We propose the Plaid Atoms Model (PAM), a novel Bayesian nonparametric model for grouped data. Founded on an idea of `atom skipping', PAM is part of a well-established category of models that generate dependent random distributions and clusters across multiple groups. Atom skipping referrs to stochastically assigning 0 weights to atoms in an infinite mixture. Deploying atom skipping across groups, PAM produces a dependent clustering pattern with overlapping and non-overlapping clusters across groups. As a result, interpretable posterior inference is possible such as reporting the posterior probability of a cluster being exclusive to a single group or shared among a subset of groups. We discuss the theoretical properties of the proposed and related models. Minor extensions of the proposed model for multivariate or count data are presented. Simulation studies and applications using real-world datasets illustrate the performance of the new models with comparison to existing models.

Vector quantization (VQ) is a technique to deterministically learn features with discrete codebook representations. It is commonly performed with a variational autoencoding model, VQ-VAE, which can be further extended to hierarchical structures for making high-fidelity reconstructions. However, such hierarchical extensions of VQ-VAE often suffer from the codebook/layer collapse issue, where the codebook is not efficiently used to express the data, and hence degrades reconstruction accuracy. To mitigate this problem, we propose a novel unified framework to stochastically learn hierarchical discrete representation on the basis of the variational Bayes framework, called hierarchically quantized variational autoencoder (HQ-VAE). HQ-VAE naturally generalizes the hierarchical variants of VQ-VAE, such as VQ-VAE-2 and residual-quantized VAE (RQ-VAE), and provides them with a Bayesian training scheme. Our comprehensive experiments on image datasets show that HQ-VAE enhances codebook usage and improves reconstruction performance.

The author's goal in this paper is to explore how artificial intelligence (AI) has been utilised to inform our understanding of and ability to estimate at scale a critical aspect of musical creativity - musical tempo. The central importance of tempo to musical creativity can be seen in how it is used to express specific emotions (Eerola and Vuoskoski 2013), suggest particular musical styles (Li and Chan 2011), influence perception of expression (Webster and Weir 2005) and mediate the urge to move one's body in time to the music (Burger et al. 2014). Traditional tempo estimation methods typically detect signal periodicities that reflect the underlying rhythmic structure of the music, often using some form of autocorrelation of the amplitude envelope (Lartillot and Toiviainen 2007). Recently, AI-based methods utilising convolutional or recurrent neural networks (CNNs, RNNs) on spectral representations of the audio signal have enjoyed significant improvements in accuracy (Aarabi and Peeters 2022). Common AI-based techniques include those based on probability (e.g., Bayesian approaches, hidden Markov models (HMM)), classification and statistical learning (e.g., support vector machines (SVM)), and artificial neural networks (ANNs) (e.g., self-organising maps (SOMs), CNNs, RNNs, deep learning (DL)). The aim here is to provide an overview of some of the more common AI-based tempo estimation algorithms and to shine a light on notable benefits and potential drawbacks of each. Limitations of AI in this field in general are also considered, as is the capacity for such methods to account for idiosyncrasies inherent in tempo perception, i.e., how well AI-based approaches are able to think and act like humans.

The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive capabilities and show great potential for data-driven modeling of complex physical systems. However, a critical and yet unaddressed challenge lies in the quantification of inherent uncertainties stemming from multiple sources. Addressing this gap, we introduce a novel method, DiffHybrid-UQ, for effective and efficient uncertainty propagation and estimation in hybrid neural differentiable models, leveraging the strengths of deep ensemble Bayesian learning and nonlinear transformations. Specifically, our approach effectively discerns and quantifies both aleatoric uncertainties, arising from data noise, and epistemic uncertainties, resulting from model-form discrepancies and data sparsity. This is achieved within a Bayesian model averaging framework, where aleatoric uncertainties are modeled through hybrid neural models. The unscented transformation plays a pivotal role in enabling the flow of these uncertainties through the nonlinear functions within the hybrid model. In contrast, epistemic uncertainties are estimated using an ensemble of stochastic gradient descent (SGD) trajectories. This approach offers a practical approximation to the posterior distribution of both the network parameters and the physical parameters. Notably, the DiffHybrid-UQ framework is designed for simplicity in implementation and high scalability, making it suitable for parallel computing environments. The merits of the proposed method have been demonstrated through problems governed by both ordinary and partial differentiable equations.

Semi-supervised learning (SSL) approaches have been successfully applied in a wide range of engineering and scientific fields. This paper investigates the generative model framework with a missingness mechanism for unclassified observations, as introduced by Ahfock and McLachlan(2020). We show that in a partially classified sample, a classifier using Bayes rule of allocation with a missing-data mechanism can surpass a fully supervised classifier in a two-class normal homoscedastic model, especially with moderate to low overlap and proportion of missing class labels, or with large overlap but few missing labels. It also outperforms a classifier with no missing-data mechanism regardless of the overlap region or the proportion of missing class labels. Our exploration of two- and three-component normal mixture models with unequal covariances through simulations further corroborates our findings. Finally, we illustrate the use of the proposed classifier with a missing-data mechanism on interneuronal and skin lesion datasets.

