Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in existing studies. To address this problem, we introduce CAF-PoNo (Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Through normalizing flows, our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification through statistical independence testing. Furthermore, the proposed approach exhibits remarkable extensibility, as it can be seamlessly expanded to facilitate multivariate causal discovery via causal order identification, empowering us to efficiently unravel complex causal relationships. Extensive experimental evaluations on both simulated and real datasets consistently demonstrate that the proposed method outperforms several state-of-the-art approaches in both bivariate and multivariate causal discovery tasks.

Bayesian causal discovery offers the power to quantify epistemic uncertainties among a broad range of structurally diverse causal theories potentially explaining the data, represented in forms of directed acyclic graphs (DAGs). However, existing methods struggle with efficient DAG sampling due to the complex acyclicity constraint. In this study, we propose a scalable Bayesian approach to effectively learn the posterior distribution over causal graphs given observational data thanks to the ability to generate DAGs without explicitly enforcing acyclicity. Specifically, we introduce a novel differentiable DAG sampling method that can generate a valid acyclic causal graph by mapping an unconstrained distribution of implicit topological orders to a distribution over DAGs. Given this efficient DAG sampling scheme, we are able to model the posterior distribution over causal graphs using a simple variational distribution over a continuous domain, which can be learned via the variational inference framework. Extensive empirical experiments on both simulated and real datasets demonstrate the superior performance of the proposed model compared to several state-of-the-art baselines.

We develop a novel measurement framework based on a Gaussian process coregionalization model to address a long-lasting debate in psychometrics: whether psychological features like personality share a common structure across the population, vary uniquely for individuals, or some combination. We propose the idiographic personality Gaussian process (IPGP) framework, an intermediate model that accommodates both shared trait structure across a population and "idiographic" deviations for individuals. IPGP leverages the Gaussian process coregionalization model to handle the grouped nature of battery responses, but adjusted to non-Gaussian ordinal data. We further exploit stochastic variational inference for efficient latent factor estimation required for idiographic modeling at scale. Using synthetic and real data, we show that IPGP improves both prediction of actual responses and estimation of individualized factor structures relative to existing benchmarks. In a third study, we show that IPGP also identifies unique clusters of personality taxonomies in real-world data, displaying great potential in advancing individualized approaches to psychological diagnosis and treatment.

Against the backdrop of the European Union's commitment to achieve climate neutrality by 2050, efforts to improve energy efficiency are being intensified. The manufacturing industry is a key focal point of these endeavors due to its high final electrical energy demand, while simultaneously facing a growing shortage of skilled workers crucial for meeting established goals. Expert systems (ESs) offer the chance to overcome this challenge by automatically identifying potential energy efficiency improvements and thereby playing a significant role in reducing electricity consumption. This paper systematically reviews state-of-the-art approaches of ESs aimed at improving energy efficiency in industry, with a focus on manufacturing. The literature search yields 1692 results, of which 54 articles published between 1987 and 2023 are analyzed in depth. These publications are classified according to the system boundary, manufacturing type, application perspective, application purpose, ES type, and industry. Furthermore, we examine the structure, implementation, utilization, and development of ESs in this context. Through this analysis, the review reveals research gaps, pointing toward promising topics for future research.

We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the inverse PDE PINN solutions. Recently, the Bayesian PINN (BPINN) method was proposed, where the posterior distribution of the PINN parameters was formulated using the Bayes' theorem and sampled using approximate inference methods such as the Hamiltonian Monte Carlo (HMC) and variational inference (VI) methods. In this work, we demonstrate that HMC fails to converge for non-linear inverse PDE problems. As an alternative to HMC, we sample the distribution by solving the stochastic optimization problem obtained by randomizing the PINN loss function. The effectiveness of the rPINN method is tested for linear and non-linear Poisson equations, and the diffusion equation with a high-dimensional space-dependent diffusion coefficient. The rPINN method provides informative distributions for all considered problems. For the linear Poisson equation, HMC and rPINN produce similar distributions, but rPINN is on average 27 times faster than HMC. For the non-linear Poison and diffusion equations, the HMC method fails to converge because a single HMC chain cannot sample multiple modes of the posterior distribution of the PINN parameters in a reasonable amount of time.

