Since its inception, Fuzzy Set has been widely used to handle uncertainty and imprecision in decision-making. However, conventional fuzzy sets, often referred to as type-1 fuzzy sets (T1FSs) have limitations in capturing higher levels of uncertainty, particularly when decision-makers (DMs) express hesitation or ambiguity in membership degree. To address this, Interval Type-2 Fuzzy Sets (IT2FSs) have been introduced by incorporating uncertainty in membership degree allocation, which enhanced flexibility in modelling subjective judgments. Despite their advantages, existing IT2FS construction methods often lack active involvement from DMs and that limits the interpretability and effectiveness of decision models. This study proposes a socio-technical co-constructive approach for developing IT2FS models of linguistic terms by facilitating the active involvement of DMs in preference elicitation and its application in multicriteria decision-making (MCDM) problems. Our methodology is structured in two phases. The first phase involves an interactive process between the DM and the decision analyst, in which a modified version of Deck-of-Cards (DoC) method is proposed to construct T1FS membership functions on a ratio scale. We then extend this method to incorporate ambiguity in subjective judgment and that resulted in an IT2FS model that better captures uncertainty in DM's linguistic assessments. The second phase formalizes the constructed IT2FS model for application in MCDM by defining an appropriate mathematical representation of such information, aggregation rules, and an admissible ordering principle. The proposed framework enhances the reliability and effectiveness of fuzzy decision-making not only by accurately representing DM's personalized semantics of linguistic information.

Probabilistic circuits (PCs) enable us to learn joint distributions over a set of random variables and to perform various probabilistic queries in a tractable fashion. Though the tractability property allows PCs to scale beyond non-tractable models such as Bayesian Networks, scaling training and inference of PCs to larger, real-world datasets remains challenging. To remedy the situation, we show how PCs can be learned across multiple machines by recursively partitioning a distributed dataset, thereby unveiling a deep connection between PCs and federated learning (FL). This leads to federated circuits (FCs) -- a novel and flexible federated learning (FL) framework that (1) allows one to scale PCs on distributed learning environments (2) train PCs faster and (3) unifies for the first time horizontal, vertical, and hybrid FL in one framework by re-framing FL as a density estimation problem over distributed datasets. We demonstrate FC's capability to scale PCs on various large-scale datasets. Also, we show FC's versatility in handling horizontal, vertical, and hybrid FL within a unified framework on multiple classification tasks.

The double hypothesis test (DHT) is a test that allows controlling Type I (producer) and Type II (consumer) errors. It is possible to say whether the batch has a defect rate, p, between 1.5 and 2%, or between 2 and 5%, or between 5 and 10%, and so on, until finding a required value for this probability. Using the two probabilities side by side, the Type I error for the lower probability distribution and the Type II error for the higher probability distribution, both can be controlled and minimized. It can be applied in the development or manufacturing process of a batch of components, or in the case of purchasing from a supplier, when the percentage of defects (p) is unknown, considering the technology and/or process available to obtain them. The power of the test is amplified by the joint application of the Limit of Successive Failures (LSF) related to the Renewal Theory. To enable the choice of the most appropriate algorithm for each application. Four distributions are proposed for the Bernoulli event sequence, including their computational efforts: Binomial, Binomial approximated by Poisson, and Binomial approximated by Gaussian (with two variants). Fuzzy logic rules are also applied to facilitate decision-making.

Research on learned cardinality estimation has achieved significant progress in recent years. However, existing methods still face distinct challenges that hinder their practical deployment in production environments. We conceptualize these challenges as the "Trilemma of Cardinality Estimation", where learned cardinality estimation methods struggle to balance generality, accuracy, and updatability. To address these challenges, we introduce DistJoin, a join cardinality estimator based on efficient distribution prediction using multi-autoregressive models. Our contributions are threefold: (1) We propose a method for estimating both equi and non-equi join cardinality by leveraging the conditional probability distributions of individual tables in a decoupled manner. (2) To meet the requirements of efficient training and inference for DistJoin, we develop Adaptive Neural Predicate Modulation (ANPM), a high-throughput conditional probability distribution estimation model. (3) We formally analyze the variance of existing similar methods and demonstrate that such approaches suffer from variance accumulation issues. To mitigate this problem, DistJoin employs a selectivity-based approach rather than a count-based approach to infer join cardinality, effectively reducing variance. In summary, DistJoin not only represents the first data-driven method to effectively support both equi and non-equi joins but also demonstrates superior accuracy while enabling fast and flexible updates. We evaluate DistJoin on JOB-light and JOB-light-ranges, extending the evaluation to non-equi join conditions. The results demonstrate that our approach achieves the highest accuracy, robustness to data updates, generality, and comparable update and inference speed relative to existing methods.

Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of random variables. Most recently, a reinforcement learning approach has been proposed to find efficient contraction orders in tensor networks. Due to the duality between graphical models and tensor networks, we adapt this approach to probabilistic inference in graphical models. Furthermore, we incorporate structure exploitation into the process of finding an optimal order. Currently, the agent's cost function is formulated in terms of intermediate result sizes which are exponential in the number of indices (i.e., random variables). We show that leveraging specific structures during inference allows for introducing compact encodings of intermediate results which can be significantly smaller. By considering the compact encoding sizes for the cost function instead, we enable the agent to explore more efficient contraction orders. The structure we consider in this work is the presence of local symmetries (i.e., symmetries within a model's factors).