This paper presents a systematic literature review (SLR) on the explainability and interpretability of machine learning (ML) models within the context of predictive process mining, using the PRISMA framework. Given the rapid advancement of artificial intelligence (AI) and ML systems, understanding the "black-box" nature of these technologies has become increasingly critical. Focusing specifically on the domain of process mining, this paper delves into the challenges of interpreting ML models trained with complex business process data. We differentiate between intrinsically interpretable models and those that require post-hoc explanation techniques, providing a comprehensive overview of the current methodologies and their applications across various application domains. Through a rigorous bibliographic analysis, this research offers a detailed synthesis of the state of explainability and interpretability in predictive process mining, identifying key trends, challenges, and future directions. Our findings aim to equip researchers and practitioners with a deeper understanding of how to develop and implement more trustworthy, transparent, and effective intelligent systems for predictive process analytics.

We develop a new efficient sequential approximate leverage score algorithm, SALSA, using methods from randomized numerical linear algebra (RandNLA) for large matrices. We demonstrate that, with high probability, the accuracy of SALSA's approximations is within $(1 + O({\varepsilon}))$ of the true leverage scores. In addition, we show that the theoretical computational complexity and numerical accuracy of SALSA surpass existing approximations. These theoretical results are subsequently utilized to develop an efficient algorithm, named LSARMA, for fitting an appropriate ARMA model to large-scale time series data. Our proposed algorithm is, with high probability, guaranteed to find the maximum likelihood estimates of the parameters for the true underlying ARMA model. Furthermore, it has a worst-case running time that significantly improves those of the state-of-the-art alternatives in big data regimes. Empirical results on large-scale data strongly support these theoretical results and underscore the efficacy of our new approach.

During the past few decades, cognitive diagnostics modeling has attracted increasing attention in computational education communities, which is capable of quantifying the learning status and knowledge mastery levels of students. Indeed, the recent advances in neural networks have greatly enhanced the performance of traditional cognitive diagnosis models through learning the deep representations of students and exercises. Nevertheless, existing approaches often suffer from the issue of overconfidence in predicting students' mastery levels, which is primarily caused by the unavoidable noise and sparsity in realistic student-exercise interaction data, severely hindering the educational application of diagnostic feedback. To address this, in this paper, we propose a novel Reliable Cognitive Diagnosis(ReliCD) framework, which can quantify the confidence of the diagnosis feedback and is flexible for different cognitive diagnostic functions. Specifically, we first propose a Bayesian method to explicitly estimate the state uncertainty of different knowledge concepts for students, which enables the confidence quantification of diagnostic feedback. In particular, to account for potential differences, we suggest modeling individual prior distributions for the latent variables of different ability concepts using a pre-trained model. Additionally, we introduce a logical hypothesis for ranking confidence levels. Along this line, we design a novel calibration loss to optimize the confidence parameters by modeling the process of student performance prediction. Finally, extensive experiments on four real-world datasets clearly demonstrate the effectiveness of our ReliCD framework.

Synthetic data has made tremendous strides in various commercial settings including finance, healthcare, and virtual reality. We present a broad overview of prototypical applications of synthetic data in the financial sector and in particular provide richer details for a few select ones. These cover a wide variety of data modalities including tabular, time-series, event-series, and unstructured arising from both markets and retail financial applications. Since finance is a highly regulated industry, synthetic data is a potential approach for dealing with issues related to privacy, fairness, and explainability. Various metrics are utilized in evaluating the quality and effectiveness of our approaches in these applications. We conclude with open directions in synthetic data in the context of the financial domain.

The problem of estimating a probability distribution density from samples (e.g., observations, measurements, or simulation data) is ubiquitous in data science, uncertainty quantification, clustering and classification, and probabilistic modeling and inference tasks. Moreover, it is common among various scientific and engineering fields, including biology [38, 14, 1, 41, 5, 7, 12, 39]. Often, wellknown parametric density functions (dependent on few parameters), such as the Gaussian or Weibull density distribution functions, are adopted. While this may simplify certain tasks (e.g., computational ones), many of these known density distribution functions are not necessarily suitable for characterizing data that exhibit complex features, such as (spatial and/or temporal) correlations and non-Gaussian characteristics. For instance, as reported in [7], accounting for differences in the distribution densities of gene expressions can lead to improved interpretation of cancer transcriptomic data. Hence, a density estimation framework capable of characterizing a diverse range of properties is highly desirable. A measure transport approach [44, 37, 36] offers this possibility. Optimal measure transport, broadly defined, deals with the problem of minimizing the cost of transporting one (probability) measure to another.