This paper presents a novel neuro-fuzzy model, termed fuzzy recurrent stochastic configuration networks (F-RSCNs), for industrial data analytics. Unlike the original recurrent stochastic configuration network (RSCN), the proposed F-RSCN is constructed by multiple sub-reservoirs, and each sub-reservoir is associated with a Takagi-Sugeno-Kang (TSK) fuzzy rule. Through this hybrid framework, first, the interpretability of the model is enhanced by incorporating fuzzy reasoning to embed the prior knowledge into the network. Then, the parameters of the neuro-fuzzy model are determined by the recurrent stochastic configuration (RSC) algorithm. This scheme not only ensures the universal approximation property and fast learning speed of the built model but also overcomes uncertain problems, such as unknown dynamic orders, arbitrary structure determination, and the sensitivity of learning parameters in modelling nonlinear dynamics. Finally, an online update of the output weights is performed using the projection algorithm, and the convergence analysis of the learning parameters is given. By integrating TSK fuzzy inference systems into RSCNs, F-RSCNs have strong fuzzy inference capability and can achieve sound performance for both learning and generalization. Comprehensive experiments show that the proposed F-RSCNs outperform other classical neuro-fuzzy and non-fuzzy models, demonstrating great potential for modelling complex industrial systems.

End-to-end (E2E) keyword search (KWS) has emerged as an alternative and complimentary approach to conventional keyword search which depends on the output of automatic speech recognition (ASR) systems. While E2E methods greatly simplify the KWS pipeline, they generally have worse performance than their ASR-based counterparts, which can benefit from pretraining with untranscribed data. In this work, we propose a method for pretraining E2E KWS systems with untranscribed data, which involves using acoustic unit discovery (AUD) to obtain discrete units for untranscribed data and then learning to locate sequences of such units in the speech. We conduct experiments across languages and AUD systems: we show that finetuning such a model significantly outperforms a model trained from scratch, and the performance improvements are generally correlated with the quality of the AUD system used for pretraining.

Tabular synthesis models remain ineffective at capturing complex dependencies, and the quality of synthetic data is still insufficient for comprehensive downstream tasks, such as prediction under distribution shifts, automated decision-making, and cross-table understanding. A major challenge is the lack of prior knowledge about underlying structures and high-order relationships in tabular data. We argue that a systematic evaluation on high-order structural information for tabular data synthesis is the first step towards solving the problem. In this paper, we introduce high-order structural causal information as natural prior knowledge and provide a benchmark framework for the evaluation of tabular synthesis models. The framework allows us to generate benchmark datasets with a flexible range of data generation processes and to train tabular synthesis models using these datasets for further evaluation. We propose multiple benchmark tasks, high-order metrics, and causal inference tasks as downstream tasks for evaluating the quality of synthetic data generated by the trained models. Our experiments demonstrate to leverage the benchmark framework for evaluating the model capability of capturing high-order structural causal information. Furthermore, our benchmarking results provide an initial assessment of state-of-the-art tabular synthesis models. They have clearly revealed significant gaps between ideal and actual performance and how baseline methods differ. Our benchmark framework is available at URL https://github.com/TURuibo/CauTabBench.

Their use as a decision support tool in business and OR has been increasing over the years, including case studies in project management (van Dorp, 2020), supply chain (Garvey et al., 2015), marketing (Hosseini, 2021), and logistics (Qazi, 2022), among others. BNs are defined by two components: a directed acyclic graph (DAG) where each node is a variable of interest and edges represent the, possibly causal, relationship between them; a conditional probability table (CPT) for each node of the DAG reporting the probability distribution of the associated variable conditional on its parents. BNs are highly interpretable due to their graphical nature, representing the probabilistic relationships between variables, making it easy for users to understand and trace the influence of one variable on another. With explainability now recognized as critical for the use of AI in applied research (Rudin, 2019), including in OR (De Bock et al., 2023), BNs stand out by providing transparent and intuitive explanations, thereby enhancing trust and clarity in decision-making processes. The underlying DAG and the associated CPTs can be learned from data using machine learning algorithms or elicited using experts' opinions and knowledge. There is now a vast amount of algorithms to learn BN from data (e.g.

Deterministic policies are often preferred over stochastic ones when implemented on physical systems. They can prevent erratic and harmful behaviors while being easier to implement and interpret. However, in practice, exploration is largely performed by stochastic policies. First-order Bayesian Optimization (BO) methods offer a principled way of performing exploration using deterministic policies. This is done through a learned probabilistic model of the objective function and its gradient. Nonetheless, such approaches treat policy search as a black-box problem, and thus, neglect the reinforcement learning nature of the problem. In this work, we leverage the performance difference lemma to introduce a novel mean function for the probabilistic model. This results in augmenting BO methods with the action-value function. Hence, we call our method Augmented Bayesian Search~(ABS). Interestingly, this new mean function enhances the posterior gradient with the deterministic policy gradient, effectively bridging the gap between BO and policy gradient methods. The resulting algorithm combines the convenience of the direct policy search with the scalability of reinforcement learning. We validate ABS on high-dimensional locomotion problems and demonstrate competitive performance compared to existing direct policy search schemes.