. The extracted knowledge graph is utilized to estimate the incidence of cyberattacks on a given graph configuration. We use publicly available collections of real cyber-incident reports to test the efficacy of our methods. The knowledge extraction is found to be sufficiently accurate, and the graph-based threat estimation demonstrates a level of correlation with the actual records of attacks. In practical use, an analyst utilizing the presented framework can infer additional information from the current cyber-landscape in terms of risk to various entities and propagation of the risk heuristic between industries and countries.

Multi-view clustering (MVC) optimally integrates complementary information from different views to improve clustering performance. Although demonstrating promising performance in various applications, most of existing approaches directly fuse multiple pre-specified similarities to learn an optimal similarity matrix for clustering, which could cause over-complicated optimization and intensive computational cost. In this paper, we propose late fusion MVC via alignment maximization to address these issues. To do so, we first reveal the theoretical connection of existing k-means clustering and the alignment between base partitions and the consensus one. Based on this observation, we propose a simple but effective multi-view algorithm termed LF-MVC-GAM. It optimally fuses multiple source information in partition level from each individual view, and maximally aligns the consensus partition with these weighted base ones. Such an alignment is beneficial to integrate partition level information and significantly reduce the computational complexity by sufficiently simplifying the optimization procedure. We then design another variant, LF-MVC-LAM to further improve the clustering performance by preserving the local intrinsic structure among multiple partition spaces. After that, we develop two three-step iterative algorithms to solve the resultant optimization problems with theoretically guaranteed convergence. Further, we provide the generalization error bound analysis of the proposed algorithms. Extensive experiments on eighteen multi-view benchmark datasets demonstrate the effectiveness and efficiency of the proposed LF-MVC-GAM and LF-MVC-LAM, ranging from small to large-scale data items. The codes of the proposed algorithms are publicly available at https://github.com/wangsiwei2010/latefusionalignment.

As machine learning (ML) models gain traction in clinical applications, understanding the impact of clinician and societal biases on ML models is increasingly important. While biases can arise in the labels used for model training, the many sources from which these biases arise are not yet well-studied. In this paper, we highlight disparate censorship (i.e., differences in testing rates across patient groups) as a source of label bias that clinical ML models may amplify, potentially causing harm. Many patient risk-stratification models are trained using the results of clinician-ordered diagnostic and laboratory tests of labels. Patients without test results are often assigned a negative label, which assumes that untested patients do not experience the outcome. Since orders are affected by clinical and resource considerations, testing may not be uniform in patient populations, giving rise to disparate censorship. Disparate censorship in patients of equivalent risk leads to undertesting in certain groups, and in turn, more biased labels for such groups. Using such biased labels in standard ML pipelines could contribute to gaps in model performance across patient groups. Here, we theoretically and empirically characterize conditions in which disparate censorship or undertesting affect model performance across subgroups. Our findings call attention to disparate censorship as a source of label bias in clinical ML models.

Nearest neighbour graphs are widely used to capture the geometry or topology of a dataset. One of the most common strategies to construct such a graph is based on selecting a fixed number k of nearest neighbours (kNN) for each point. However, the kNN heuristic may become inappropriate when sampling density or noise level varies across datasets. Strategies that try to get around this typically introduce additional parameters that need to be tuned. We propose a simple approach to construct an adaptive neighbourhood graph from a single parameter, based on quadratically regularised optimal transport. Our numerical experiments show that graphs constructed in this manner perform favourably in unsupervised and semi-supervised learning applications.

This study focuses on exploring the use of local interpretability methods for explaining time series clustering models. Many of the state-of-the-art clustering models are not directly explainable. To provide explanations for these clustering algorithms, we train classification models to estimate the cluster labels. Then, we use interpretability methods to explain the decisions of the classification models. The explanations are used to obtain insights into the clustering models. We perform a detailed numerical study to test the proposed approach on multiple datasets, clustering models, and classification models. The analysis of the results shows that the proposed approach can be used to explain time series clustering models, specifically when the underlying classification model is accurate. Lastly, we provide a detailed analysis of the results, discussing how our approach can be used in a real-life scenario.