In recent years, the exceptional performance of generative models in generative tasks has sparked significant interest in their integration into decision-making processes. Due to their ability to handle complex data distributions and their strong model capacity, generative models can be effectively incorporated into decision-making systems by generating trajectories that guide agents toward high-reward state-action regions or intermediate sub-goals. This paper presents a comprehensive review of the application of generative models in decision-making tasks. We classify seven fundamental types of generative models: energy-based models, generative adversarial networks, variational autoencoders, normalizing flows, diffusion models, generative flow networks, and autoregressive models. Regarding their applications, we categorize their functions into three main roles: controllers, modelers and optimizers, and discuss how each role contributes to decision-making. Furthermore, we examine the deployment of these models across five critical real-world decision-making scenarios. Finally, we summarize the strengths and limitations of current approaches and propose three key directions for advancing next-generation generative directive models: high-performance algorithms, large-scale generalized decision-making models, and self-evolving and adaptive models.

Wireless signal recognition (WSR) is a crucial technique for intelligent communications and spectrum sharing in the next six-generation (6G) wireless communication networks. It can be utilized to enhance network performance and efficiency, improve quality of service (QoS), and improve network security and reliability. Additionally, WSR can be applied for military applications such as signal interception, signal race, and signal abduction. In the past decades, great efforts have been made for the research of WSR. Earlier works mainly focus on model-based methods, including likelihood-based (LB) and feature-based (FB) methods, which have taken the leading position for many years. With the emergence of artificial intelligence (AI), intelligent methods including machine learning-based (ML-based) and deep learning-based (DL-based) methods have been developed to extract the features of the received signals and perform the classification. In this work, we provide a comprehensive review of WSR from the view of applications, main tasks, recent advances, datasets and evaluation metrics, challenges, and future directions. Specifically, intelligent WSR methods are introduced from the perspective of model, data, learning and implementation. Moreover, we analyze the challenges for WSR from the view of complex, dynamic, and open 6G wireless environments and discuss the future directions for WSR. This survey is expected to provide a comprehensive overview of the state-of-the-art WSR techniques and inspire new research directions for WSR in 6G networks.

Bayesian inference for hierarchical models can be very challenging. MCMC methods have difficulty scaling to large models with many observations and latent variables. While variational inference (VI) and reweighted wake-sleep (RWS) can be more scalable, they are gradient-based methods and so often require many iterations to converge. Our key insight was that modern massively parallel importance weighting methods (Bowyer et al., 2024) give fast and accurate posterior moment estimates, and we can use these moment estimates to rapidly learn an approximate posterior. Specifically, we propose using expectation maximization to fit the approximate posterior, which we call QEM. The expectation step involves computing the posterior moments using high-quality massively parallel estimates from Bowyer et al. (2024). The maximization step involves fitting the approximate posterior using these moments, which can be done straightforwardly for simple approximate posteriors such as Gaussian, Gamma, Beta, Dirichlet, Binomial, Multinomial, Categorical, etc. (or combinations thereof). We show that QEM is faster than state-of-the-art, massively parallel variants of RWS and VI, and is invariant to reparameterizations of the model that dramatically slow down gradient based methods.

Traditional Federated Learning (FL) necessitates numerous rounds of communication between the server and clients, posing significant challenges including high communication costs, connection drop risks and susceptibility to privacy attacks. One-shot FL has become a compelling learning paradigm to overcome above drawbacks by enabling the training of a global server model via a single communication round. However, existing one-shot FL methods suffer from expensive computation cost on the server or clients and cannot deal with non-IID (Independent and Identically Distributed) data stably and effectively. To address these challenges, this paper proposes FedCGS, a novel Federated learning algorithm that Capture Global feature Statistics leveraging pre-trained models. With global feature statistics, we achieve training-free and heterogeneity-resistant one-shot FL. Furthermore, we extend its application to personalization scenario, where clients only need execute one extra communication round with server to download global statistics. Extensive experimental results demonstrate the effectiveness of our methods across diverse data heterogeneity settings. Code is available at https://github.com/Yuqin-G/FedCGS.

Optimal allocation of scarce resources is a common problem for decision makers faced with choosing a limited number of locations for intervention. Spatiotemporal prediction models could make such decisions data-driven. A recent performance metric called fraction of best possible reach (BPR) measures the impact of using a model's recommended size K subset of sites compared to the best possible top-K in hindsight. We tackle two open problems related to BPR. First, we explore how to rank all sites numerically given a probabilistic model that predicts event counts jointly across sites. Ranking via the per-site mean is suboptimal for BPR. Instead, we offer a better ranking for BPR backed by decision theory. Second, we explore how to train a probabilistic model's parameters to maximize BPR. Discrete selection of K sites implies all-zero parameter gradients which prevent standard gradient training. We overcome this barrier via advances in perturbed optimizers. We further suggest a training objective that combines likelihood with a decision-aware BPR constraint to deliver high-quality top-K rankings as well as good forecasts for all sites. We demonstrate our approach on two where-to-intervene applications: mitigating opioid-related fatal overdoses for public health and monitoring endangered wildlife.